mathematics phd salary

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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

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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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PhD Salaries and Lifetime Earnings

PhDs employed across job sectors show impressive earning potential:

“…[T]here is strong evidence that advanced education levels continue to be associated with higher salaries. A study by the Georgetown Center on Education and the Workforce showed that across the fields examined, individuals with a graduate degree earned an average of 38.3% more than those with a bachelor’s degree in the same field. The expected lifetime earnings for someone without a high school degree is $973,000; with a high school diploma, $1.3 million; with a bachelor’s degree, $2.3 million; with a master’s degree, $2.7 million; and with a doctoral degree (excluding professional degrees), $3.3 million. Other data indicate that the overall unemployment rate for individuals who hold graduate degrees is far lower than for those who hold just an undergraduate degree.” - Pathways Through Graduate School and Into Careers , Council of Graduate Schools (CGS) and Educational Testing Service (ETS), pg. 3.

Average salaries by educational level and degree (data from the US Census Bureau, American Community Survey 2009-2011, courtesy of the Georgetown University Center on Education and the Workforce):

The Bureau of Labor and Statistics reports higher earnings and lower unemployment rates for doctoral degree holders in comparison to those with master’s and bachelor’s degrees:

According to national studies, more education translates not only to higher earnings, but also higher levels of job success and job satisfaction:

“Educational attainment – the number of years a person spends in school – strongly predicts adult earnings, and also predicts health and civic engagement. Moreover, individuals with higher levels of education appear to gain more knowledge and skills on the job than do those with lower levels of education and they are able, to some extent, to transfer what they learn across occupations.” - Education for Life and Work (2012), National Research Council of the National Academies, pg. 66.

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Phd in mathematics: requirements, salary, jobs, & career growth, what is phd in mathematics.

A PhD in Mathematics is a highly specialized degree that entails completing original research in a specific area of mathematics and making a significant contribution to the field.

Students in a PhD program generally take advanced mathematics courses to expand their understanding of the subject and to obtain the abilities needed to undertake research.

They collaborate extensively with faculty mentors and other researchers to create a research project that takes several years to finish.

A PhD in Mathematics study typically results in the discovery of new mathematical theories, proofs, or algorithms that can be applied in a variety of domains such as computer science, physics, finance, and engineering.

A PhD in Mathematics is a tough and rigorous curriculum that needs great mathematical competence, strong analytical skills, and endurance.

Graduates of mathematics PhD programs frequently move on to positions in academia, research, or business, where they can use their mathematical skills to solve challenging issues and make substantial contributions to their field.

How much money do people make with a PhD in Mathematics?

Individuals with a PhD in Mathematics can expect to earn more than those with a bachelor’s or master’s degree in the subject.

As of May 2020, the median annual income for mathematicians and statisticians, which includes individuals with a PhD in Mathematics, was $96,660, according to the US Bureau of Labor Statistics.

However, depending on the field and region, earnings might range from $59,500 to more than $160,000 per year.

I ndividuals with a PhD in Mathematics are frequently employed in academia, where salaries vary according to the type of institution, rank, and years of experience.

For the 2021-2022 academic year, the median income for full-time faculty members in the mathematical sciences was $92,000, according to the American Mathematical Society.

What is expected job growth with PhD in Mathematics?

According to the U.S. Bureau of Labor Statistics, employment of mathematicians and statisticians, which includes people with a PhD in Mathematics, is expected to expand 33 percent from 2020 to 2030, substantially faster than the national average.

The rising use of data and the need for quantitative analysis in a range of areas, including healthcare, finance, and technology, are projected to drive this expansion.

Scientific research and development services, which are expected to grow 48 percent from 2020 to 2030, and management, scientific, and technical consulting services, which are expected to grow 37 percent over the same period, are expected to see the most growth in mathematicians and statisticians’ employment.

What can you do with a PhD in Mathematics?

Individuals holding a PhD in Mathematics have numerous job options. Here are a couple such examples:

1. Academia: Individuals with a PhD in Mathematics can pursue academic careers such as professorships or research positions in universities or research institutions. Graduate students and postdoctoral researchers can also be supervised by them.

2. Data Science: As the amount of data in many businesses grows, there is a great demand for people with extensive mathematical skills who can work as data scientists, data analysts, or statisticians.

3. Financial Services: Individuals with a PhD in Mathematics can work as quantitative analysts, risk managers, or financial analysts in the financial industry.

4. Technology: Individuals with a PhD in Mathematics can work in technology organizations as data scientists or machine learning engineers, thanks to the rising use of artificial intelligence and machine learning.

5. Government Agencies: Individuals with a PhD in Mathematics can work for government organizations such as the National Security Agency (NSA), the Department of Defense, or the National Aeronautics and Space Administration (NASA) in positions such as cryptographers, systems analysts, or aerospace engineers.

6. Consulting: Individuals with a PhD in Mathematics can work for consulting firms, where they can provide analytical and modeling services to clients in a variety of industries.

What are the requirements for a PhD in Mathematics?

The specific requirements for obtaining a PhD in Mathematics can vary depending on the institution and program, but generally, the following are common requirements:

1. Bachelor’s or Master’s Degree: Applicants to most PhD programs in Mathematics must have a Bachelor’s degree from a recognized university. Although it is not usually required, certain schools may accept applicants with a Master’s degree in a related discipline.

2. Academic Transcripts: Applicants are usually expected to present certified transcripts of their undergraduate and graduate education, which demonstrate their academic performance and achievement.

3. Statement of Purpose: Applicants are typically expected to provide a personal statement or statement of purpose detailing their research interests, academic ambitions, and reason for pursuing a PhD in Mathematics.

4. Standardized Test Scores: Applicants to many PhD programs may be required to submit scores from standardized tests such as the Graduate Record Examination (GRE) or other related assessments.

5. Letters of Recommendation: Applicants to PhD programs in Mathematics are frequently required to provide letters of recommendation from academic or professional sources who may speak to the applicant’s academic talents, research potential, and eligibility for a PhD program.

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How long does it take to get a phd in mathematics.

The length of time it takes to earn a PhD in Mathematics can vary depending on a number of factors, such as the program’s structure, the student’s progress, and the research area. However, in general, it takes around 4-6 years to complete a PhD in Mathematics in the United States.

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Do you need a masters in mathematics to get a phd in mathematics.

In most circumstances, a master’s degree in mathematics is not required to pursue a PhD in mathematics.

Many PhD programs in Mathematics accept students who have a bachelor’s degree in Mathematics or a related field and a strong academic record and research potential.

However, some PhD programs may offer a master’s degree as part of the PhD requirements. This is known as a “master’s on the way to a PhD” program.

In this instance, students would normally complete the master’s degree coursework and research requirements before enrolling in the PhD program.

What are the Best PhD in Mathematics Degree programs?

1. massachusetts institute of technology (mit) 2. university of california, berkeley 3. stanford university 4. harvard university 5. princeton university 6. university of chicago 7. california institute of technology (caltech) 8. university of michigan 9. new york university (courant institute) 10. university of texas at austin, leave a comment cancel reply.

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Ph.D. Program in Mathematics

Degree requirements.

A candidate for the Ph.D. degree in mathematics must fulfill a number of different departmental requirements.

NYU Shanghai Ph.D. Track

The Ph.D. program also offers students the opportunity to pursue their study and research with Mathematics faculty based at NYU Shanghai. With this opportunity, students generally complete their coursework in New York City before moving full-time to Shanghai for their dissertation research. For more information, please visit the  NYU Shanghai Ph.D. page .

Sample course schedules (Years 1 and 2) for students with a primary interest in:

Applied Math (Math Biology, Scientific Computing, Physical Applied Math, etc.)

Additional information for students interested in studying applied math is available here .

Probability

PDE/Analysis

The Written Comprehensive Examination

The examination tests the basic knowledge required for any serious mathematical study. It consists of the three following sections: Advanced Calculus, Complex Variables, and Linear Algebra. The examination is given on three consecutive days, twice a year, in early September and early January. Each section is allotted three hours and is written at the level of a good undergraduate course. Samples of previous examinations are available in the departmental office. Cooperative preparation is encouraged, as it is for all examinations. In the fall term, the Department offers a workshop, taught by an advanced Teaching Assistant, to help students prepare for the written examinations.

Entering students with a solid preparation are encouraged to consider taking the examination in their first year of full-time study. All students must take the examinations in order to be allowed to register for coursework beyond 36 points of credit; it is recommended that students attempt to take the examinations well before this deadline. Graduate Assistants are required to take the examinations during their first year of study.

For further details, consult the page on the written comprehensive exams .

The Oral Preliminary Examination

This examination is usually (but not invariably) taken after two years of full-time study. The purpose of the examination is to determine if the candidate has acquired sufficient mathematical knowledge and maturity to commence a dissertation. The phrase "mathematical knowledge" is intended to convey rather broad acquaintance with the basic facts of mathematical life, with emphasis on a good understanding of the simplest interesting examples. In particular, highly technical or abstract material is inappropriate, as is the rote reproduction of information. What the examiners look for is something a little different and less easy to quantify. It is conveyed in part by the word "maturity." This means some idea of how mathematics hangs together; the ability to think a little on one's feet; some appreciation of what is natural and important, and what is artificial. The point is that the ability to do successful research depends on more than formal learning, and it is part of the examiners' task to assess these less tangible aspects of the candidate's preparation.

The orals are comprised of a general section and a special section, each lasting one hour, and are conducted by two different panels of three faculty members. The examination takes place three times a year: fall, mid-winter and late spring. Cooperative preparation of often helpful and is encouraged. The general section consists of five topics, one of which may be chosen freely. The other four topics are determined by field of interest, but often turn out to be standard: complex variables, real variables, ordinary differential equations, and partial differential equations. Here, the level of knowledge that is expected is equivalent to that of a one or two term course of the kind Courant normally presents. A brochure containing the most common questions on the general oral examination, edited by Courant students, is available at the Department Office.

The special section is usually devoted to a single topic at a more advanced level and extent of knowledge. The precise content is negotiated with the candidate's faculty advisor. Normally, the chosen topic will have a direct bearing on the candidate's Ph.D. dissertation.

All students must take the oral examinations in order to be allowed to register for coursework beyond 60 points of credit. It is recommended that students attempt the examinations well before this deadline.

The Dissertation Defense

The oral defense is the final examination on the student's dissertation. The defense is conducted by a panel of five faculty members (including the student's advisor) and generally lasts one to two hours. The candidate presents his/her work to a mixed audience, some expert in the student's topic, some not. Often, this presentation is followed by a question-and-answer period and mutual discussion of related material and directions for future work.

Summer Internships and Employment

The Department encourages Ph.D. students at any stage of their studies, including the very early stage, to seek summer employment opportunities at various government and industry facilities. In the past few years, Courant students have taken summer internships at the National Institute of Health, Los Alamos National Laboratory, Woods Hole Oceanographic Institution, Lawrence Livermore National Laboratory and NASA, as well as Wall Street firms. Such opportunities can greatly expand students' understanding of the mathematical sciences, offer them possible areas of interest for thesis research, and enhance their career options. The Director of Graduate Studies and members of the faculty (and in particular the students' academic advisors) can assist students in finding appropriate summer employment.

Mentoring and Grievance Policy

For detailed information, consult the page on the Mentoring and Grievance Policy .

Visiting Doctoral Students

Information about spending a term at the Courant Institute's Department of Mathematics as a visiting doctoral student is available on the Visitor Programs  page.

• 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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PhD in Mathematics Salary

The most apparent reason to consider a PhD in mathematics is the salary. For private industry jobs, math PhDs earn high starting wages. In fact, salaries for math PhDs are among the highest for any advanced degree, especially when employed in technology.

According to PayScale.com, the average salary for math PhDs is $106,000 .

One reason salaries are so high: a PhD in mathematics qualifies individuals for some of the best-paying jobs in data science and machine learning. For example, PhDs in math commonly land senior data scientist roles ( $130,000 / year ) and machine learning engineer jobs ( $120,000 ).

Yet, beyond salary, you might be wondering: Is a PhD in mathematics worth it? Sure, the degree results in a salary bump, but the trade-offs include opportunity costs (these programs usually take 3-5 years to complete) and they do require you to learn skills on your own like analytics, SQL and Python.

Below we’ve taken a closer look at math PhD salaries. Read on for a look at salaries by job title, PhD in math salaries vs. other fields, and if a PhD in math is good for a data science career. Afterward, we explore the other considerations for your decision-making by also checking the most up-to-date data science salary statistics.

PhD in Math: Salary by Job Title

Math PhDs that seek private industry jobs tend to fall into three areas: IT, finance, or business administration. In terms of IT careers, some of the best starting salaries for math PhDs are in data science, with many jobs starting at $120,000+.

Here is a look at some of the top private industry data science jobs for math PhDs, as well as their starting salaries in data science :

• Data Scientist: $106,000
• Senior Data Scientist: $130,000
• Lead Data Scientist: $143,000
• Quantitative Analyst: $100,000
• Machine Learning Engineer: $120,000
• Senior Machine Learning Engineer: $150,000
• Research Scientist: $98,000

Source: PayScale.com

PhD in Math Salary vs Other Fields

PhDs in math earn some of the highest wages of all STEM PhDs, behind just a small set of subjects including computer science and engineering. The industry you enter does have a significant effect on salary however.

Almost all PhDs who go into teaching and academia, for example, earn a similar median wage of around $75,000. For private industry jobs, PhDs earn significantly more.

According to the 2019 Survey of Doctorate Recipients , math PhDs have the fourth-highest median salary once they are in the field of IT:

• Computer Science - $162,000 / year
• Electrical Engineering - $160,000 / year
• Engineering (All fields) - $149,000 / year
• Mathematics and Statistics - $148,000 / year
• Industrial Engineering - $145,000 / year
• Physics - $144,000 / year
• Physical Science - $131,000 / year
• Economics - $114,000 / year

Source: National Center for Science and Engineering Statistics

According to the survey, math PhDs also command high median salaries in the fields of management, sales or administration ( $164,000 ) and professional services ( $142,000 ). Considering another PhD program? See our salary guides for PhD in economics and PhD in statistics .

PhD in Math for Data Science

Mathematics PhDs receive training and experience that is relevant to data science careers, and provide training to others on a number of subjects that data scientists use every day. For instance, a PhD program in math would provide training in:

• Experimental design and research
• Working with complex, real-world datasets
• Math and statistics
• Researching or advancing new methods and techniques

In particular, many tech companies hire PhDs for research and development (R&D) roles. A PhD is often a required or preferred qualification, especially in the roles of Research Scientist and Machine Learning Scientists for example. In these positions the main responsibility of the scientist is to help advance machine learning or data science exploration for the company.

As such, PhDs in data science roles typically research and/or develop new algorithms or create machine learning libraries. They can also be asked to provide leadership on a niche specialization like machine learning, computer vision, or robotics.

With advanced degrees becoming increasingly common in data science – within the industry more than 80% have a master’s or PhD – a math PhD can help make you more competitive for a data science job. In fact, mathematics is the No. 2 subject amongst data scientists holding a PhD, according to the Burtch Works 2021 Salary survey :

Is a PhD in Mathematics Worth It?

Looking only at median salary, a math PhD is a valuable investment. But the PhD cannot be taken in a vacuum, and it is important to evaluate the other skills you may need to invest in for a private sector employer. Programming and SQL knowledge being high among them.

To help understand some of the other aspects of pursuing this advanced degree, we talked with a math PhD who now works in the data science field. They highlighted five areas to give thought to before committing to a program:

Consider a master’s first - An accelerated master’s program can help prepare you for a PhD, as well as help you better understand if you want to make the commitment. And you can complete a master’s program in as little as one year.

Do you like teaching? - Math PhDs typically are required to teach undergraduate students. If you are not interested in teaching, or you don’t like it, a PhD in math might not be right for you.

Why do you want to pursue a PhD? Answer this question. You should be able to articulate exactly why you want to make this commitment, and you should be able to explain it to someone outside of the field. If you understand your motivations, you will be more likely to succeed.

Consult with an advisor - Ask a potential advisor about the work they do. This will help you better understand the PhD research component. Hint: It should interest and excite you. If it sounds tedious, chances are, you likely won’t excel in a PhD program.

Know where you want to focus - If you are interested in a career in data science, you should focus your research in an area that is applicable to the career you want. Some research areas that are applicable to data science include: algorithms, machine learning, deep learning and artificial intelligence.

Beyond these questions, you also have to bear the opportunity costs. Completing a PhD requires a significant investment of time, typically five to six years, and can incur significant expenses, both in the direct (tuition) or indirect (delayed earnings).

Let’s briefly expand on those costs. PhD candidates usually earn a stipend of about $35,000 / year, and depending on the program, may have to pay tuition. If you stack that up against the earnings you are delaying – starting salaries for master’s in data science programs can start at $126,000 / year – you can calculate as your opportunity cost roughly $90,000 / year, starting your second year (the first year would be required for an accelerated master’s regardless).

Weigh all of the factors we’ve discussed here in your decision: starting and median salary, on the job responsibilities and opportunities, alternative pathways to your goals, and associated costs. With all of this aggregated knowledge and the linked resources we’ve sprinkled throughout, you are well on your way to making the best choice for your career!

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Department of Mathematics

Thanks to its international focus, the Department of Mathematics offers doctoral students the best possible start to a career in academic or industrial research. A doctorate usually takes between three and five years.

The Department of Mathematics offers a broad spectrum of research areas for doctoral students ranging from pure mathematics, such as algebra, analysis, geometry, number theory or probability, to more applied mathematics, such as insurance mathematics, finance, mathematical physics, numerical analysis, operations research and statistics.

About twenty to thirty doctoral students complete their doctoral thesis at the Department every year: overview of upcoming and successfully passed doctoral examinations.

Research environment

Doctoral students work as scientific assistants and are employed for up to six years. They attend the external page Zurich Graduate School in Mathematics. call_made

The benefits are:

• internationally highly respected professors
• research funded by the external page Swiss National Science Foundation call_made
• offices in the ETH Zurich Main Building
• access to the Mathematics Library and the ETH Library , access to online publications
• conferences organised by the Forschungsinstitut für Mathematik to support the scientific exchange of ideas

Teaching activities

Passing on knowledge to future mathematicians, other scientists and engineers is a key part of doing doctoral studies at ETH Zurich. The teaching workload depends on the doctoral student's salary level. Teaching generally comprises:

• teaching exercise classes
• organising exercises for a lecture
• assisting in student seminars
• interacting with the lecturer and/or teaching assistants (undergraduate students)
• providing assistance for lectures ranging from basic mathematics for biologists to advanced lectures for mathematicians
• coordinating and correcting exams

Additional courses

Research lives from acquiring knowledge about current theory and discussing it with experts. During the regular doctoral studies, at least 12 ECTS credits must be acquired to cover the following objectives:

• Deepening of knowledge in the research field of the doctoral thesis and expansion of knowledge beyond the original discipline
• Acquisition of transferable skills
• Integration into the scientific community  

Courses and seminars:

• wide variety of high-level lectures, minicourses and student seminars: see ETH Zurich Course Catalogue or external page graduate courses call_made offered by the Zurich Graduate School in Mathematics
• Reseach seminars organised by professors and research groups where experts from different mathematical fields give talks and exchange their knowledge
• The FIM - Institute for Mathematical Research and the Institute for Theoretical Studies invite academic guests for scientific exchange

Life in Zurich

• largest city in Switzerland with a top ranking for quality of life
• charming medieval old town very close to the ETH Main Building and the Department
• fantastic water activities, winter sports or hiking because of the lake and the Alps within close proximity
• variety of cultural events and night life, very cosmopolitan  

Further activities

• The external page Zurich Graduate School of Mathematics (ZGSM) call_made organises language courses and social events such as barbecues and fondue dinners.
• The Association of Scientific Staff at ETH (AVETH) and the Association of Academic Staff at the D-MATH (VMM) represent the interests of doctoral students and organise events.
• The external page Academic Sports Association Zurich (ASVZ) call_made offers a wide range of sports that fulfil every wish.

More Information

• chevron_right ETH Zurich – Doctorate
• chevron_right Student portal – Doctorate
• chevron_right Welcome Center
• chevron_right Continuing education in university teaching
• external page call_made German courses (ZGSM)
• external page call_made Language center
• protected page lock Help@D-MATH (ETH login required)

Legal matters

• chevron_right Ordinance on Doctoral Studies at ETH Zurich
• chevron_right Rector’s Implementation Provisions for the Ordinance on Doctoral Studies 2021

Associations

• protected page lock VMM – Association of the academic mid-level faculty at D-MATH
• chevron_right AVETH – Association of Scientific Staff at ETH
• chevron_right AVETH – Survival Guide

• Department of Mathematical Sciences
• Study programmes
• PhD program

The PhD program

The PhD program at the Department of Mathematical Sciences usually lasts 3 years, for students enrolled with a Master's Degree, and 4-5 years for students enrolled in the integrated program with a bachelor's degree (or equivalent). The program consists first of all of an independent research project resulting in the end of a PhD thesis with publishable results.

It is also a part of the PhD program to follow some PhD courses, and our PhD students are expected to spend an extended period (up to 3-6 months) at a foreign research institution during the PhD program.

PhD students (except industrial PhDs) are required to teach, typically as teaching assistants. Our advanced courses are taught in English. Our PhD students must be able to teach in English and to follow courses taught in English.

A PhD in mathematics will make you qualified for a wide range of career possibilities including continuing an academic career or going into the private or the public sector.

PhD students who hold a stipend from the University of Copenhagen will receive funding as follows: Students enrolled in the 3-year program will receive a salary throughout the PhD period. Students enrolled in the integrated program will receive a number of state education grant portions until they acquire the master's degree 2 years before handing in their PhD thesis. For the remaining 2 years they will receive a salary.

Both stipends also include a travel allowance for participation in conferences and for research visits to foreign research institutions.

For more information about the PhD programme see https://science.ku.dk/phd/

The Department of Mathematical Sciences offers PhD degrees in pure and applied mathematics, statistics, insurance and financial mathematics within four research sections and two centres:

• Algebra & Geometry
• Analysis & Quantum
• Insurance and Economics
• Statistics and Probability
• Copenhagen Centre for Geometry and Topology (GeoTop)
• Centre for the Mathematics of Quantum Theory (QMATH)

The department has about 45 tenured faculty, 30 postdocs, and 60 PhD students.

Applying for a PhD

• After accepting a PhD stipend  
• Mini-guide on how to fill the online application form

For current PhD students

See MATHnet  (department intranet) for courses, economy, travel etc.

PhD students

Theodor Henningsen, PhD student

Silvan Vollmer, PhD student

Taro Spirig, PhD student

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