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.
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
| School | Program | Online Option |
|---|---|---|
| Columbia University | Mathematics PhD | No |
| Harvard University | Mathematics PhD | No |
| Massachusetts Institute of Technology | Doctor of Philosophy or Doctor of Science Mathematics Degree | No |
| Princeton University | Applied and Computational Math PhD | No |
| Rochester Institute of Technology | Mathematical Modeling PhD | No |
| Stanford University | Mathematics PhD Program | No |
| University of California, Berkeley | PhD Program in Applied Mathematics | No |
| University of Michigan – Ann Arbor | Applied & Interdisciplinary Mathematics PhD | No |
| University Of Wisconsin | Mathematics, PhD | No |
| Yale University | PhD in Applied Mathematics | No |
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.
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
| School | Program | Length |
|---|---|---|
| Atlantic International University | Doctorate in Mathematics | Custom pace |
| Edith Cowan University | Mathematics PhD | 4 years |
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.
Related Mathematics Degrees
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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.
Best Master’s Degrees
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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.
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
- Actuary
- Economist
- 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
| Mathematics PhD Jobs | Average Salary |
|---|---|
| Data Scientist | $108,660 |
| Actuary | $105,900 |
| Economist | $105,630 |
| Mathematician or Statistician | $96,280 |
| Operations Research Analyst | $82,360 |
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.
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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