math phd blog

17 Best Mathematics Blogs in 2024

Although finding good math materials on the Internet might be difficult, there are countless outstanding resources available, including blogs that provide informative explanations, practice problems with step-by-step directions, and more.  So, to spare you time in your search, we've filtered the entire internet with this list of our favorite mathematics blog websites. Whether you’re a student looking to learn more about mathematics or a professional looking to keep up with the latest techniques and trends, you’ll enjoy the blogs on our list. Happy reading!

Best Advanced Mathematics Blog

1. math with bad drawings.

Math With Bad Drawings is one of the top math blogs to follow. This blog, written and drawn by math teacher Ben Orlin, uses stick figures and humorous text to explain math concepts. The drawings catch everyone's attention. It's incredible how he uses the drawing as a metaphor for so many things. It isn't overly technical, but it does cover a wide range of mathematics-related topics, such as math education, math culture, current events in the math world, math humor, and so on.

https://mathwithbaddrawings.com/  

2. Stephen Wolfram Blog

On his blog, Stephen Wolfram writes about his activities and thoughts regularly. In case you didn’t know, Stephen Wolfram is a British-American computer scientist, physicist, and businessman. He is well-recognized for his contributions to cellular automata, the development of the algebraic software system Mathematica, and the search engine Wolfram Alpha. His blog is chock-full of advanced math resources, covering everything from artificial intelligence to data science to computational thinking. It's ideal for professionals and math enthusiasts who want to brush up on their knowledge.

https://writings.stephenwolfram.com/  

3. Terence Tao’s What’s New Blog

Terrence Tao is a young star in mathematics, having received the Fields Medal for his work on partial differential equations in computer modeling. His blog covers a wide range of topics, including mathematical research updates, expository articles, discussions of open mathematics problems, mathematicians’ career advice, and much more. Reading his blog is like going to a free lecture series given by a young genius. While most of the posts are intended for readers with a graduate degree, Tao does occasionally publish non-technical posts aimed at a broader audience.

https://terrytao.wordpress.com/

4. Math ∩ Programming

For those unfamiliar with the symbol in the blog's name, it stands for "The intersection of Math and Programming," which is precisely what Jeremy Kun's blog is about. Jeremy Kun is a Google engineer with a solid foundation in computer science and a passion for finding solutions to programming problems. Kun started Math Programming out of his fascination with finding mathematical answers to programming problems, and he has an extensive collection of articles that is at least novel-length. If you’re looking for a comprehensive approach to the math of computer science, Kun’s Math ∩ Programming is the perfect blog for you.

https://jeremykun.com/

5. Tanya Khovanova's Math Blog

Brimming with uncommon Math information, Dr. Tanya Khovanova manages this exceptional blog. She is a freelance mathematician, a Mathletics coach at the Advanced Math and Sciences Academy in Massachusetts, and a math research coordinator at MIT. Although the website seems outdated, it is still highly active. From algorithms, sequences, statistics, and even math humor, there are plenty of categories to choose from. For starters, take a look at this blog post on how to solve a probability puzzle .

https://blog.tanyakhovanova.com/

6. Theorem of the Day

This blog has a simple design and a straightforward goal: to convey mathematical theorems. The theorems are simplified so that a broad audience can easily understand each of them. Every day, you’ll be presented with a new theorem, lemma, law, postulate, formula, or identity from the vast universe of mathematics. For those who want to delve deeper into a theorem, a "further reading" link is also provided. It will direct you to the relevant bibliographical entry, frequently accompanied by links to helpful book reviews. If you want to learn math on a daily basis, this is an excellent site to visit.

https://www.theoremoftheday.org/

Best Math Blogs for Kids

7. the mathletics blog.

Mathletics is an engaging, supportive online learning environment that aims to pique students’ interest in mathematics while also teaching state standards. Their blog section has a wealth of math articles, teaching ideas, and inspiration, as well as news from the world of mathematics. The website's design is modern and user-friendly, so you'll have no trouble finding the topic you're looking for.

https://www.mathletics.com/blog/  

8. Math only Math

This blog is for math students of all ages. Here, you'll find a lot of math resources, as well as a lot of fun when learning and teaching mathematics step by step. They have solved and described every topic of mathematics on this blog. Each subject provides the right amount of information. Basic topics are explained through engaging examples, and there are numerous practice exercises for students of all grades to reinforce their knowledge.

https://www.math-only-math.com/  

9. Math Geek Mama

Math Geek Mama's Bethany knows exactly how difficult it is to be a teacher. Her goal is to eliminate the need for teachers and instructors to commit their whole weekend to lesson planning by providing recommendations and tools on her blog to assist them and their students in teaching and learning math! She offers free math teaching resources, math games, and enjoyable activities to assist students in improving their mathematical skills. Her blog truly reflects her enthusiasm and passion for mathematics.

https://mathgeekmama.com/  

Best Math Blogs for Students

10. yummymath.

YummyMath was established by Brian Marks and Leslie Lewis to make it simple for teachers to include real-life experiences in their math classes. This blog is ideal for students in grades 2 through 12. Each grade level has its own section with exercises designed to align with the NCTM Process Standards and the CCSS Standards for Mathematical Practice. Although the website might look dated, it has been updated with new activities and blogs every week since 2010.

https://www.yummymath.com/  

11. Maths Ed Ideas

Maths Ed Ideas is run by a school leader and mathematics and statistics instructor. It's a wonderful site where he provides teachers and students ideas, challenges, and tools to help them grasp mathematics. The website is easy to navigate, thanks to a well-organized menu bar that includes a list of ideas, inspiration, and additional math resources. There are many math topics to choose from, and if you're unsure where to begin, check out the popular posts area!

https://mathsedideas.blogspot.com/  

12. Cambridge Mathematics

The blog is about Cambridge Math education as the name implies. Cambridge Mathematics aspires to deliver world-class math education. They are committed to advocating for and ensuring that all children receive a top-notch mathematics education that is relevant to both national and international contexts and is founded on research and practice. Mathematical Salad, their blog page, publishes new content once a month. Despite the lesser frequency of posting, the content is of unrivalled quality. Math lessons, research, interviews, and math events are just a few of the topics you can find.

https://www.cambridgemaths.org / blogs/  

Dan Meyer, a former math teacher and proponent of improved mathematics education, is the founder of dy/dan. He constantly strives to improve the approach and structure of mathematical instruction. Meyer made a career out of teaching math to youngsters who disliked it. Hence, he is the ideal person to help students understand math concepts. All of his experiments are documented on this site. There are some amazing video pieces on this blog as well. Even a non-mathematical person can grasp math concepts with the help of this blog. Despite the fact that he focuses on elementary and high school, his approach would make college classes much more enjoyable.

https://blog.mrmeyer.com/  

14. Math Doubts

Math Doubts is an international mathematics education company that was founded in 2012. It enables students to study mathematics more easily with practical knowledge, helps math professionals to teach mathematics to their students in a clear and understandable manner, and lets math researchers share their research projects with the rest of the world of mathematics. You'll discover a wide range of math topics here, from algebra to trigonometry to geometry to calculus. There is also a section where you can put what you've learned into practice by working through math problems. Students at all levels, from beginner to advanced, will benefit from this math blog.

https://www.mathdoubts.com/  

Best Math Blogs for General Readers

15. fractal kitty.

Sophia Wood is a perpetual asker of “why” who is fascinated by arithmetic, tinkering, and art. She is a math expert, an engineer, and a tutor. Her blog is a must-read for math nerds! The website is divided into categories, one of which is " 52 Weeks of Hands-On Math ," which allows visitors to learn mathematics while engaging in entertaining activities such as stitching, sketching, haiku writing, and even singing and dancing! You’ll find not only fun exercises but also sections where mathematics and art intersect in the form of math comics and the " math bird series "! 

https://fractalkitty.com/     

16. MathFour

MathFour is a constantly updated and dynamic free website for creatively teaching mathematics. With the exception of the occasional guest article, Bon Crowder is almost exclusively responsible for the content. Bon has taught and coached over 15,000 adults in math in living rooms, classrooms, and conferences. The blog includes textual, audio, and video content. This is one of the blogs that students learning mathematics should visit!

http://mathfour.com/  

17. The Dean of Math

The Dean of Math is a blog that began in 2017 and has been sharing new content ever since. The author is a seventh-grade math teacher who evidently loves their job. The blog shares personal views, ideas, and passions for mathematics. Other fascinating subjects include " More than Algorithms ," " Exploring Proportionality ," and " Ignoring the Decimal Points ". It's an excellent blog for both math students and teachers.

https://deanofmath. wordpress .com/

Frequently Asked Questions (FAQs):

What are the best math blogs.

Here are the 17 best math blogs in 2022:

• Math with Bad Drawings
• Stephen Wolfram Blog
• Terence Tao’s What’s New Blog
• Math ∩ Programming
• Tanya Khovanova's Math Blog
• Theorem of the Day
• The Mathletics Blog
• Math only Math
• Math Geek Mama
• Maths Ed Ideas
• Cambridge Mathematics
• Math Doubts
• Fractal Kitty
• The Dean of Math

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Ph.D. Program Overview

Description.

The graduate program in the field of mathematics at Cornell leads to the Ph.D. degree, which takes most students five to six years of graduate study to complete. One feature that makes the program at Cornell particularly attractive is the broad range of  interests of the faculty . The department has outstanding groups in the areas of algebra, algebraic geometry,  analysis, applied mathematics, combinatorics, dynamical systems, geometry, logic, Lie groups, number theory, probability, and topology. The field also maintains close ties with distinguished graduate programs in the fields of  applied mathematics ,  computer science ,  operations research , and  statistics .

Core Courses

A normal course load for a beginning graduate student is three courses per term. 

There are no qualifying exams, but the program requires that all students pass four courses to be selected from the six core courses. First-year students are allowed to place out of some (possibly, all) of the core courses. In order to place out of a course, students should contact the faculty member who is teaching the course during the current academic year, and that faculty member will make a decision. The minimum passing grade for the core courses is B-; no grade is assigned for placing out of a core course.

At least two core courses should be taken (or placed out) by the end of the first year. At least four core courses should be taken (or placed out) by the end of the second year (cumulative). These time requirements can be waived for students with health problems or other significant non-academic problems. They can be also waived for students who take time-consuming courses in another area (for example, CS) and who have strong support from a faculty; requests from such students should be made before the beginning of the spring semester. 

The core courses  are distributed among three main areas: analysis, algebra and topology/geometry. A student must pass at least one course from each group. All entering graduate students are encouraged to eventually take all six core courses with the option of an S/U grade for two of them. 

The six core courses are:

MATH 6110, Real Analysis

MATH 6120, Complex Analysis

MATH 6310, Algebra 1

MATH 6320, Algebra 2

MATH 6510, Introductory Algebraic Topology

MATH 6520, Differentiable Manifolds.

Students who are not ready to take some of the core courses may take MATH 4130-4140, Introduction to Analysis, and/or MATH 4330-4340, Introduction to Algebra, which are the honors versions of our core undergraduate courses.

"What is...?" Seminar

The "What Is...?" Seminar is a series of talks given by faculty in the graduate field of Mathematics. Speakers are selected by an organizing committee of graduate students. The goal of the seminar is to aid students in finding advisors.

Schedule for the "What Is...?" seminar

Special Committee

The Cornell Graduate School requires that every student selects a special committee (in particular, a thesis adviser, who is the chair or the committee) by the end of the third semester.

The emphasis in the Graduate School at Cornell is on individualized instruction and training for independent investigation. There are very few formal requirements and each student develops a program in conjunction with his or her special committee, which consists of three faculty members, some of which may be chosen from outside the field of mathematics. 

Entering students are not assigned special committees. Such students may contact any of the members on the Advising Committee if they have questions or need advice.

Current Advising Committee

Analysis / Probability / Dynamical Systems / Logic: Lionel Levine Geometry / Topology / Combinatorics: Kathryn Mann Probability / Statistics:  Philippe Sosoe Applied Mathematics Liaison: Richard Rand

Admission to Candidacy

To be admitted formally to candidacy for the Ph.D. degree, the student must pass the oral admission to candidacy examination or A exam. This must be completed before the beginning of the student's fourth year. Upon passing the A exam, the student will be awarded (at his/her request) an M.S. degree without thesis.

The admission to candidacy examination is given to determine if the student is “ready to begin work on a thesis.” The content and methods of examination are agreed on by the student and his/her special committee before the examination. The student must be prepared to answer questions on the proposed area of research, and to pass the exam, he/she must demonstrate expertise beyond just mastery of basic mathematics covered in the core graduate courses. 

To receive an advanced degree a student must fulfill the residence requirements of the Graduate School. One unit of residence is granted for successful completion of one semester of full-time study, as judged by the chair of the special committee. The Ph.D. program requires a minimum of six residence units. This is not a difficult requirement to satisfy since the program generally takes five to six years to complete. A student who has done graduate work at another institution may petition to transfer residence credit but may not receive more than two such credits.

The candidate must write a thesis that represents creative work and contains original results in that area. The research is carried on independently by the candidate under the supervision of the chairperson of the special committee. By the time of the oral admission to candidacy examination, the candidate should have selected as chairperson of the committee the faculty member who will supervise the research. When the thesis is completed, the student presents his/her results at the thesis defense or B Exam. All doctoral students take a Final Examination (the B Exam, which is the oral defense of the dissertation) upon completion of all requirements for the degree, no earlier than one month before completion of the minimum registration requirement.

Masters Degree in the Minor Field

Ph.D. students in the field of mathematics may earn a Special Master's of Science in Computer Science. Interested students must apply to the Graduate School using a form available for this purpose. To be eligible for this degree, the student must have a member representing the minor field on the special committee and pass the A-exam in the major field. The rules and the specific requirements for each master's program are explained on the referenced page.

Cornell will award at most one master's degree to any student. In particular, a student awarded a master's degree in a minor field will not be eligible for a master's degree in the major field.

Graduate Student Funding

Funding commitments made at the time of admission to the Ph.D. program are typically for a period of five years. Support in the sixth year is available by application, as needed. Support in the seventh year is only available by request from an advisor, and dependent on the availability of teaching lines. Following a policy from the Cornell Graduate School, students who require more than seven years to complete their degree shall not be funded as teaching assistants after the 14th semester.

Special Requests

Students who have special requests should first discuss them with their Ph.D. advisor (or with a field member with whom they work, if they don't have an advisor yet). If the advisor (or field faculty) supports the request, then it should be sent to the Director of Graduate Studies.  

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Staying the path: Motivation through graduate school

Student Authors: Alberto Alonso, Jasmine Camero, Alejandra Castillo, Fabrice O. Ulysse, Victoria Uribe, Andrés R. Vindas Meléndez, and Organizer Authors: Alexander Diaz-Lopez, Pamela E. Harris, Vanessa Rivera Quiñones, Luis Sordo Vieira, Shelby Wilson, Aris Winger, Michael Young Graduate school is a journey. It has its positive moments and its struggles, but one thing is clear: the goal is to obtain the PhD. So what is our drive and motivation for obtaining a PhD? This was a topic for reflection and discussion among the participants and organizers of Math SWAGGER. The Mathematics Summer Workshop for Achieving Greater Graduate Educational Readiness (Math SWAGGER — www.mathswagger.com ) is a five-week virtual program that brings together a group of underrepresented current and incoming graduate students (including women, underrepresented minorities – African Americans, American Indians including Native Alaskans, Latinxs/Hispanics, and Native Pacific Islanders – and persons with disabilities) for a workshop on graduate school readiness to address and create action plans for underrepresented students to navigate challenges and situations while successfully completing a PhD in the mathematical sciences.

In this article, three incoming PhD students and two current graduate students provide their reflections on their motivation to complete their graduate studies and what mentors could do to help strengthen, support, and further motivate them throughout their journeys. As you read some of the authors’ reflections you will get a glimpse into their lives and also see some similarities in motivation factors, including, a passion for mathematics, people, and community.

____________________________________________

Alberto Alonso

Alberto Alonso is a Mexican-American who will be pursuing a PhD in Mathematical Modelling at the Rochester Institute of Technology. He graduated with degrees in Applied Mathematics and Sociology from SUNY Geneseo. Alberto intends to focus his studies in Mathematical Biology to better understand the spread of diseases, or medicinal drug transportation in the human body. In his spare time, he enjoys baking, playing classical music, and crocheting. Alberto Alonso: Pursuing a PhD in mathematics has always been the end goal in my academic career since high school. Initially, my motivation for pursuing such a degree came from wanting to wear the doctoral regalia. However, as I continued through to my undergraduate studies, I realized that earning a PhD meant much more. The title of being called “Dr.” brings such a different tone when people address you– a level of respect that was not always apparent during my experience in mathematics, and in academia as a whole. Being able to prove to “the world” that a gay Latino can earn a PhD is a motivator, but definitely not the main one that comes to mind. What really pushes me forward is the support of my family. Being the first-born in a Latino family, a first-generation student in college, from immigrant parents who moved to America not knowing the language, what motivates me is achieving the “American Dream” for my family. To give back to them the way they have always provided for me– that is the greatest motivator. My parents have always believed that working hard, and staying focused will get you far in life, and I am willing to make any sacrifices that may come my way. Secondary to the latter, I want to be able to be “the person” for anyone who is pursuing a career in STEM. It would have been great to see a reflection of me in academia sooner, to affirm that I can make it in STEM, and that I’m not alone in academia. I want to be the recluse for someone to be able to relate to and empathize with where they are coming from. Right before I started undergrad, my institution had a program that brought together a cohort of people from underrepresented groups to help prepare students for undergraduate work. The cohort was structured in a way that helped expand our thinking socially and academically, to notice nuances in our experiences that may not be apparent or present for others; and this was aided with the help of mentors in the program as well. The mentorship that was provided by upperclassmen and facilitators really prepared me for my academic career, and being a participant in Math SWAGGER could have not come at a better time. As I was applying to graduate schools, there was this constant fear of not being ready for graduate studies. Having also taken a two-year hiatus from school to work a corporate job also did not help in mitigating my fears. No one in my extended family ever sought out to pursue a higher degree–I felt completely alone until I became a part of Math SWAGGER. The group reminds me of the summer before my undergraduate studies, and I could not be more grateful for the people that brought this group of people together. To be able to listen to other people’s experiences, and to be able to learn from professors and 3rd, 4th years alike, is an experience that will be irreplaceable. Moreover, the mentorship that the group exudes is helping me prepare for what to expect in graduate school. It perpetuates the feeling of unity, and togetherness that I would not otherwise find once I start my program. Being connected to a group of bright, humble, funny people gives me the confidence to pursue the PhD program, and motivates me to “make it.”

Jasmine Camero

Jasmine Camero is a Mexican-American who, in the fall, will be an incoming Mathematics PhD student at Emory University. Born in Santa Ana, California, she earned her B.A. in Mathematics from California State University, Fullerton. With a PhD, she plans on becoming a professor and serving as a role model for all underrepresented groups, especially women of color like herself. As a professor, one of her goals is to plunge into spreading her admiration for such an influential subject to others. During Jasmine’s free time, she enjoys cooking and baking, working out, and playing with her dog. Jasmine Camero: Motivation is described as something that causes a person to behave in a certain way. To me, motivation is defined as the desire and passion to do something you want, but that may not always be easy. Now, motivation, from the perspective of a graduate student, can hold many meanings. However, for a person of color who is navigating academia, motivation is not something that is always constant. When tackling a responsibility that will take five to six years of your life, such as completing a PhD, you will need a lot of grit because the secret to success is not purely from talent, but from perseverance. So, why go to graduate school? Following the motivation session in Math SWAGGER, I realized that my purpose and my motivation is an amalgamation of reasons. It has to start with the mathematics. If you plan on dedicating an extensive portion of your time doing something, you have to enjoy it. We must relish in the idea of further uncovering the world of mathematics because the discoveries we make in the field can hopefully one day gear the societal progress we need. However, it is never just about this. It has to be more than that. Graduate school is definitely not going to be easy, so if I am going to put myself through that, there has to be more. There has to be people. Much like Math SWAGGER has been emphasizing, community is critical and extremely influential in building our framework as people and as students. Being a part of Math SWAGGER, I am now part of a welcoming environment that only celebrates the stories and experiences of underrepresented folks. It has made me more aware that we must take the extra steps to create these spaces for us to connect, relate to one another, and support each other through the ups and downs of this journey. Another incentive to continue my academic journey is my family. As a first-generation, Latina student studying mathematics, I obtain pleasure in the anomaly that my presence in the world of academia holds. I have never felt prouder to be a first-generation student. I am the first in my family to earn my bachelor’s degree and I cannot wait to earn my doctoral degree in mathematics. My parents were not afforded the opportunities that I have had so it is really important to me to do this not only for myself, but for my entire family. Although they may not completely understand this journey that I am on, I know I can eternally count on their encouragement. After obtaining a PhD in mathematics, my ultimate career goal is to become a professor. I would like to be at an academic institution where I can research, teach, and facilitate the development of future mathematicians because I believe mentors have a strong impact on students. The latter of these tasks is super important to me because, as a person of color who loves math, I recognize that members of underrepresented groups wanting to enter STEM fields still face systemic hurdles. I want to do my part in removing those hurdles by becoming a role model and mentor for those looking to enter the field. This is what I believe mentoring is about–providing productive direction and encouragement while being an advocate for the success of the students. Motivation can hold various definitions for everyone and requires a subjective aspect for each individual, but one thing that can be agreed on is that motivation is what keeps us going–this can be your family, your cohort, or simply people you have encountered along the way. I constantly remind myself that everyone’s journey is different, and it may not be perfect, but as long as you enjoy what you are doing, then it is all worth it.

Alejandra Castillo

Alejandra Castillo is a graduate student in Statistics at Oregon State University with research interests in unsupervised learning, statistical inference, and statistics education. She received her B.A. in math from Pomona College and calls the nearby San Gabriel Valley home. Alejandra also enjoys hiking, finding good boba places, listening to podcasts, and reading. Alejandra Castillo: My motivation to pursue a graduate degree has changed a few times. There are aspects that have not, such as the support from my family, working on problems in/with statistics and my goal to help broaden the path for others in higher education. As a current graduate student, I’ve come to see that there is no one way to do well in graduate school because growing and growing pains are at the center of it all. In college, I learned that there were intellectually enriching professions. I became interested in this active exchange of ideas. I could not believe that these were jobs. I could not believe that part of professors’ jobs was to learn, teach, and keep learning. Representation is powerful, so being surrounded by people with PhDs, I became interested in graduate school. While I enjoyed what I was learning, ultimately it was fellow classmates and professors who kept me engaged despite the obstacles. Mentors throughout college were instrumental in supporting my interest in math. They have been key in humanizing math and thereby making it accessible. In discussing the topic of motivation with the Math SWAGGER community, similar themes of family and representation emerged for many of us. The organizers also shared with us their motivations throughout graduate school. Their willingness to share personal stories has been moving because it reminds me that no one really has a perfect graduate school experience, but people can help make it better. In an effort to help us grow, one organizer challenged us to think more critically about how we will use any source of motivation to persist in challenging circumstances. This resonated with me because of the instances in graduate school where I have felt isolated. There have been times where, as much as my family wants to help, they can’t. I believe that this is where graduate mentors can help. They can meet students where they are, be advocates and share opportunities, among other things. I’ve been fortunate to find mentors who are willing to listen, offer advice, and demonstrate care beyond the academic transaction that might be coursework. I can’t help but think about how helpful having these conversations would have been prior to beginning graduate school. This is why I am very excited to learn and share what I’ve learned with incoming graduate students. I have found a new community in the space Math SWAGGER has created.

Fabrice O. Ulysse

Fabrice O. Ulysse is a Haitian-American incoming PhD Student in the Department of Mathematics at the University of Notre Dame. His current research interests are in Algebra and Logic. Born and raised in Canarsie, Brooklyn, NY, he received his A.B. Cum Laude in Mathematics from Cornell University. He hopes to become a Professor. His interests outside of mathematics are politics, music, film, the Premier League, NBA, and NCAA Ice Hockey. Fabrice O. Ulysse: When I finished my Bachelor of Arts in May, some of my fellow math majors let me know they’ve had enough of math and are glad they don’t have to do it again. Other undergraduates could not entertain the idea of spending any more time in school, at least not at the moment, and felt that they’d learned enough. I, on the other hand, still feel like I have more to learn and more to do in mathematics. This hunger to learn more in math, and one day contribute to math, made me realize that I see myself being a professor, hence further motivating me to pursue a PhD. Even when I’m tired of doing mathematics, I always enjoy reading pieces and books about the History of Mathematics and reading articles about the current state of Mathematics research on Quanta Magazine . I am fortunate that my love for mathematics has kept me going. Passion for mathematics is often the first source of motivation to get through graduate school mentioned by incoming grad students. However, that passion for mathematics gets tested during the PhD years. Furthermore, it can completely go away from time to time. So the love of the subject alone won’t get one through the 5-6 years of the PhD. I know that Abstract Algebra would not have been nearly as fun without the study group I formed. We spent many hours together, suffered, bonded, and enjoyed lots of funny moments. This study group even made doing mathematics more fun and exciting. I looked forward to studying with them every week, and this group was vital to my success in the course. Likewise, the great friends and mentors at MSRI-UP in 2019 , kept my dream of pursuing a PhD alive, even when I almost gave up on it. There are several spaces where I’ve met many URMs in the mathematical sciences. Those spaces have given me the confidence to pursue a PhD, partly because I know that other people that look like me have succeeded and are even thriving. Math SWAGGER is now one of those spaces, and it is allowing me to make more meaningful connections with other black and brown mathematicians, hence helping me build a community. These are people I can contact for professional, academic, or even life advice, with the added benefit that they can understand my experiences as a minority in math. I know that I will not be lonely for the next 5 years, because of this network of support. So far, during Math SWAGGER, the personal stories from professors and graduate students have often emphasized the importance of community. It became clear how crucial having a good community was during the darkest hours of the PhD, which is one of my biggest takeaways from last week. I now know that building and finding communities, even if they’re not on campus, will be essential to get through graduate school. Lastly, I believe that mentors should not make their mentees feel guilty about wanting a life outside of mathematics. It could make them question if they’re a fan of mathematics, and ultimately negatively affects their motivation. It also denies the reality that we are multifaceted beings, and are capable of enjoying more than a select few related activities.

Victoria Uribe

Victoria Uribe is a Mexican-American PhD student in Applied Mathematics at Arizona State University. Her current research interests include inverse problems, numerical linear algebra, and machine learning. Raised in Paradise, California, she received her B.S. in Applied Mathematics from California State University, Chico. After graduation, she hopes to work as an Applied Mathematician in the aerospace industry. Her interests outside of mathematics include triathlon, weightlifting, traveling, and writing. Victoria Uribe: My motivation for completing my PhD program is generated in large part from having eliminated alternative career paths. Before starting graduate school for applied mathematics, I first attended a semester of law school. Despite getting my undergraduate degree in applied mathematics, I decided in 8th grade that I would become an attorney, and I was determined to see it through. I had always enjoyed math but thought that I needed to become an attorney to really help people. I thought that it would be the most tangible way to make a positive impact in the Latinx community. Within two weeks of law school, however, I knew that I was in the wrong place. I felt as though I was missing out on the “next thing” I would have otherwise learned in math. I quickly dismissed these thoughts, believing that the math PhD I was dreaming of would be considered selfish: something that only benefitted my own interests. It wasn’t until I met with the Dean of Students about leaving law school that I realized how getting a PhD in applied mathematics could positively impact the Latinx community as well. She pointed out that few in the mathematics community look like me and that my success could help inspire others to pursue mathematics. Transitioning from law school back into mathematics didn’t happen overnight. While studying for admissions exams and applying to graduate programs, I worked in an ice cream shop before finding a job in a corporate office. Having these jobs really made me appreciate being in school and pursuing my own interests. When it finally came time to start graduate school again, I couldn’t wait. Many PhD students have told me that the first year is the hardest. Having just completed my first year, I certainly hope so! This past year brought many challenges, but I never truly considered giving up. I believe that taking several years between my undergraduate and graduate programs in applied mathematics allowed me to determine that, above anything else, this is what I want to be doing. Being a part of the Math SWAGGER workshop and community this summer has been a huge blessing. Going forward through the rest of my PhD journey, I am motivated by knowing that I have 37 allies in the other participants and leaders. Taking part in this group of underrepresented mathematicians, who want to create real and lasting change in our field, reaffirms my decision to positively impact the Latinx community via a PhD in applied mathematics. Supportive mentors have been instrumental in my success thus far. My best mentors have been good listeners, have been invested in my well-being, and have been quick to share opportunities such as Math SWAGGER with me. It is important that mentors see their mentees as more than just students. While school is a full-time job, many students are also facing challenges outside of the classroom. Knowing that you have faculty cheering you on can make all the difference.

____________________________________________ Acknowledgements: We acknowledge funding support for Math SWAGGER through the National Science Foundation Award #1744463.

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Graduate Program

Our graduate program is unique from the other top mathematics institutions in the U.S. in that it emphasizes, from the start, independent research. Each year, we have extremely motivated and talented students among our new Ph.D. candidates who, we are proud to say, will become the next generation of leading researchers in their fields. While we urge independent work and research, there exists a real sense of camaraderie among our graduate students. As a result, the atmosphere created is one of excitement and stimulation as well as of mentoring and support. Furthermore, there exists a strong scholarly relationship between the Math Department and the Institute for Advanced Study, located just a short distance from campus, where students can make contact with members there as well as attend the IAS seminar series.  Our program has minimal requirements and maximal research and educational opportunities. We offer a broad variety of advanced research topics courses as well as more introductory level courses in algebra, analysis, and geometry, which help first-year students strengthen their mathematical background and get involved with faculty through basic course work. In addition to the courses, there are several informal seminars specifically geared toward graduate students: (1) Colloquium Lunch Talk, where experts who have been invited to present at the Department Colloquium give introductory talks, which allows graduate students to understand the afternoon colloquium more easily; (2) Graduate Student Seminar (GSS), which is organized and presented by graduate students for graduate students, creating a vibrant mathematical interaction among them; and, (3) What’s Happening in Fine Hall (WHIFH) seminar where faculty give talks in their own research areas specifically geared towards graduate students. Working or reading seminars in various research fields are also organized by graduate students each semester. First-year students are set on the fast track of research by choosing two advanced topics of research, beyond having a strong knowledge of three more general subjects: algebra, and real and complex analysis, as part of the required General Examination. It is the hope that one, or both, of the advanced topics will lead to the further discovery of a thesis problem. Students are expected to write a thesis in four years but will be provided an additional year to complete their work if deemed necessary. Most of our Ph.D.'s are successfully launched into academic positions at premier mathematical institutions as well as in industry .

Chenyang Xu

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Welcome to the Math PhD program at Harvard University and the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.

Learn more about Harvard’s Math community and our statement on diversity and inclusion.

The Harvard Griffin GSAS Office of Equity, Diversity, Inclusion & Belonging offers student affinity groups for graduate students and many other resources.

The Harvard University Office for Gender Equity has dedicated GSAS Title IX resource coordinators who work with and support graduate students.

open. The application deadline is December 15, 2021. -->

The application deadline for fall 2024 admission has passed. Applications for fall 2025 admission will open in September 2024.

For information on admissions and financial support, please visit the Harvard Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.

Harvard Griffin GSAS is committed to ensuring that our application fee does not create a financial obstacle. Applicants can determine eligibility for a fee waiver by completing a series of questions in the Application Fee section of the application. Once these questions have been answered, the application system will provide an immediate response regarding fee waiver eligibility.

PhD in Mathematics

The PhD in Mathematics provides training in mathematics and its applications to a broad range of disciplines and prepares students for careers in academia or industry. It offers students the opportunity to work with faculty on research over a wide range of theoretical and applied topics.

Degree Requirements

The requirements for obtaining an PhD in Mathematics can be found on the associated page of the BU Bulletin .

• Courses : The courses mentioned on the BU Bulletin page can be chosen from the graduate courses we offer here . Half may be at the MA 500 level or above, but the rest must be at the MA 700 level or above. Students can also request to use courses from other departments to satisfy some of these requirements. Please contact your advisor for more information about which courses can be used in this way. All courses must be passed with a grade of B- or higher.
• Analysis (examples include MA 711, MA 713, and MA 717)
• PDEs and Dynamical Systems (examples include MA 771, MA 775, and MA 776)
• Algebra and Number Theory (examples include MA 741, MA 742, and MA 743)
• Topology (examples include MA 721, MA 722, and MA 727)
• Geometry (examples include MA 725, MA 731, and MA 745)
• Probability and Stochastic Processes (examples include MA 779, MA 780, and MA 783)
• Applied Mathematics (examples include MA 750, MA 751, and MA 770)
• Comprehensive Examination : This exam has both a written and an oral component. The written component consists of an expository paper of typically fifteen to twenty-five pages on which the student works over a period of a few months under the guidance of the advisor. The topic of the expository paper is chosen by the student in consultation with the advisor. On completion of the paper, the student takes an oral exam given by a three-person committee, one of whom is the student’s advisor. The oral exam consists of a presentation by the student on the expository paper followed by questioning by the committee members. A student who does not pass the MA Comprehensive Examination may make a second attempt, but all students are expected to pass the exam no later than the end of the summer following their second year.
• Oral Qualifying Examination: The topics for the PhD oral qualifying exam correspond to the two semester courses taken by the student from one of the 3 subject areas and one semester course each taken by the student from the other two subject areas. In addition, the exam begins with a presentation by the student on some specialized topic relevant to the proposed thesis research. A student who does not pass the qualifying exam may make a second attempt, but all PhD students are expected to pass the exam no later than the end of the summer following their third year.
• Dissertation and Final Oral Examination: This follows the GRS General Requirements for the Doctor of Philosophy Degree .

Admissions information can be found on the BU Arts and Sciences PhD Admissions website .

Financial Aid

Our department funds our PhD students through a combination of University fellowships, teaching fellowships, and faculty research grants. More information will be provided to admitted students.

More Information

Please reach out to us directly at [email protected] if you have further questions.

Department of Mathematics

Mathematics phd program.

The Ph.D. program in the Department of Mathematics provides students with in-depth knowledge and rigorous training in all the subject areas of mathematics. A core feature is the first-year program, which helps bring students to the forefront of modern mathematics. Students work closely with faculty and each other and participate fully in both research and student-run seminars.

Questions? Email [email protected]

• The firm deadline for applications for Autumn 2025, is December 5, 2024.
• The (general and advanced) GRE tests are no longer accepted. Please do not submit these scores.

PhD Qualifying Exams

The requirements for the PhD program in Mathematics have changed for students who enter the program starting in Autumn 2023 and later. 

Requirements for the Qualifying Exams

Students who entered the program prior to autumn 2023.

To qualify for the Ph.D. in Mathematics, students must pass two examinations: one in algebra and one in real analysis. 

Students who entered the program in Autumn 2023 or later

To qualify for the Ph.D. in Mathematics, students must choose and pass examinations in two of the following four areas: 

• real analysis
• geometry and topology
• applied mathematics

The exams each consist of two parts. Students are given three hours for each part.

Topics Covered on the Exams:

• Algebra Syllabus
• Real Analysis Syllabus
• Geometry and Topology Syllabus
• Applied Mathematics Syllabus

Check out some Past and Practice Qualifying Exams to assist your studying.

Because some students have already taken graduate courses as undergraduates, incoming graduate students are allowed to take either or both of the exams in the autumn. If they pass either or both of the exams, they thereby fulfill the requirement in those subjects. However, they are in no way penalized for failing either of the exams.

Students must pass both qualifying exams by the autumn of their second year. Ordinarily first-year students take courses in algebra and real analysis throughout the year to prepare them for the exams. The exams are then taken at the beginning of Spring Quarter. A student who does not pass one or more of the exams at that time is given a second chance in Autumn. 

Students who started in Autumn 2023 and later

Students must choose and pass two out of the four qualifying exams by the autumn of their second year. Students take courses in algebra, real analysis, geometry and topology, and applied math in the autumn and winter quarters of their first year to prepare them for the exams. The exams are taken during the first week of Spring Quarter. A student who does not pass one or more of the exams at that time is given a second chance in Autumn. 

Exam Schedule

Unless otherwise noted, the exams will be held each year according to the following schedule:

Autumn Quarter:  The exams are held during the week prior to the first week of the quarter. Spring Quarter:  The exams are held during the first week of the quarter.

The exams are held over two three-hour blocks. The morning block is 9:30am-12:30pm and the afternoon block is 2:00-5:00pm.

For the start date of the current or future years’ quarters please see the  Academic Calendar

Upcoming Exam Dates

Spring 2024.

The exams will be held on the following dates:

Monday, April 1st

Analysis Exam, Room 384H

Wednesday, April 3rd

Algebra Exam, Room 384I

Thursday, April 4th 

Geometry & Topology Exam, Room 384I

Friday, April 5th

Applied Math Exam, Room 384I

Mathematical Sciences

Mellon college of science, ph.d. programs, doctor of philosophy in mathematical sciences.

Students seeking a Ph.D. in Mathematical Sciences are expected to show a broad grasp of mathematics and demonstrate a genuine ability to do mathematical research. The Doctor of Philosophy in Mathematical Sciences is a traditional research degree, and its requirements are representative of all doctoral programs.

After being admitted to graduate status by the Department, a student seeking a Ph.D. must be admitted to candidacy for this degree by fulfilling the appropriate program requirements.

The most important requirement for the Ph.D. degree is timely completion and public defense of an original Ph.D. thesis. The Ph.D. thesis is expected to display depth and originality and be publishable by a refereed journal.

Doctor of Arts in Mathematical Sciences

The Doctor of Arts degree shares all requirements and standards with the Ph.D., except with regard to the thesis. The D.A. thesis is not expected to display the sort of original research required for a Ph.D. thesis, but rather to demonstrate an ability to organize, understand, and present mathematical ideas in a scholarly way, usually with sufficient innovation and worth to produce a publishable work. Whenever practical, the department provides D.A. candidates with the opportunity to use materials developed to teach a course. While a typical Ph.D. recipient will seek a position that has a substantial research component, the D.A. recipient will usually seek a position where research is not central.

Doctor of Philosophy in Algorithms, Combinatorics, and Optimization (ACO)

This program is administered jointly by the Department of Mathematical Sciences, the Department of Computer Science, and the Tepper School of Business. It focuses on discrete mathematics and algorithmic issues arising in computer science and operations research, particularly the mathematical analysis of these issues. The participating units evaluate applicants separately. The requirements for this degree and information on participating faculty are available at the ACO page .

Doctor of Philosophy in Pure and Applied Logic (PAL)

This is an interdisciplinary program with faculty from the Department of Mathematical Sciences, the Department of Philosophy, and the School of Computer Science. The participating units evaluate applicants separately and set their own program requirements. Students who have been admitted to the PAL program, and who complete the requirements for the Ph.D. in Mathematical Sciences with a thesis in the area of logic, can choose to receive either a Ph.D. in Pure and Applied Logic or a Ph.D. in Mathematical Sciences. The choice of which degree to receive is usually based on the intended career path.

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Advice and Resources for Mathematics Graduate Students

Advice for beginning Math PhD Students

• Familiarize yourself with the requirements for the Math PhD program by clicking around our math department website. For now, focus on the “Stage I” requirements . Most students are in Stage I for one to two years.
• Your main goal as a Stage I student is to master the material in the three core areas: topology, algebra, and analysis. The “alpha courses” are designed to help you meet this goal. These are Math 591, 592 (topology), Math 593, 594 (algebra) and Math 596, 597 (analysis) . [If you are inclined toward applied math, there is an option to substitute Applied Analysis (Math 556, 572) for  topology or algebra.]
• Make a plan now for achieving this goal. Remember that every student is different! Your office mate with a Master’s degree may pass some QR exam immediately upon arrival. However, another may choose to take alpha courses in topology and analysis this year and save algebra for year two. Both are reasonable plans likely to lead to timely completion of Stage I.
• Our department publishes a list of graduate courses offered each semester. Read and admire these courses, but do not let them entice you away from the goal of Stage I: to master the material of the three core areas.
• You will be assigned a doctoral committee advisor, whom you will meet in August. Come prepared to that meeting with your tentative plan for and/or questions about completing Stage I. Your advisor will help you choose courses and refine your plan.
• Usually, the only good reason to skip an alpha course is that you have passed the QR Exam in the corresponding subject. In some cases, a student might substitute certain “beta” courses (600 level). For example, a student who has solved many hard problems in a graduate course on the same topics as Math 593 might substitute Math 614 for Math 593 and plan to take Math 594 in the winter.
• Be ambitious, but reasonable and flexible. If you are tempted to take all three QR exams upon arrival in August, go for it! Adjust your plan after getting the results.
• First year students should generally avoid “topics courses” ( most 700 and some 600 level courses ), intended primarily for PhD candidates. These courses are more specialized and may not prepare you as well for writing your PhD . Take courses where you will turn in regular assignments, bond with your peers over difficult problems, and allow your professors to get to know you mathematically.
• Remember that you are also adjusting to teaching! Taking two intense courses of your own, with problem sets and exams, may be enough. Four demanding courses plus teaching is not recommended.
• Revisit and revise your plans and goals regularly. It is wise to take QR exams as soon as you think you have a chance of passing. There is no penalty for failing, as long as you pass by the deadline.
• Looking ahead, the main goal of a Stage II student is to find a dissertation advisor. We will help you! Although you should not worry about this yet, it is never too early to get to know professors and older students, both mathematically and personally. Similarly, it is never too early to keep an eye on the  Seminar Offerings   or get involved once you feel adjusted and ready.  Start  by attending Junior Colloquium , at the very least.

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• Doing a PhD in Mathematics
• Doing a PhD

What Does a PhD in Maths Involve?

Maths is a vast subject, both in breadth and in depth. As such, there’s a significant number of different areas you can research as a math student. These areas usually fall into one of three categories: pure mathematics, applied mathematics or statistics. Some examples of topics you can research are:

• Number theory
• Numerical analysis
• String theory
• Random matrix theory
• Graph theory
• Quantum mechanics
• Statistical forecasting
• Matroid theory
• Control theory

Besides this, because maths focuses on addressing interdisciplinary real-world problems, you may work and collaborate with other STEM researchers. For example, your research topic may relate to:

• Biomechanics and transport processes
• Evidence-based medicine
• Fluid dynamics
• Financial mathematics
• Machine learning
• Theoretical and Computational Optimisation

What you do day-to-day will largely depend on your specific research topic. However, you’ll likely:

• Continually read literature – This will be to help develop your knowledge and identify current gaps in the overall body of knowledge surrounding your research topic.
• Undertake research specific to your topic – This can include defining ideas, proving theorems and identifying relationships between models.
• Collect and analyse data – This could comprise developing computational models, running simulations and interpreting forecasts etc.
• Liaise with others – This could take many forms. For example, you may work shoulder-to-shoulder with individuals from different disciplines supporting your research, e.g. Computer scientists for machine learning-based projects. Alternatively, you may need frequent input from those who supplied the data for your research, e.g. Financial institutions or biological research colleagues.
• Attend a wide range of lectures, seminars and events.

Browse PhD Opportunities in Mathematics

Application of artificial intelligence to multiphysics problems in materials design, study of the human-vehicle interactions by a high-end dynamic driving simulator, physical layer algorithm design in 6g non-terrestrial communications, machine learning for autonomous robot exploration, detecting subtle but clinically significant cognitive change in an ageing population, how long does it take to get a phd in maths.

The average programme duration for a mathematics PhD in the UK is 3 to 4 years for a full-time studying. Although not all universities offer part-time maths PhD programmes, those that do have a typical programme duration of 5 to 7 years.

Again, although the exact arrangement will depend on the university, most maths doctorates will require you to first register for an MPhil . At the end of your first year, your supervisor will assess your progress to decide whether you should be registered for a PhD.

Additional Learning Modules

Some Mathematics departments will require you to enrol on to taught modules as part of your programme. These are to help improve your knowledge and understanding of broader subjects within your field, for example, Fourier Analysis, Differential Geometry and Riemann Surfaces. Even if taught modules aren’t compulsory in several universities, your supervisor will still encourage you to attend them for your development.

Most UK universities will also have access to specialised mathematical training courses. The most common of these include Pure Mathematics courses hosted by Mathematics Access Grid Conferencing ( MAGIC ) and London Taught Course Centre ( LTCC ) and Statistics courses hosted by Academy for PhD Training in Statistics ( APTS ).

What Are the Typical Entry Requirements for A PhD in Maths?

In the UK, the typical entry requirements for a Maths PhD is an upper second-class (2:1) Master’s degree (or international equivalent) in Mathematics or Statistics [1] .

However, there is some variation on this. From writing, the lowest entry requirement is an upper second-class (2:1) Bachelor’s degree in any math-related subject. The highest entry requirement is a first-class (1st) honours Master’s degree in a Mathematics or Statistics degree only.

It’s worth noting if you’re applying to a position which comes with funding provided directly by the Department, the entry requirements will usually be on the higher side because of their competitiveness.

In terms of English Language requirements, most mathematics departments require at least an overall IELTS (International English Language Testing System) score of 6.5, with no less than 6.0 in each individual subtest.

Tips to Consider when Making Your Application

When applying to any mathematics PhD, you’ll be expected to have a good understanding of both your subject field and the specific research topic you are applying to. To help show this, it’s advisable that you demonstrate recent engagement in your research topic. This could be by describing the significance of a research paper you recently read and outlining which parts interested you the most, and why. Additionally, you can discuss a recent mathematics event you attended and suggest ways in how what you learnt might apply to your research topic.

As with most STEM PhDs, most maths PhD professors prefer you to discuss your application with them directly before putting in a formal application. The benefits of this is two folds. First, you’ll get more information on what their department has to offer. Second, the supervisor can better discover your interest in the project and gauge whether you’d be a suitable candidate. Therefore, we encourage you to contact potential supervisors for positions you’re interested in before making any formal applications.

How Much Does a Maths PhD Typically Cost?

The typical tuition fee for a PhD in Maths in the UK is £4,407 per year for UK/EU students and £20,230 per year for international students. This, alongside the range in tuition fees you can expect, is summarised below:

Note: The above tuition fees are based on 12 UK Universities [1]  for 2020/21 Mathematic PhD positions. The typical fee has been taken as the median value.

In addition to the above, it’s not unheard of for research students to be charged a bench fee. In case you’re unfamiliar with a bench fee, it’s an annual fee additional to your tuition, which covers the cost of specialist equipment or resources associated with your research. This can include the upkeep of supercomputers you may use, training in specialist analysis software, or travelling to conferences. The exact fee will depend on your specific research topic; however, it should be minimal for most mathematic projects.

What Specific Funding Opportunities Are There for A PhD in Mathematics?

Alongside the usual funding opportunities available to all PhD Research students such as doctoral loans, departmental scholarships, there are a few other sources of funding available to math PhD students. Examples of these include:

You can find more information on these funding sources here: DiscoverPhDs funding guide .

What Specific Skills Do You Gain from Doing a PhD in Mathematics?

A doctorate in Mathematics not only demonstrates your commitment to continuous learning, but it also provides you with highly marketable skills. Besides subject-specific skills, you’ll also gain many transferable skills which will prove useful in almost all industries. A sample of these skills is listed below.

• Logical ability to consider and analyse complex issues,
• Commitment and persistence towards reaching research goals,
• Outstanding verbal and written skills,
• Strong attention to detail,
• The ability to liaise with others from unique disciple backgrounds and work as part of a team
• Holistic deduction and reasoning skills,
• Forming and explaining mathematical and logical solutions to a wide range of real-world problems,
• Exceptional numeracy skills.

What Jobs Can You Get with A Maths PhD?

One of the greatest benefits maths PostDocs will have is the ability to pursue a wide range of career paths. This is because all sciences are built on core principles which, to varying extents, are supported by the core principles of mathematics. As a result, it’s not uncommon to ask students what path they intend to follow after completing their degree and receive entirely different answers. Although not extensive by any means, the most common career paths Math PostDocs take are listed below:

• Academia – Many individuals teach undergraduate students at the university they studied at or ones they gained ties to during their research. This path is usually the preferred among students who want to continue focusing on mathematical theories and concepts as part of their career.
• Postdoctoral Researcher – Others continue researching with their University or with an independent organisation. This can be a popular path because of the opportunities it provides in collaborative working, supervising others, undertaking research and attending conferences etc.
• Finance – Because of their deepened analytical skills, it’s no surprise that many PostDocs choose a career in finance. This involves working for some of the most significant players in the financial district in prime locations including London, Frankfurt and Hong Kong. Specific job titles can include Actuarial, Investment Analyst or Risk Modeller.
• Computer Programming – Some students whose research involves computational mathematics launch their career as a computer programmer. Due to their background, they’ll typically work on specialised projects which require high levels of understanding on the problem at hand. For example, they may work with physicists and biomedical engineers to develop a software package that supports their more complex research.
• Data Analyst – Those who enjoy number crunching and developing complex models often go into data analytics. This can involve various niches such as forecasting or optimisation, across various fields such as marketing and weather.

What Are Some of The Typical Employers Who Hire Maths PostDocs?

As mentioned above, there’s a high demand for skilled mathematicians and statisticians across a broad range of sectors. Some typical employers are:

• Education – All UK and international universities
• Governments – STFC and Department for Transport
• Healthcare & Pharmaceuticals – NHS, GSK, Pfizer
• Finance & Banking – e.g. Barclays Capital, PwC and J. P. Morgan
• Computing – IBM, Microsoft and Facebook
• Engineering – Boeing, Shell and Dyson

The above is only a small selection of employers. In reality, mathematic PostDocs can work in almost any industry, assuming the role is numerical-based or data-driven.

How Much Can You Earn with A PhD in Maths?

As a mathematics PhD PostDoc, your earning potential will mostly depend on your chosen career path. Due to the wide range of options, it’s impossible to provide an arbitrary value for the typical salary you can expect.

However, if you pursue one of the below paths or enter their respective industry, you can roughly expect to earn [3] :

Academic Lecturer

• Approximately £30,000 – £35,000 starting salary
• Approximately £40,000 with a few years experience
• Approximately £45,000 – £55,000 with 10 years experience
• Approximately £60,000 and over with significant experience and a leadership role. Certain academic positions can earn over £80,000 depending on the management duties.

Actuary or Finance

• Approximately £35,000 starting salary
• Approximately £45,000 – £55,000 with a few years experience
• Approximately £70,000 and over with 10 years experience
• Approximately £180,000 and above with significant experience and a leadership role.

Aerospace or Mechanical Engineering

• Approximately £28,000 starting salary
• Approximately £35,000 – £40,000 with a few years experience
• Approximately £60,000 and over with 10 years experience

Data Analyst

• Approximately £45,000 – £50,000 with a few years experience
• Approximately £90,000 and above with significant experience and a leadership role.

Again, we stress that the above are indicative values only. Actual salaries will depend on the specific organisation and position and responsibilities of the individual.

Facts and Statistics About Maths PhD Holders

The below chart provides useful insight into the destination of Math PostDocs after completing their PhD. The most popular career paths from other of highest to lowest is education, information and communication, finance and scientific research, manufacturing and government.

Note: The above chart is based on ‘UK Higher Education Leavers’ data [2] between 2012/13 and 2016/17 and contains a data size of 200 PostDocs. The data was obtained from the Higher Education Statistics Agency ( HESA ).

Which Noteworthy People Hold a PhD in Maths?

Alan turing.

Alan Turing was a British Mathematician, WW2 code-breaker and arguably the father of computer science. Alongside his lengthy list of achievements, Turning achieved a PhD in Mathematics at Princeton University, New Jersey. His thesis titled ‘Systems of Logic Based on Ordinals’ focused on the concepts of ordinal logic and relative computing; you can read it online here . To this day, Turning pioneering works continues to play a fundamental role in shaping the development of artificial intelligence (AI).

Ruth Lawrence

Ruth Lawrence is a famous British–Israeli Mathematician well known within the academic community. Lawrence earned her PhD in Mathematics from Oxford University at the young age of 17! Her work focused on algebraic topology and knot theory; you can read her interesting collection of research papers here . Among her many contributions to Maths, her most notable include the representation of the braid groups, more formally known as Lawrence–Krammer representations.

Emmy Noether

Emmy Noether was a German mathematician who received her PhD from the University of Erlangen, Germany. Her research has significantly contributed to both abstract algebra and theoretical physics. Additionally, she proved a groundbreaking theorem important to Albert Einstein’s general theory of relativity. In doing so, her theorem, Noether’s theorem , is regarded as one of the most influential developments in physics.

Other Useful Resources

Institute of Mathematics and its Applications (IMA) – IMA is the UK’s professional body for mathematicians. It contains a wide range of useful information, from the benefits of further education in Maths to details on grants and upcoming events.

Maths Careers – Math Careers is a site associated with IMA that provides a wide range of advice to mathematicians of all ages. It has a section dedicated to undergraduates and graduates and contains a handful of information about progressing into research.

Resources for Graduate Students – Produced by Dr Mak Tomford, this webpage contains an extensive collection of detailed advice for Mathematic PhD students. Although the site uses US terminology in places, don’t let that put you off as this resource will prove incredibly helpful in both applying to and undertaking your PhD.

Student Interviews – Still wondering whether a PhD is for you? If so, our collection of PhD interviews would be a great place to get an insider perspective. We’ve interviewed a wide range of PhD students across the UK to find out what doing a PhD is like, how it’s helped them and what advice they have for other prospective students who may be thinking of applying to one. You can read our insightful collection of interviews here .

[1] Universities used to determine the typical (median) and range of entry requirements and tuition fees for 2020/21 Mathematics PhD positions.

• http://www.lse.ac.uk/study-at-lse/Graduate/Degree-programmes-2020/MPhilPhD-Mathematics
• https://www.ox.ac.uk/admissions/graduate/courses/dphil-mathematics?wssl=1
• https://www.graduate.study.cam.ac.uk/courses/directory/mapmpdpms
• https://www.ucl.ac.uk/prospective-students/graduate/research-degrees/mathematics-mphil-phd
• http://www.bristol.ac.uk/study/postgraduate/2020/sci/phd-mathematics/
• https://www.surrey.ac.uk/postgraduate/mathematics-phd
• https://www.maths.ed.ac.uk/school-of-mathematics/studying-here/pgr/phd-application
• https://www.lancaster.ac.uk/study/postgraduate/postgraduate-courses/mathematics-phd/
• https://www.sussex.ac.uk/study/phd/degrees/mathematics-phd
• https://www.manchester.ac.uk/study/postgraduate-research/programmes/list/05325/phd-pure-mathematics/
• https://warwick.ac.uk/study/postgraduate/research/courses-2020/mathematicsphd/
• https://www.exeter.ac.uk/pg-research/degrees/mathematics/

[2] Higher Education Leavers Statistics: UK, 2016/17 – Outcomes by subject studied – https://www.hesa.ac.uk/news/28-06-2018/sfr250-higher-education-leaver-statistics-subjects

[3] Typical salaries have been extracted from a combination of the below resources. It should be noted that although every effort has been made to keep the reported salaries as relevant to Math PostDocs as possible (i.e. filtering for positions which specify a PhD qualification as one of their requirements/preferences), small inaccuracies may exist due to data availability.

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Best Doctorates in Mathematics: Top PhD Programs, Career Paths, and Salaries

Given that only a small proportion of the general population holds a PhD in Mathematics, there aren’t many people pursuing doctoral studies in the math field. It requires a high level of intelligence and mathematical ability which a typical person doesn’t possess. It also requires a decent work ethic and the ability to commit five to seven years to research and study.

However, PhD in Mathematics salaries are high. If you’re interested in pursuing a PhD in Mathematics, check out our article to find the best mathematics PhDs and what mathematics jobs you can get. First, let’s find out what a PhD in Mathematics is.

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What is a phd in mathematics.

A PhD in Mathematics is a doctoral degree obtained by a graduate student in mathematics. This kind of mathematics graduate program allows students to develop their research capabilities in mathematics and its potential applications.

PhD in Mathematics can be a Doctor of Philosophy, Doctor of Science, or Doctor of Applied Mathematics degree. Students need to submit their PhD thesis in order to complete the math degree program they are pursuing. Math doctorate programs can take between three and six years to complete, depending on how much time is dedicated to the thesis and its required research.

How to Get Into a Mathematics PhD Program: Admission Requirements

The requirements to get into a mathematics PhD program typically include application fees, school transcripts, a professional resume, three letters of recommendation, and a statement of academic purpose. The admission process for most mathematical PhD programs is similar.

Some schools also require that students have mastered the material roughly equivalent to the undergraduate mathematics major, such as several semesters of calculus and experience with differential equations. Other doctoral math programs require applicants to submit essays or a minimum GPA score as entrance requirements.

PhD in Mathematics Admission Requirements

• Professional CV or resume
• Statement of academic purpose
• Application fee
• At least three recommendation letters
• Undergraduate and graduate school transcripts

Mathematics PhD Acceptance Rates: How Hard Is It to Get Into a PhD Program in Mathematics?

It is extremely hard to get into a PhD program in Mathematics. For example, the Harvard PhD acceptance rate is 4.59 percent and the University of Wisconsin has a zero percent PhD acceptance rate over a five-year median. Doctoral studies in mathematics are rigorous and have a low acceptance rate, making it difficult to get into and obtain a Doctorate in Mathematics.

How to Get Into the Best Universities

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Best PhDs in Mathematics: In Brief

Best Universities for Mathematics PhDs: Where to Get a PhD in Mathematics

The best universities for mathematics PhDs are Harvard University, Massachusetts Institute of Technology, Princeton University, Stanford University, University of California, Berkeley, and Yale University.

Other universities also have excellent PhD in Mathematics programs that we haven’t mentioned in our list, like Johns Hopkins University, Colorado State University, University of California, Los Angeles, and University of Chicago.

Columbia University is a private Ivy League research university founded in 1754 as King's College. It is among the top five national universities and is known as the oldest institution of higher education in New York. At Columbia University, students can find doctoral studies in biological sciences, astronomy, chemistry, economics, music, psychology, and religion.

Mathematics PhD

The PhD mathematics program is designed for full-time students interested in research and teaching at the university level. It is an intense course also meant for students that seek careers in quantitative research and development in business or government. It covers subjects like analysis and probability, Riemann surfaces, cumulative algebra, and modern geometry.

Mathematics PhD Overview

• Program Length: 4 years
• Acceptance Rate: 6%
• Tuition and Fees: $25,248/semester
• PhD Funding Opportunities: Department of Defense Funding, NIH Fellowship Parent Funding 

Mathematics PhD Admission Requirements

• A completed online application form at the Online Application System
• $120 application fee
• Statement of purpose
• A video essay (to be completed in the Online Application System)
• A current resume or CV
• Official transcripts from each university you attended
• Two letters of reference

Harvard University was established in 1636 by the Puritan clergyman John Harvard. It is known as the oldest institution of higher learning in the US and as one of the most prestigious universities in the world. It offers many PhD programs in subjects such as anthropology, statistics, virology, physics, neuroscience, mathematics, immunology, and history of science.

This doctoral program is intended for students who aspire to be research mathematicians and have demonstrated a strong interest in this field. The math graduate courses cover topics like commutative algebra, advanced real analysis, differential geometry evolution dynamics, Riemann surfaces, and Hodge theory.

• Program Length: 4-5 years
• Acceptance Rate: 7%
• Tuition and Fees: $50,928/first two years of study; $13,240/second two years of study
• PhD Funding Opportunities: Hertz Foundation, National Defense Science and Engineering Graduate Fellowship Program, National Physical Science Consortium for Minorities and Women, National Science Foundation
• Application
• $105 application fee 
• Transcripts
• Letters of recommendation
• Demonstration of English proficiency (for non-native speakers)

Massachusetts Institute of Technology (MIT) is a land-grant research university in Cambridge. Founded in 1861, MIT is best known for its programs in physical science and engineering. It offers a wide array of doctoral studies in aeronautics and astronautics, physics, political science, economics, chemical engineering, biology, brain, and cognitive sciences.

Doctor of Philosophy or Doctor of Science Mathematics Degree

In addition to choosing between a Doctor of Philosophy and a Doctor of Science program, students can choose to apply to the Pure or Applied Mathematics programs. Geometry, number theory, algebra, logic, statistics, topology, astrophysics, combinatorics, analysis, probability, numerical analysis, and theoretical physics, are covered in the Pure and Applied Mathematics curricula.

Doctor of Philosophy or Doctor of Science Mathematics Degree Overview

• Acceptance Rate: N/A
• Tuition and Fees: $27,755/term
• PhD Funding Opportunities: Postdoctoral and Senior Research Awards, Faculty Early Career Development Program, Mathematical Sciences Postdoctoral Research Fellowships (MSPRF)

Doctor of Philosophy or Doctor of Science Mathematics Degree Admission Requirements

• Fill out the online application
• Transcripts including grades in math/science/engineering courses
• At least three names and email addresses of recommendation letter writers
• Educational and work history
• Statement of objectives
• Outside financial support and potential outside support
• Credit/debit card payment of the $75 application fee
• Self-reported grades
• Arrange for submission of official transcripts and letters of recommendation

Princeton University is a private Ivy League research university that was founded in 1746. It is known as the fourth-oldest institution of higher education in the US. Princeton University has many PhD programs in subjects like philosophy, mechanical and aerospace engineering, electrical and computer engineering, and neuroscience.

Applied and Computational Math PhD

In this program, students gain a thorough understanding of areas of mathematics critical to scientific and engineering applications, such as numerical analysis and other computational approaches. In the first year, students choose three topics from six applied mathematics categories. At the end of the first year, students need to take a preliminary exam. 

Before the third year, students need to pass the general examination which culminates in a seminar on a research topic. The final requirement for this program is the doctoral dissertation which can be a mathematical contribution to one field of science or engineering.

Applied and Computational Math PhD Overview

• Tuition and Fees : $58,790/year 
• PhD Funding Opportunities: University, departmental, and program fellowships, research and teaching assistantships, external financial support

Applied and Computational Math PhD Admission Requirements

• $75 application fee
• Recommendation letters
• Fall semester grades (for students currently enrolled in master’s degree programs)
• English language tests (for international students)

Established in 1829, Rochester Institute of Technology is known for its excellent technology, engineering, and computing programs. It offers PhDs in Astrophysical Sciences and Technology, Biomedical and Chemical Engineering, Color Science, Imaging Science Sustainability, and many more disciplines.

Mathematical Modeling PhD

Students in this program plan their own trajectory based on required coursework, research, and their selected concentration. They can select from concentrations in the areas of applied inverse problems, biomedical, and discrete mathematics, among others. Some of the program’s courses cover subjects like numerical analysis and computing for mathematical modeling. 

Mathematical Modeling PhD Overview

• Acceptance Rate: 74%
• Tuition: $54,176/year 
• PhD Funding Opportunities: Federal loans, Outside Scholarships, Yellow Ribbon Program, employment through co-ops, internships, or assistantships

Mathematical Modeling PhD Admission Requirements

• Online graduate application
• Copies of official transcripts of all previously completed undergraduate and graduate courses
• Bachelor’s degree from an accredited university or college
• Current resume/CV
• Two letters of recommendation
• Personal statement of educational objectives
• TOEFL, IELTS, or PTE score (international students)
• $65 application fee

Stanford University is well-known for its enterprising student population and high return on investment. Founded in 1885 by California senator Leland Stanford, Stanford University is consistently ranking in the top 10 national universities. Stanford offers many PhD programs in its Graduate School of Engineering, including programs in engineering, medicine, and education.

Mathematics PhD Program

Students in this PhD program take courses in algebraic topology, differential topology, differential geometry, algebraic geometry, theory of probability, real analysis, modern algebra, and mathematical methods of imaging. In the first year, the coursework prepares the students for the qualifying examinations which test them on their skills in algebra and real-world analysis. 

Students must have a dissertation advisor and seek candidacy in their second year. Students will take their Area Examination during their third year, which must be completed by the conclusion of the Winter Quarter. In the fourth and fifth years, students are expected to finish their dissertation research.

Mathematics PhD Program Overview

• Acceptance Rate: 5.7%
• Tuition and Fees: $56,487
• PhD Funding Opportunities: Federal programs, university fellowships, research assistantships, teaching assistantships

Mathematics PhD Program Admission Requirements

• Bachelor’s degree from a regionally accredited US college or university 
• Unofficial transcripts/academic records
• Names and contact information of those who can provide between three and six letters of recommendation
• Online application
• $125 application fee or fee waiver

University of California, Berkeley was founded in 1868. UC Berkeley is known for strict academic criteria for its undergraduate programs. The school has more than 130 academic departments and 80 multidisciplinary research areas. UC Berkeley is among the top universities in the world.

PhD Program in Applied Mathematics

The applied mathematics program requires doctoral students with previous graduate study in mathematics must demonstrate exceptional mathematical research skills. Students in this course can learn about linear algebra and differential equations, multivariable calculus, and discrete mathematics. There are also major electives like mathematical biology and statistics.

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PhD Program in Applied Mathematics Overview

• Program Length: 5-6 years
• Acceptance Rate: 18%
• Tuition and Fees: $10,248.75/semester (resident); $17,799.75/semester (non-resident)
• PhD Funding Opportunities : Berkeley Fellowships, Chancellor’s Fellowships, Cota-Robles Fellowships, Mentored Research Awards, UC Dissertation-Year Fellowships, Conference Travel Grants, Parent and Caregiver Grants

PhD Program in Applied Mathematics Admission Requirements

• A bachelor’s degree or equivalent from an accredited institution
• A minimum GPA of 3.0
• Enough experience in your undergraduate program to complete the program
• At least three letters of recommendation
• $120 application fee (California residents); $140 application fee (all other applicants)

The University of Michigan - Ann Arbor is among the top 30 national universities. It was founded in 1817 in Ann Arbor. Some of the most popular majors from this university are business administration, experimental psychology, and economics. It also has good PhD level programs in education, electrical and computer engineering, and computer and information science.

Applied & Interdisciplinary Mathematics PhD

This PhD degree's purpose is to create graduates who are well-prepared to pursue successful careers in the mathematical sciences, whether in government or academia. Students in the applied and interdisciplinary mathematics course can learn about risk management and modeling of financial losses, mathematical theory of probability, and modern mathematics.

Applied & Interdisciplinary Mathematics PhD Overview

• Program Length: 5-6 years 
• Acceptance Rate: 26%
• Tuition and Fees: $25,230.38 (in state); $50,646.38 (out of state)
• PhD Funding Opportunities: Graduate Student Instructorship (GSI): Mathematics Graduate Student Instructor Teacher Training Program, and Graduate Student Research Assistantship (GSRA)

Applied & Interdisciplinary Mathematics PhD Admission Requirements

• Three letters of recommendation
• Personal Statement (500-word limit)
• TOEFL or IELTS Exam (non-native English speakers)
• Three semesters of calculus
• One or two semesters of differential equation courses
• One semester course in modern algebra, linear algebra, geometry or topology
• Advanced calculus of one and several variables 
• $75 application fee (US citizens); $90 application fee (international applicants)

Nelson Dewey, the first governor of Wisconsin, founded the University of Wisconsin in 1848. It has one of the best engineering and business majors. It also has several good graduate degrees from its Department of Mathematics like Doctor of Philosophy, Master of Arts – Foundations of Advanced Studies, and Master of Arts – Foundations for Research.

Mathematics, PhD

The University of Wisconsin’s Doctor of Philosophy program offers a foundation in fundamental and advanced graduate mathematics. Students in this PhD program can learn about linear algebra, abstract algebra, differential equations, knot theory, and real analysis.

Mathematics, PhD Overview

• Program Length: 5 years
• Acceptance Rate: 16%
• Tuition and Fees: $12,176/year (in state); $25,504/year (out of state)
• PhD Funding Opportunities: Graduate assistantships, fellowships, traineeships, student loans, student jobs, research and travel grants

Mathematics, PhD Admission Requirements

• Application to the UW–Madison Graduate School
• Master’s degree in mathematics or a related field
• Official transcripts
• Supplementary information form
• Three academic letters of recommendation and one additional letter
• Proof of English proficiency (for non-native speakers)
• One-page statement of purpose

Yale University was founded in 1701 in New Haven, Connecticut. It is among the top 10 national universities and is known for its Ivy League reputation . Yale has many PhD programs like anthropology, applied physics, architecture, biomedical engineering, chemical, and environmental engineering. 

PhD in Applied Mathematics

The applied mathematics program entails the study and application of mathematics to issues prompted by a diverse set of application fields. Students study and apply mathematics concepts to questions driven by a variety of applicable fields.

It covers topics such as discrete algorithms, linear and nonlinear partial differential equations, statistical theory and applications, information theory, econometrics, and classical and modern applied harmonic analysis. This program also covers topics like financial statistics, financial mathematics, econometrics probability theory, and information theory. 

PhD in Applied Mathematics Overview

• Acceptance Rate: 6.2%
• Tuition and Fees: $45,700/year
• PhD Funding Opportunities: Financial aid, university fellowships, dissertation fellowships, teaching fellowships

PhD in Applied Mathematics Admission Requirements

• A list of all the prior colleges or universities you’ve attended 
• Unofficial transcripts from each school
• TOEFL scores (non-native English-speaking applicants)

Can You Get a PhD in Mathematics Online?

Yes, you can get a PhD in Mathematics online. However, there aren’t many online PhD math programs out there because of two reasons. The first reason is that there isn’t a big demand for PhDs in Mathematics, so online universities are not inclined to find ways to make those programs more accessible.

The second reason is that in traditional doctoral studies graduate students in mathematics are used as research and teaching assistants. Usually, math doctoral studies take place within a community in which PhD students are apprentices learning alongside instructors and one another.

Best Online PhD Programs in Mathematics

How Long Does It Take to Get a PhD in Mathematics?

It takes about five years to get a PhD in Mathematics. Depending on the academic institution and the specifications of the program, it can take between three and six years. Some students prefer to have a master’s degree before entering a doctoral program in mathematics, but most programs do not require students to have more than a bachelor’s degree .

Some doctoral mathematics academic programs offer two degrees called dual degree programs. You can begin pursuing a Master’s Degree in Mathematics and begin earning credits for a PhD at the same time.

Is a PhD in Mathematics Hard?

Yes, a PhD in Mathematics is hard. Doctoral studies that require advanced knowledge of mathematics would be extremely difficult for most people. Whether you choose to pursue a PhD in Applied Mathematics or Pure Mathematics, you will encounter complex theoretical concepts.

How Much Does It Cost to Get a PhD in Mathematics?

On average, it costs $12,171 per year to get a PhD in Mathematics . This data is based on the National Center for Educational Statistics’s (NCES) report for the average costs of postgraduate studies at public institutions from 2018 to 2019. According to this data, it would cost a total of $48,684 for four years of studies. The cost to get a PhD in Mathematics has likely risen since 2019.

How to Pay for a PhD in Mathematics: PhD Funding Options

The PhD funding options that students can use to pay for a PhD in Mathematics include research fellowships, teaching assistantships, and tuition waivers. In the previous section, we mentioned the cost of doctoral degrees , but this number is with a deduction in the tuition.

These funding options enable students to lower the cost of tuition. For example, domestic students receive lower tuitions. Without funding options or deductions, a PhD can cost from $20,000 to $30,000 per year.

Best Online Master’s Degrees

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What Is the Difference Between a Mathematics Master’s Degree and PhD?

The difference between a Master’s Degree in Mathematics and a PhD is the career opportunities they provide graduates. People who pursue a PhD in Mathematics usually seek jobs in research and academia, while people who pursue master’s degrees are more interested in advancing their professional careers.

A PhD in Math is more research-intensive and focused on historical and current perspectives within the mathematics field. Master’s degrees are a bit broader. Master’s degrees can take up to three years to complete, while PhD can take up to six years. Math PhD students also teach and engage in departmental activities, while master’s students do not.

Master’s vs PhD in Mathematics Job Outlook

It is usually required for postsecondary teachers to have PhDs. According to the Bureau of Labor Statistics (BLS), these professionals have a job outlook of 12 percent , four percent higher than the average for all occupations.

Mathematics and statisticians are usually required to hold a master’s degree and they have a job outlook of 33 percent , nearly three times the average for all occupations. According to these numbers, the job outlook for Master’s Degrees in Mathematics is higher than for PhDs in Mathematics. However, these are just two examples of careers available to master’s and PhD holders.

Difference in Salary for Mathematics Master’s vs PhD

According to PayScale, mathematicians with a master’s degree earn $85,000 per year, and mathematicians with a PhD degree earn $110,000 a year. This is a difference of $25,000 per year for mathematics master’s vs PhD holders.

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Why You Should Get a PhD in Mathematics

You should get a PhD in Mathematics because it expands your academic career opportunities and salary options. With a PhD in Math, you can work for private businesses or government agencies. Many PhD grads work in engineering, medicine, and software development, where they apply the advanced mathematical knowledge they acquired from their doctoral programs.

Reasons for Getting a PhD in Mathematics

• Specialized skills. A PhD in Mathematics equips you with highly valuable and marketable skills. Aside from subject-specific abilities, you can obtain several transferable skills that will be beneficial in practically any industry, such as exceptional numeracy, logical ability, holistic deduction, and reasoning skills.
• Higher salary. A PhD is a terminal graduate degree, meaning it is the highest level of academic certification you can achieve in this field. So with a PhD you will gain the highest skills and knowledge in mathematics. High-level skills and knowledge often translate to a high salary.
• Career opportunities. One of the best advantages math PhDs have is the option of following a variety of employment pathways. To some extent, all sciences are built on basic mathematical principles, so there are many career opportunities with a PhD in Mathematics. With this kind of degree, you can work in finance, academia, or IT.
• Research opportunities. Doctoral Degrees in Mathematics cover theoretical mathematics which is one of the best areas for research and research methodology. During your doctoral studies in math, you will study and research with some of the smartest people in the world.

Getting a PhD in Mathematics: Mathematics PhD Coursework

Getting a PhD in Mathematics is not an easy task. Students need to learn different math courses, some of which require advanced knowledge of mathematics. There is some standard mathematics PhD coursework, like classes in mathematical analysis or mathematical logic. Find out more details on common mathematics PhD courses below.

Mathematical Analysis

These kinds of courses explain the principles of mathematical analysis, including differentiability, continuity, sequence and series convergence, the Riemann integral, function sequences, and series. Students can also learn real applications of real-world analysis, including the estimation of indeterminate integrals, Laurent series, WKB theory, Cauchy theorem, and residual theorem.

Differential Topology

Courses in differential topology are a part of the theory of differential forms and De Rham’s theory. Somer differential topology courses teach about multilinear algebra, Stokes’ theorem, and an introduction to cohomology. But, in most cases, these courses teach about winding numbers, vector fields, index, smooth maps, transversality, and differential manifolds.

Discrete Mathematics

Courses in discrete mathematics usually cover finite geometry, finite groups, finite topology, finite fields, fundamental algebraic topology, combinatorics, and graph theory. Students can learn about the symmetry group of the regular icosahedron because it is a reoccurring subject throughout the course.

Theory of Probability

Theory of probability courses introduce students to discrete and continuous random variables, independent random variables, conditional probability, distribution functions, Poisson distributions, Bayes theorem, and joint distribution. Students in this course will learn how to use math principles in the analysis of random phenomena.

Algebraic Geometry

In most cases, algebraic geometry courses teach students about complex algebraic varieties, cohomology, affine, and projective algebraic geometry. They also cover the fundamental concepts of complex analytic varieties, Bezout’s theorem, algebraic curves, and surfaces, the language of schemes, and properties of morphisms.

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How to Get a PhD in Mathematics: Doctoral Program Requirements

Some of the most common doctoral program requirements to get a PhD in Mathematics are coursework, qualifying exams, research, classroom teaching, and thesis defense. Some doctoral program requirements may vary, but there are a few common steps for most math programs. Keep reading to find out more.

PhD students must finish eight or nine-term courses at the graduate level, in most cases maintaining at least a C average grade. The time for completion of a PhD math coursework is four to five years.

The residency requirement can vary from university to university. For most math PhD candidates, the usual residency requirement is around three years. The whole point of residency is to continue the education and training of students in a specialized field of mathematics.

A committee of three faculty members administers the Qualifying Examination, which is an oral test. Each student selects three qualifying test subjects and discusses them with appropriate examiners. Subjects must be in separate, reasonably broad mathematical fields. 

Typically, the primary topic is decided in cooperation with the potential thesis advisor. After completing the qualifying test, students must choose a thesis advisor, who is usually the primary topic examiner.

In academic positions, teaching is important, especially in mathematical doctoral studies. Many people in math PhD programs aspire to academic positions, so teaching is one of the best ways to learn about the mathematics academic profession. It is an excellent way to learn public presentation skills by completing at least one semester of classroom teaching.

Writing and defending a thesis for a PhD in Mathematics is the culmination of this graduate program. Usually, a thesis is anticipated to contain original research of a high enough quality to be published in a high-level research journal. The defense is usually held in the classroom of the Institute and is presented to the Thesis Examination Committee.

Potential Careers With a Mathematics Degree

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PhD in Mathematics Salary and Job Outlook

People with a PhD in Mathematics earn above the average annual salaries and have careers with above the average job growth. For example, actuaries have a 24 percent job growth till 2030. According to the Bureau of Labor Statistics, the average job growth rate for all occupations is 7.7 percent .

Earning a mathematics PhD is difficult but you will graduate with a wide range of job opportunities. People with a PhD in Math earn between $82,360 to $108,660 per year. Overall, people with PhDs in Mathematics have a good salary and job outlook.

What Can You Do With a PhD in Mathematics?

With a PhD in Mathematics, you can work in education or IT and for private, corporate, or government corporations. You can work as a postdoctoral research associate, a math professor in postsecondary or higher education, a director of analytics, a research scientist, a principal software engineer, or an asset manager.

Best Jobs with a PhD in Mathematics

• Data Scientist
• Mathematicians and Statistician
• Operations Research Analyst

What Is the Average Salary for a PhD in Mathematics?

The average salary for a PhD in Mathematics is $110,000 , according to PayScale. The salary range for doctorate-level degree mathematics jobs ranges from $48,690 to $167,040 per year. Lower-earning operations research analysts make an average of $48,690 , while top-earning data scientists earn $167,040 annually, according to the Bureau of Labor Statistics.

Highest-Paying Mathematics Jobs for PhD Grads

Best Mathematics Jobs with a Doctorate

There are many jobs you can find with a math PhD. The skills you will gain are applicable to almost any field. Find out more about the best PhD in Mathematics jobs below.

Data scientists are specialists who know how to extract and interpret data. They know how to use models and algorithms to analyze massive data repositories. They use various strategies to determine the optimal methods for developing a data model for a business. Data scientist is one of the most in-demand and highest-paid jobs in 2022. 

• Salary with a Mathematics PhD: $108,660
• Job Outlook: 22% job growth from 2020 to 2030
• Number of Jobs: 105,980
• Highest-Paying States: Washington, California, Delaware, New York, New Jersey

Actuaries are more concerned with the financial implications of risk and uncertainty. Actuaries are financial analysts who analyze past and present financial data and forecast future risks. They assess risk using financial theory, statistics, and math and develop plans that reduce the cost of risk.

• Salary with a Mathematics PhD: $105,900
• Job Outlook: 24% job growth from 2020 to 2030
• Number of Jobs: 27,700
• Highest-Paying States: Georgia, New Hampshire, New York, Connecticut, Vermont

Some of the main responsibilities economists have are to predict the customer demand for the firm's products and the firm's product sales. They deal extensively with microeconomic issues while researching trends, collecting, evaluating, and analyzing data. Economists also investigate how to efficiently allocate resources like raw materials, labor, land, or machines.

• Salary with a Mathematics PhD: $105,630
• Job Outlook: 13% job growth from 2020 to 2030
• Number of Jobs: 18,600
• Highest-Paying States: New York, District of Columbia California, New Hampshire, Illinois

In most cases mathematicians and statisticians work in academia and government. Usually, both of the positions require the use of analyzing data or applying statistical and mathematical techniques that help solve problems. 

Statisticians are increasingly involved in statistics and research methodology. Mathematicians are more involved in researching mathematical models or abstractly measuring values and creating results. Mathematics and statistics are the best duos that understand the principles of probability.

• Salary with a Mathematics PhD: $96,280
• Job Outlook: 33% job growth from 2020 to 2030
• Number of Jobs: 44,800
• Highest-Paying States: District of Columbia, New York, New Jersey, Virginia, Maryland

Operations research analysts utilize mathematics and logic to assist businesses in making informed decisions and solving complex problems. They are high-level problem solvers that use sophisticated approaches such as mathematical modeling and statistical analysis to help companies operate more economically.

• Salary with a Mathematics PhD: $82,360
• Job Outlook: 25% job growth from 2020 to 2030
• Number of Jobs: 104,100
• Highest-Paying States: Virginia, Alabama, Maryland, Hawaii, New York

Is a PhD in Mathematics Worth It?

Yes, a PhD in Mathematics is worth it if you are interested in solving math problems and analytical thinking. You also have to be willing to commit to the long educational journey and research required to achieve this level of degree.

Exploring the mathematical fields is challenging and demanding but with time it provides excellent career opportunities. Math positions are respected and well-paid with positive job outlooks. Other than its academic difficulty, there aren’t many downsides when it comes to doctoral math degrees because you can go on to work in many fields.

Additional Reading About Mathematics

[query_class_embed] https://careerkarma.com/blog/best-schools-for-mathematics/ https://careerkarma.com/blog/mathematics-for-computer-science/ https://careerkarma.com/blog/jobs-that-use-math/

PhD in Mathematics FAQ

Yes, a math PhD is useful because it will help you acquire some transferable skills that will be useful in virtually any industry. It is also useful for those interested in mathematics research or academia. If you wonder what you can do with a math degree , a PhD will equip you with many valuable skills.

Yes, a PhD in Mathematics is difficult to learn. It is difficult to be admitted to a doctoral program in mathematics, and it is also difficult and too abstract for most people to grasp advanced mathematical principles taught in PhD studies. Doctoral math studies are objectively difficult, even for those who are naturally strong at math and have excelled at it their whole life.

Mathematicians need several skills like active learning, complex problem-solving, critical thinking, and analytical skills. A good mathematician also needs information ordering and inductive and deductive reasoning abilities.

Mathematicians mainly explore mathematical principles or models and create their own mathematical theories and concepts. Most of the work they do is in the theoretical realm, that is why they mainly want to work in IT, social science, engineering, or financial fields.

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Khalilah beal, catherine k. a. cannizzo, colleen delaney, zhiyan ding, emiliano gómez, nicolle gonzalez, peter haine, ryan a. hass, jiang hu (户将), mihaela ifrim, eyal kaplan, sergei korotkikh, patrick lutz, borislav mladenov, federico pasqualotto, rohil prasad, kendric schefers, arun sharma, norman sheu, forte shinko, kevin stubbs, kelli talaska, krutika tawri, alexandra utiralova, jikang wang, mengxuan yang, dongxiao yu.

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Undergrads planning to apply for PhD programs in science, math, engineering, and social/behavioral science fields:

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Are you an undergrad or alumnus planning to apply for PhD programs in science, math, engineering, and social/behavioral science fields? Are you a 1st year PhD student at UMD?

The National Science Foundation’s Graduate Research Fellowship Program (NSF GRFP) provides 3 years of full support for PhD studies, with an annual living expenses stipend of $37,000. You can visit the NSF informational website by  clicking here .

The UMD National Scholarships Office has developed an ELMS resource to help you plan effectively for your NSF GRFP applications.  To gain access click here to complete a brief questionnaire.  All current UMD undergraduates, alumni, and 1st year grad students planning to apply this fall 2024 will benefit from using this resource. In particular, please view the following presentations available there:

• ZOOM NSF GRFP Prep Session #1 – Introduction
• ZOOM NSF GRFP Prep Session #2 – Writing the Essays

Eligibility: You must be a US citizen or Permanent Resident to apply for the NSF graduate research fellowship. You must be applying for graduate studies in an NSF supported field. If you are a graduate student, you may apply once in your first two years of graduate study.  Click here for full eligibility details.

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The Use of Robotics and Simulators in the Education Environment

Advances in technology continue to push the envelope in healthcare, travel, communication and education. The use of robotic and simulation technologies have proven themselves to be worthy components of available educational resources. These technologies use in the education environment have shown their value in everyday learning and in the specialized education of students with disabilities.

Robotics and Simulators in Education

The use of robotics has allowed complicated medical procedures to be simplified, the work of dangerous construction projects to be safer and the discovery of our universe to be possible. When applied to education, robotics and simulators can change the way students learn and ultimately create a more knowledgeable and well-adjusted student.

Elementary and High School Education

• Robotics – Robots can be used to bring students into the classroom that otherwise might not be able to attend. In New York, a second grader with severe, life-threatening allergies was unable to attend school due to his condition. A four-foot-tall robot provided a ‘real school’ experience for the boy, ‘attending’ school and bringing the boy with him via an internal video conferencing system. Robots such as the one mentioned are able to ‘bring school’ to students who cannot be present physically.
• Simulators – High school sees the strongest example of simulators within drivers’ education courses. Simulators provide a true-to-life experience while removing any real dangers or risk from scenarios. In drivers’ education, students can experience the feeling of being behind the wheel without ever leaving the safety of the classroom. Simulators offer a chance for ‘what if’ scenarios, which can better prepare student drivers for real-life hazards and obstacles on the roadway.

Higher Education

• Robotics – Many careers require specialized knowledge in delicate practices, specifically in the realm of healthcare. When receiving a medical education, many students find benefits in the use of robotics. When learning to perform complicated medical procedures, a human subject isn’t feasible, so educators are employing the use of robots as stand-ins. Robots can be created and programmed to give off all indications of human life, including breath and heartbeat. Their use can also be seen in such procedures as injections, surgeries and even delivering children.
• Simulators – Simulation technology is utilized in a variety of college degree focuses, offering 360 degree real-life scenarios and 3D projections of real experiences. In addition to providing medical students with the means for thorough exploration of the human body, simulators also provide exceptional methods of crisis and disaster training for emergency response and law enforcement trainees. These types of all-encompassing simulators offer a choice and response technology, requiring officers to make split-second decisions and immediately see the ramifications of their actions. These types of scenarios can include violent altercations or behind-the-wheel high-speed chases.

Special Education

• Robotics – Students with special requirements are reaching new levels of learning through the use of robotics in the classroom. With these technologies children with autism are learning communication and social skills and students with developmental issues and attention disorders are learning focus. Individuals with severe physical disabilities are also offered a constant companion and health monitoring system – all through the use of robotics. Robots can be programmed to suit each individual child’s need, offering special education in a much simpler, accessible format.
• Simulators – Simulators are able to offer students with special needs an introduction to real-world scenarios in a non-threatening environment. Everyday lessons can be taught at a comfortable pace, including subjects ranging from basic self-care to stay-safe techniques in emergency situations. Simulators have also provided a way for special education educators to see the world from their students’ perspectives, including hearing-impaired or blind simulations.

Assistive technology is growing, and the abilities it provides to special education students are limitless. Simulation and robotics technologies offer a range of possibilities within education, with a helpful solution for every student’s learning needs. As the technological world unveils new innovations daily, the educational world will continue to benefit from the opportunities offered with these groundbreaking tools.

You can help shape the influence of technology in education with an Online Master of Science in Education in Learning Design and Technology from Purdue University Online. This accredited program offers studies in exciting new technologies that are shaping education and offers students the opportunity to take part in the future of innovation.

Learn more about the online MSEd in Learning Design and Technology at Purdue University today and help redefine the way in which individuals learn. Call (877) 497-5851 to speak with an admissions advisor or request more information.

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MyLab Math: Purpose-built to meet students where they are on their unique learning journeys

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Located in the heart of downtown Indianapolis, Indiana University – Purdue University Indianapolis (IUPUI) is a vibrant higher learning institution, enrolling a diverse student body that includes more than 16,000 undergraduates.

At IUPUI, Math faculty have long trusted and adopted MyLab Math from Pearson, a dynamic platform that’s driving improved performance and high satisfaction for students and faculty alike. It’s described as an integral part of the math curriculum, purpose-built to effectively adapt to individual students and their unique learning needs.

The adoption and success of MyLab Math at IUPUI goes hand in hand with Pearson’s commitment to going above and beyond as a dedicated partner every step of the way.

An integral part of the student journey – from beginning to end

Kristen Weddington, an IUPUI math instructor and course coordinator for the school’s developmental math offering, is a longtime MyLab Math user and ardent advocate.

“We have a large student population on different skill levels,” she says. “The best part about MyLab is it meets students where they are.”

IUPUI students are required to complete a math course to graduate. About 50 instructors staff the department. Intermediate Algebra, mostly comprised of freshmen and sophomores, enrolls about 1,500 students per year, and MyLab Math shines in the course as a key component of each student’s journey, regardless of proficiency level.

“MyLab is a big part of their learning,” says Weddington. “Students use it from day one until they take their final exam. They’re on MyLab maybe more than they’re in class.”

Delivering engaging tools that drive effective learning

With students and MyLab Math joined at the hip, it’s critical that it provides what students and instructors need – and it does.

A broad suite of intuitive interactive tools caters to students at various levels of math proficiency and with different learning preferences.

Weddington notes that MyLab Math can start students at ground level and build them up.“Students do find it valuable. It really helps them understand the material after they’ve left class,” she says. “They find the platform easy to use, and they feel like it gives them good feedback.”

For example, a student who’s stuck on a homework problem may use “Help Me Solve This” – a feature quickly accessible on the student’s MyLab Math homework window. The interactive tool guides the student, step by step, through a similar problem, providing prompts that help the student understand how to solve it. The student can then return to the actual homework problem and apply what they’ve learned.

Videos embedded within the Pearson eTextbook , Intermediate Algebra: Concepts & Applications , 11th Edition , by Martin L. Bittenger, David J. Ellenbogen, and Barbara L. Johnson, provide students with another valuable learning resource too.

“I’ve had students who are really far behind, went and watched the videos for each section, and caught up and understood the material,” says Weddington, noting one of her non-traditional adult students caught up in about a week and felt a boost in motivation.

She and other instructors regularly use the Personalized Homework feature, which assigns homework questions based on each student’s performance on a previous test or quiz. The student receives credit for questions answered correctly on the test and can skip similar questions in the homework. Personalized Homework also helps motivate students by allowing them to focus on what they need to learn without having to spend time on what they already know.

Weddington has observed that students who complete their Personalized Homework assignments in MyLab tend to outperform students in classes that use other courseware platforms.

Actionable analytics for just-in-time intervention

Another key feature, Performance Analytics, located in the Instructor Gradebook, empowers instructors to monitor each student’s progress in real-time, identify ideas where support is needed, and deploy just-in-time personalized interventions to help bring lagging students back on track.

When the Early Alert feature in Performance Analytics flags low-performing students, Weddington contacts their instructors, requesting they engage with the students and help them improve.

She and other faculty also use Performance Analytics for their personal development.

“I love Performance Analytics,” she says. “I dig into them to see where I can do better, and where I can help my teachers do better. I’ve used it a lot to see what sections of the book aren’t going well and what we can do to improve.”

Delivering better outcomes – especially when broadly deployed

MyLab Math’s impact on student outcomes is amplified when it’s used across multiple courses. Students gain familiarity with the platform, which transfers to math courses they take later.

“We’ve seen that, compared to classes that use other platforms, MyLab has produced better outcomes,” says Weddington. “Students have done better in the next class. They do better because they already understand the platform.”

An unparalleled partner in fostering success

Underpinning the popularity and effectiveness of MyLab Math at IUPUI is Pearson’s unwavering reputation as a highly engaged, hyper-responsive partner that’s committed to going above and beyond.

Weddington notes that Pearson representatives make regular campus visits to engage with faculty and to discuss any areas in need of improvement.

“Pearson is great. Anytime I ask for anything, they’ve been helpful,” she says. “We use a few publishers, and Pearson has been the best. You can ask anybody that. I get immediate feedback if I need anything. I could email someone right now and I’d get good feedback within five or ten minutes.”

A partnership for the future, primed for growth

All signs point to MyLab Math featuring prominently in the department’s future.

“We don’t plan on letting it go because it’s been a really good resource,” says Weddington.

In fact, she’s eager to bring MyLab Math with her when she transitions to a new role in the fall as course coordinator for a STEM version of Intermediate Algebra.

“I plan to continue to use MyLab Math to the best of its ability. We want to keep integrating it and using all the tools that we can,” she says. “Students who use it well, learn.”

About the author

Patrick Golden

Patrick Golden is a writer, marketing and communications specialist, and former journalist based in Massachusetts.   

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More math? Oklahoma bill could change some requirements to graduate high school

Oklahoma students could be required to take a fourth math credit to graduate high school, but they would have an extra year to complete it, if a new proposal becomes law.

The state House overwhelmingly approved a measure on Wednesday in a 95-2 vote to add a fourth math credit to graduation requirements.  House Bill 3278  would allow students to begin taking high school credits in eighth grade.

The bill would take effect in the 2025-26 school year. It now advances to the Senate for consideration.

Two of the credits would have to be Algebra I and either Algebra II or geometry. The other two credits must be any math course with “content and/or rigor above Algebra I.”

This could include traditional upper-level courses like Algebra II, geometry, trigonometry, calculus and statistics. Schools also could apply a math credit to a postsecondary career and technology program or to a course that teaches math through real-world application.

More: Oklahoma County to begin negotiating for jail land near Crooked Oak schools

In Oklahoma City Public Schools, this could mean an HVAC or construction trade class could count as a math credit, if the local school board approves it, said Superintendent Sean McDaniel during a Monday board meeting.

“It would make sense because of the amount of math that kids will use in those pathways that we might be able to award credit,” McDaniel said.

Bill would also change some career credit requirements for Oklahoma high school students

Existing requirements to complete four credits of English language arts, three credits of laboratory science and three credits of history would be unchanged.

Six high school credits would have to relate to a student’s aspirations after high school, under the bill. 

Oklahoma students already have to create an Individual Career and Academic Plan (ICAP) to prepare for entering college, the military or the workforce. The bill would mandate that six courses, or “pathway units,” correspond to students’ ICAP goals.

Mandatory courses in English, math, science and history would count toward these credits. Students also could fulfill the requirement by taking a world language, computer technology, fine arts, Advanced Placement credits, college concurrent enrollment or Junior Reserve Officers’ Training Corps (JROTC), among other options.

The bill’s author, Rep. Rhonda Baker, R-Yukon, said the measure encourages students to take classes that are most relevant to their career goals.

“We are revamping this so that their pathway will fit whatever they deem necessary and important to them,” she said during discussion on the House floor.