Online Ph.D.  Mathematics

By Nikita Nath

Updated March 15, 2024

Nikita Nath

Nikita is a psychologist working primarily with children using a child rights-based approach. She also writes content for various websites and blogs on diverse topics, focusing primarily on academia. Her hobbies include traveling, reading, and discovering different coffee-making techniques.


Bachelors in English, Journalism, and Psychology; Masters in psychology with clinical specialization

Areas of Expertise & Credentials

  • 2 years of experience working as a content writer with various start-ups
  • 1 year of experience working as a child psychologist with Insight
  • Working on various projects of inclusion for neurodivergent children
  • 2+ years of experience teaching psychology online

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Students who enroll in the Ph.D. in mathematics program are prepared for jobs in academia or business. A wide range of areas can benefit from the program’s instruction in mathematics and its applications. It allows students to collaborate with professors on research projects, including various academic and practical subjects. There are several options for research in both pure and applied mathematics with the Ph.D. (such as the applied math Ph.D.), commonly known as the doctorate in mathematics. On their road to a Ph.D., all doctoral students are required to complete some teaching. This guide highlights the critical aspects of the online Ph.D. mathematics program to help prospective students make informed decisions for their academic pursuits.


Best Online Ph.D. Mathematics

One of the most complex decisions students ever must make is choosing a school or institution to enroll in for a doctorate in mathematics. The cost, placements, beginning pay, employment rates, acceptance rates, and other aspects should all be considered. FBD teams searched through each of these matrices to create a list of the top math education Ph.D. programs. Listed below are our rankings for the best online Ph.D. mathematics programs: *

The Massachusetts Institute of Technology (MIT), established in 186, is a private land-grant research university in Cambridge, Massachusetts. MIT is a large, highly residential research university with more than 11,900 students, most being graduate and professional students.
Univ Address Tuition Grad Rate
Massachusetts Institute of Technology(On-Campus) 77 Massachusetts Avenue, Cambridge, Massachusetts 02139 $55,510 96%

Universities and programs are ranked by various factors, such as affordability, curriculum and coursework, reputation and availability, program length, statistics, the potential of employment, and return on investment for the students. For a more in-depth analysis, please read about our rankings methodology page

What to Expect from Online Ph.D.
Mathematics Programs

In terms of scope and depth, math is an extensive topic. As a result, there are many diverse fields that online Ph.D. mathematics students can explore. Pure mathematics, applied mathematics, and statistics are the three categories into which these fields often fall. Mathematical biology, applied dynamical systems, combinatorics, matrix and operator theory, geometry, optics, inverse issues, probability, numerical analysis, and partial differential equations are some areas of study.

Additionally, as math concentrates on solving multidisciplinary issues in the actual world, students could cooperate with other STEM researchers or students of other online science Ph.D. programs. For an online doctorate in mathematics student, the research topic can be related to fluid mechanics, financial mathematics, theoretical and computational optimization, etc.

Prior coursework and study, qualifying tests, a candidacy exam with an advisor, and creative research culminate in a written dissertation and defense for the Ph.D. in mathematics. Candidates for the Ph.D. in mathematics must complete at least 36 credits of graduate-level courses, as well as preliminary written and oral exams, 24 credits of thesis work, and a doctorate thesis with a final defense.

A typical day for an online doctorate in mathematics student would entail the following:

  • Study scholarly works to expand expertise and spot current gaps in the body of knowledge related to the research topic.
  • Identify linkages between models, prove theorems, and define concepts as the research goes on, specifically related to the topic.
  • Collect data and analyze it to help create computer models, perform simulations, evaluate projections, etc.
  • Liaise with others – There are several ways to do this. For instance, one could collaborate closely with experts from several fields supporting one’s study, such as computer scientists, for projects using machine learning. Alternatively, one can require regular feedback from those who provided the data for one’s research, such as financial institutions or colleagues in biological research.
  • Attend a variety of seminars, lectures, and activities.

Listed below are a few typical online Ph.D. mathematics courses:

Numerical analysis

This research involves numerical analysis for integral equations, partial differential equations (finite difference, finite element, domain decomposition), and optimization.

Financial Mathematics

This course focuses on quantitative thinking and the capacity to relate cutting-edge mathematical theories to facts. Students will undertake in-depth analysis and build intricate models and financial instruments.

Machine Learning

In this course, students learn how to innovate, build machine learning models, and use them to solve significant real-world data-intensive challenges by integrating and using ideas from computers, statistics, optimization, engineering, mathematics, and science.

Algorithms, Combinatorics, and Optimization

This course uses algorithms, combinatorics, and optimization to integrate research on the mathematical structure of discrete objects with the creation and analysis of algorithms in fields like Network Optimization, Combinatorial Optimization, Integer Programming, Polyhedral Theory, Computational Algebra, Convex and Discrete Geometry, and Number Theory.

Computational Fluid Dynamics

This course touches upon the difficulties that arise when liquids and gases flow across surfaces that are solved and analyzed by researchers using numerical analysis and data structures.

Areas of Specialization for Online
Ph.D. Mathematics Programs

Several separate subjects and areas may be explored and investigated within a certain discipline of study. These academic specialties are referred to as specializations. A specialization often requires delving deeply into the significant subject selected for the study. To support the specialization, additional supporting or minor courses must be taken. Some of the concentrations and degree variants of an online Ph.D. in mathematics students can choose from are as follows:

Area of Specialization Description Career Options
Ph.D. in Mathematics (Education Emphasis)Advanced mathematics, mathematics education, and quantitative and qualitative research methods in education are all studied as part of the Ph.D. in mathematics specializing in mathematics education. The program focuses on K–12 mathematics instruction and learning, including teacher preparation or professional development, curriculum, instruction, and assessment.Graduates work in school, district, and state curriculum leadership positions.
Ph.D. in Mathematics, specialization in Statistics (Online Ph.D. statistics)The Ph.D. in mathematics with a specialization in statistics program or online Ph.D. programs in statistics is created to give students a strong foundation in statistical theory and methodology, which have broad applications in the natural, biomedical, and social sciences as well as engineering, finance, business management, and governmental regulations.Data scientists, big data architects
Ph.D. in Math specializing in Algorithms, Combinatorics, and Optimization (ACO)The obligatory coursework in the ACO Program curriculum is created to guarantee that students have a solid, foundational intellectual foundation that helps to facilitate and improve their research alternatives.Graduates of the program can be found in diverse settings in academia and industry; some choose careers in finance.
Ph.D. in Computational Sciences and EngineeringThis program is highly multidisciplinary and strongly emphasizes combining and using concepts from math, physics, engineering, and computers to build computational models that address real-world issues.Computational development, research institutions, technology jobs
Ph.D. in Machine Learning (ML)The study of machine learning involves a wide range of disciplines that utilize data to identify patterns in the design and operation of both living and artificial systems, including robots and the human body.Data scientists, data modelers, data analysts
Ph.D. in BioinformaticsThis program combines research and instruction on using information technology in biology and medicine. It educates and trains graduate students to become leaders in the fields of bioinformatics and computational biology.Researchers, scientists

Some other examples of concentrations and variants related to the mathematics Ph.D. program include:

  • Applied Math Ph.D./applied Ph.D. Programs
  • Doctorate in Probability
  • Ph.D. in Calculus
  • Ph.D. Applied Statistics Online

Why should I do an Online
Ph.D. Mathematics?

A Ph.D. in mathematics broadens a student’s options for academic careers and how they may spend their careers learning more about their interests as students and later as professors. Additionally, the field of mathematics has a vast spectrum in breadth and depth. As a result, there are many diverse fields that online Ph.D. mathematics students can explore.

The best thing about a doctorate in applied mathematics is that it can be used in any field, whether in the banking or healthcare industries, engineering or education, logistics, or neuroscience. The online Ph.D. mathematics education will provide students with the analytical and problem solving abilities required for any position following graduation, whether in academia, the commercial or public sectors, or both.

There are several chances to work for government agencies or commercial businesses too. Many Ph.D. in mathematics holders today work in fields like software development, engineering, and medicine, using the skills they learned in their programs to assist tackle difficulties and challenges in the real world.

A Ph.D. in mathematics shows that one is dedicated to lifelong study and equips one with highly employable talents. With subject-specific knowledge, one will acquire transferable abilities that apply to practically any industry. For example, one would have to ability to:

  • reason through and evaluate complicated topics;
  • show dedication and perseverance in pursuing scientific objectives;
  • demonstrate exceptional communication and writing abilities;
  • communicate with people from various religious origins, and operate as a team;
  • demonstrate comprehensive deduction and reasoning abilities;
  • form and articulate logical and mathematical answers to a variety of issues encountered in daily life; and
  • exhibit excellent numeracy abilities.

Read the Guide to PH.D. Programs for more information on doctoral programs.

Free Courses for Online Ph.D. in
Mathematics Students

When a student has enrolled in an online Ph.D. mathematics, there might be a subject that might need a quick brush-up, or there might be a reason to brush up on a few concepts that someone might have not rehearsed or come across a post a bachelor’s or masters. For those courses, students would not have to look too far away from free online courses. Here are a few to explore:

Course Description Provided by
Introduction to Linear Models and Matrix AlgebraThis course will utilize matrix algebra to express the linear models frequently employed to model changes between experimental units in this beginning data analysis course. Based on these disparities, students will draw statistical conclusions.Harvard Univ
Statistical Inference and Modeling for High-throughput ExperimentsIn this course, students will study multiple testing issues, error rates, error rate management techniques, false discovery rates, q-values, and exploratory data analysis. The introduction of statistical modeling and its use with high-throughput data will follow.Harvard Univ
Graph Theory and Additive CombinatoricsThis course addresses traditional and contemporary advancements in additive combinatorics and graph theory, emphasizing issues and themes that link the two fields. Students are also introduced to recent research areas and outstanding issues in the course.MIT
Numerical Methods for Partial Differential EquationsThe advanced theory and applications of numerical techniques for solving differential equations are covered in this graduate-level course. The course specializes in physically arising partial differential equations and the fundamental concepts that underlie diverse approaches.MIT

How to get into the Online
Ph.D. Mathematics?

Enrolling in a math Ph.D. program may vary a little bit per the Ph.D. specialization, but the typical requirements for Ph.D. in mathematics programs would be as follows:

  • A master’s in mathematics or bachelor’s degree with advanced mathematics courses
  • A minimum cumulative Grade Point Average (GPA) of 3.0 on a scale of 4.0
  • Two Letters of Recommendation are required: one for academic reference from past educational experience and the other for a reference who can vouch for the applicant’s caliber of work as an accountant professionally
  • Personal Statement
  • Résumé or Curriculum Vitae

The math Ph.D. program acceptance rates vary per the institution being applied to but are typically between 9% and 15% (unverified).

Online Ph.D. Mathematics No
GRE Programs

Those applying to Ph.D. programs in business, law, STEM, and other fields, must take the GRE general exam and the GRE subject tests. Since more than 60 years ago, admissions and fellowship panels at hundreds of graduate institutions throughout the globe have taken GRE results into account, along with an applicant’s undergraduate grades and other requirements for graduate study.

A GRE score continues to be often required for admission to Ph.D. programs, including the online Ph.D. in mathematics degree program. However, few universities no longer require GRE scores for enrollment and offer Ph.D. in mathematics no GRE programs since graduate student demographics have changed so much over the past 50 years. The main grading criteria for graduate admission now include GPA and job experience at these universities. Examples include the University of Michigan – Ph.D. in Mathematics and Applied and Interdisciplinary Mathematics, and the University of Illinois Urbana-Champaign – PH.D. in Mathematics.

How Long does it take to complete the Online
Ph.D. Mathematics Program?

The average length of online Ph.D. programs in mathematics is around five to six years. Basic courses in algebra, analysis, and topology are examples of typical subject requirements. The degree program culminates in a doctoral dissertation and at least 72 credit hours beyond an undergraduate degree, comprising at least 48 hours of classroom credits and a maximum of 24 hours of research credits.

The eight-course requirement is usually satisfied for students by the end of the third year. The first two years must be completed with Honors grades. Each term, a set of three qualifying exams—on typical subjects like topology, real and complex analysis, and algebra and number theory—is offered. By the conclusion of the second year, all qualifying exams must be passed. Students should take the tests as soon as possible because there is no restriction on the number of times they may do so. During the third year, the dissertation prospectus should be sent in. The thesis must be completed independently and with the help of an adviser.

Accelerated Online Ph.D. Mathematics

Enrolling in an accelerated math program might benefit students if they are full-time math students who are highly driven and have a knack for the subject’s principles and ideas. These accelerated programs are pretty difficult and move swiftly, as one might anticipate. They allow excellent students enrolled in undergraduate/graduate programs to get graduate/PH.D. credits. Since these programs are very demanding on students, they should do their research before applying because not everyone is eligible for these programs. However, it would be hard to come across an accelerated online Ph.D. mathematics program in most instances.

Accreditations for Online Ph.D.
Mathematics Programs

Accreditation is a voluntary process that institutions go through to demonstrate the quality of their educational programs. For students seeking online mathematics degrees, enrolling in accredited Ph.D. colleges for mathematics could be essential because doing so can often be a prerequisite for receiving federal financial aid and transferring credits across educational programs. Employing applicants with degrees from recognized schools may be preferred by many firms. There is a list of authorized regional and national accrediting agencies on the Council for Higher Education Accreditation (CHEA) website. Students should check to see if the institution they consider attending is certified.

One entity that assesses institutions rather than specific college programs is the Middle States Commission on Higher Education (MSCHE). It is a non-profit membership organization that uses a range of student demographics and resources to define, defend, and promote educational excellence.

Also, the United States is a unique country that uses private groups of schools and colleges, rather than a government body, to vouch for a college’s eligibility to receive government-funded student aid. The Mathematical Associating of America (MAA) is an organization that overlooks this and maintains accreditation for institutions of higher learning for mathematics.

The Guide to College Accreditation is a good place for students to learn more about accreditation.

How to Pay for an Online Ph.D.
Mathematics Program?

Giving one’s payment options for one’s online Ph.D. mathematics program great thought is essential, especially considering the current state of student debt, the price of education, and the average debt each student accrues. The most intelligent method to pay for education is through scholarships. If an applicant does not meet the requirements for a scholarship, they may inquire with their employers about tuition reimbursement if they are employed professionals. Also, applying for a student loan is another option for paying for an online Ph.D. mathematics program. Additionally, students can check their eligibility for federal student funding.

Discover more about funding higher education through these guides: What is Financial Aid? | How to Pay for College? | Donors for Student Loans | Grants for Student Loans | FAFSA Student Aid.

Fully Funded Online Ph.D.
Mathematics Programs

Fully funded mathematics Ph.D. programs are those where students can get a full scholarship to fund their tuition and studies. Full scholarships are financial awards made to students for their education that may consider their financial situation in addition to other factors, such as their academic status. Here are a few to explore:

AMS-AAAS Mass Media Fellowship

The American Mathematical Society (AMS) partners with the American Association for the Advancement of Science (AAAS) to provide ten-week fellowships for graduate math students who wish to work full-time as reporters, researchers, or production assistants in American mass media outlets such as radio and television stations, newspapers, and magazines during the summer.

American Mathematical Society Centennial Fellowships

Outstanding mathematicians receive yearly prizes from the AMS Centennial Research Fellowship Program to further their scientific careers. A fellowship winner must have held their PH.D. degree for at least three years and no more than twelve when the award was announced. Applications will be accepted from those now employed in a tenured, tenure-track, postdoctoral, or equivalent (as determined by the selection committee) in a North American university.

AMS Congressional Fellowships

This fellowship is sponsored by the American Mathematical Society (AMS) and the American Association for the Advancement of Science (AAAS).

FAQs Related to the Online Ph.D.
Mathematics Program

Can you get a PH.D. in math online?

Yes, you may do an online Ph.D. in mathematics. However, it is uncommon to discover online Ph.D. programs, mainly in statistics, mathematics, or applied mathematics. Students who want to work in the disciplines of education, analytics-based mathematics, or information technology may choose an online Ph.D. program.

Is a Ph.D. in math worth it?

Is doing a Ph.D. in math difficult?

Is it mandatory to do a master’s to get into a Ph.D. in math?

Why would someone get a Ph.D. in math?

Do mathematicians make good money?

What is the difference between a Ph.D. and a doctorate?

What are the requirements for doing a Ph.D. in mathematics?

Should I skip my master’s and go straight to Ph.D.?

Career Opportunities and Salaries after obtaining
an Online Ph.D. Mathematics

Math, statistics, and financial theories are frequently used in math occupations to evaluate risk or resolve challenging issues, etcetera. Successful professionals in this industry possess good mathematics, communication, and problem-solving abilities.

For students who put in the effort to obtain a Ph.D. in mathematics, this profession provides several profitable job prospects. Between 2020 and 2030, the Bureau of Labor Statistics (BLS) forecasts a 27% job growth rate for math-related jobs, a pace that is much higher than the 4% average for all occupations. Data is being used extensively, which helps to explain why there is such a great demand for qualified statisticians, analysts, and mathematicians.

The typical annual compensation for math professionals is $98,680, according to the BLS. Those passionate about math and who possess the necessary abilities may have a rewarding and successful future. So, as one can see, if a student invests their time in a higher degree in mathematics, it can be gratifying. Listed below are a few career options for online Ph.D. mathematics graduates:

OccupationJob DescriptionSkills RequiredMedian Annual SalaryJob Growth (up to 2030)
Financial AnalystsFinancial analysts advise companies and people on how to spend money to make a profit. They evaluate the performance of bonds, equities, and other financial products. Financial analysts assess investment possibilities and options to make a profit.Decision-making skills, analytical skills, computer skills, math skills, communication skills, detail-oriented$81,4106% (as fast as average)
Market Research AnalystsTo determine if a product or service will be sold, market research experts look at current market circumstances. They assist businesses in determining who will buy certain things and at what price by conducting market research and collecting data.Communication skills, critical-thinking skills, analytical skills, detail-oriented$63,92022% (much faster than average)
Advertising, Promotions, and Marketing ManagersManagers of marketing, advertising, and promotions create campaigns to spark interest in their companies’ goods and services. They collaborate with finance employees, advertising salespeople, and art directors. They generate curiosity among potential customers about a good or service.Interpersonal skills, organizational skills, communication skills, analytical skills, decision-making skills, creativity$133,38010% (as fast as average)
Financial ManagersThe financial stability of a company is the responsibility of the financial managers. They prepare financial reports, oversee investment operations, and plan for the organization’s long-term financial objectives. Most of the financial manager’s time is spent evaluating data and advising senior managers on how to increase profitability.Math skills, communication skills, analytical skills, organizational skills, detail-oriented$131,71017% (much faster than average)
Computer and Information Research ScientistsComputer and information scientists provide creative applications for both new and current technologies. They research and address challenging issues in computers for many industries, including business, science, and medicine.Interpersonal skills, communication skills, analytical skills, math skills, problem-solving skills, logical thinking, detail-oriented$131,49022% (much faster than average)

Certifications and Licensing for Online
Ph.D. Mathematics Graduates

Post an online Ph.D. mathematics,  it is recommended that students entering the field get certifications from established professional organizations to connect with established players and find greater acceptance in the industry. In general, to practice the profession of mathematics, no certification or licensing requirement is mandated by state or federal laws. Nevertheless, certifications add heft to a resumé, leading to better job prospects and higher pay. Here are a few certification programs to consider:

Mathematical Association of America: College Mathematics Instructor Development Source (CoMInDS)

The MAA CoMInDS initiative assists mathematics departments in creating or updating their graduate student professional development programs by providing teaching materials and advice. The workshop offers interested teachers the chance to learn how to create a successful program and access a vast library of lessons, exercises, and assignments that they may utilize at their schools.

American Statistical Association: Classes in Methodology and Practice

This program involves classes in methodology and practice to keep candidates up to date with new theories and techniques, assist them in staying connected with best practices, enable them to advance in areas they have not studied before, and help them gather concepts and directions for future research.

American Statistical Association: Workshops in Technology

The workshops in technology teach students about new software tools and computational approaches so they can keep on top of technological changes and new data sources.

Fellow of the Society of Actuaries (FSA)

Exams, e-Learning courses and modules, a proctored project evaluation, validation of educational experiences outside the SOA Education system, a professionalism seminar, and the Fellowship Admissions Course are requirements for receiving the FSA designation.

Additional Resources for Online Ph.D.
Mathematics Graduates

After earning a Ph.D. mathematics online in the topic of choice, the next big step would be to join a professional organization as a member, become accredited, and be committed to the field of study. Doing so connects students to their professional peers and keeps them informed of the most recent developments in mathematics. Here are a few resources graduates can tap into:

Research Council on Mathematics Learning (RCML)The Research Council on Mathematics Learning (RCML), founded in 1974, may be seen as a tool its members might utilize to achieve objectives. RCML offers a space for inquiry, analysis, and professional development for math educators at all levels.
Society of Actuaries (SOA)With more than 30,000 actuaries as members, the Society of Actuaries (SOA) is the largest actuarial professional association in the world. The SOA develops actuaries as pioneers in assessing and managing risk to enhance financial outcomes for people, businesses, and the general public through education and research.
Mathematical Association of America (MAA)The Mathematical Association of America is the largest community of mathematicians, students, and enthusiasts in the world. The MAA’s purpose is to enhance understanding of mathematics and its impact on our planet.
The Conference Board of the Mathematical Sciences (CBMS)One of the main goals of the nineteen professional societies that make up the Conference Board of the Mathematical Sciences (CBMS) is to expand or disperse knowledge in one or more mathematical sciences. CBMS aims to advance research, enhance teaching, and broaden the applications of mathematics.
Society for Industrial and Applied Mathematics (SIAM)The Society for Industrial and Applied Mathematics (SIAM) is a non-profit organization dedicated to disseminating superior mathematical knowledge to other professionals who may apply mathematical theory in practical, industrial, or scientific applications.

Author Bio:

Nikita Nath

Nikita is a psychologist working primarily with children using a child rights-based approach. She also writes content for various websites and blogs on diverse topics, focusing primarily on academia. Her hobbies include traveling, reading, and discovering different coffee-making techniques.


Bachelors in English, Journalism, and Psychology; Masters in psychology with clinical specialization

Areas of Expertise & Credentials

  • 2 years of experience working as a content writer with various start-ups
  • 1 year of experience working as a child psychologist with Insight
  • Working on various projects of inclusion for neurodivergent children
  • 2+ years of experience teaching psychology online


The average tuition (based on degree type for in-state students), average graduation rates, and rankings are based on data from various sources, including the Integrated Postsecondary Education Data System (IPEDS), and are variable over time. All rankings and statistics are subject to change. The rankings are solely the opinion of Find Best Degrees (FBD) and are based on our proprietary methodology. They do not represent the views of the institutions or organizations mentioned, nor do they represent any official government census or survey. Furthermore, any views or opinions expressed on this page are of FBD’s researchers and teams. Unless otherwise specified, they do not represent the thoughts and opinions of the individuals, institutions, or organizations mentioned. This page’s content is provided solely for informational purposes, with data drawn from various sources, including IPEDS. FBD and its employees make no guarantees regarding the accuracy or completeness of any information found on this page or by following any link. FBD will not be held liable for any errors or omissions in this material nor any losses, injuries, or damages resulting from the exposure or use of this information. Although the information on this page is/was correct at the time of publication, readers should exercise caution because some or all of the provided information may have changed over time, potentially resulting in inaccuracies. For more information, please read our Terms of Service. Trademarks and logos are the property of their registered owners.