Mathematicians
Also called Computational Scientist, Cryptographer, Mathematician, or Research Scientist
Updated · Source: O*NET 31.0
What Mathematicians do
Mathematicians invent and apply the math behind codes, models, and science, turning tangled real-world problems into equations someone can actually solve.
A mathematician works with numbers, symbols, and logic to answer questions nobody has answered yet. Some push the field itself forward, developing new principles in areas like algebra, geometry, probability, and logic. Others apply existing methods to practical problems in business, engineering, and the sciences, building models that simulate how something behaves. Job titles include cryptographer (someone who works on codes and secure information) and computational scientist (someone who uses computer programs and math to model how things work).
The work is quiet and deep, but not solitary. You spend hours alone with a problem, then explain it: mentoring colleagues on techniques, emailing collaborators, presenting at conferences, and writing up results. This is a small field. Openings are around 100 per year, and projected growth is +0.6% compared with +3.5% for all jobs.
A day in the life
You start by clearing email, much of it from collaborators picking apart a proof or asking for data. Then you settle into the hard part: laying out a set of assumptions and following them to see what breaks. You run computations, check the numbers against real data, and rewrite a model that did not behave the way you expected. Midday, a younger colleague comes by stuck on a method, and you walk through it at the whiteboard. In the afternoon you read a journal paper that changes how you see your own problem. You draft a few pages of a report. Progress can be slow. Some days you end where you started, minus one idea that did not work.
This could fit you if you…
- ✓Enjoy sitting with a hard problem for days without a clear answer
- ✓Like math itself, not just using it to get a result
- ✓Can explain complicated ideas patiently to people who are stuck
- ✓Want to keep learning from journals, conferences, and other researchers
- ✓Are comfortable committing to years of schooling
You might not like it if you…
- –Need quick wins and visible results every week
- –Dislike writing reports and presenting your work to an audience
- –Want a large field with plenty of openings to choose from
- –Would rather not spend years in graduate school before starting
How people get in
- 1Take all the math you can in high school, and get comfortable with computers and physics alongside it.
- 2Earn a bachelor's degree in a field like mathematics, applied mathematics, financial mathematics, mathematics and statistics, or mathematics and computer science.
- 3Work with a professor on research as an undergraduate so you learn what unsolved problems actually feel like.
- 4Go on to a master's degree, which is the typical entry-level education for this work. Many research roles expect further study beyond that.
- 5Present at conferences and publish what you find, since sharing results is a core part of the job.
- 6Look at related paths too, such as statistician, data scientist, or teaching math at a college, in case they fit you better.
Who tends to enjoy it
Curious
People who like figuring things out, research, science, and solving problems.
Organizing
People who like keeping things accurate, orderly, and running on schedule.
Creative
People who like making things, design, writing, music, and self-expression.
Official task list
Mathematicians conduct research in fundamental mathematics or in application of mathematical techniques to science, management, and other fields. Solve problems in various fields using mathematical methods. (O*NET)
- Mentor others on mathematical techniques.
- Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
- Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
- Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
- Assemble sets of assumptions, and explore the consequences of each set.
- Perform computations and apply methods of numerical analysis to data.
- Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
- Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.
A typical day involves
Skills that matter most
- Mathematics
- Critical Thinking
- Reading Comprehension
- Active Learning
- Complex Problem Solving
- Judgment and Decision Making
What you'll need to know
- Mathematics
- Education and Training
- Computers and Electronics
- English Language
- Physics
How much Mathematicians make
The median pay for Mathematicians in the U.S. is $126,710 a year ($60.92 an hour). Most earn between $69,240 and $195,190. (Bureau of Labor Statistics, May 2025)
Pay depends a lot on where you live: the median is highest in Washington ($162,280) and lowest in Michigan ($65,510).
Pay by state and territory
| State | Median pay | Jobs |
|---|---|---|
| California | $126,710 | 250 |
| Colorado | $86,020 | 60 |
| Illinois | $130,970 | 60 |
| Indiana | $88,050 | 40 |
| Maryland | $131,810 | 160 |
| Massachusetts | $104,190 | 40 |
| Michigan | $65,510 | 90 |
| Nevada | $102,890 | 70 |
| New York | $126,950 | 150 |
| Rhode Island | $109,260 | 100 |
| Virginia | $148,030 | 400 |
| Washington | $162,280 | 100 |
Where to study for this
College programs that commonly lead to this career, and how many US colleges offer each.
- Mathematics 1,482 colleges
- Financial Mathematics 138 colleges
- Applied Mathematics 275 colleges
- Mathematics and Computer Science 97 colleges
- Mathematics and Statistics 52 colleges
- Computational and Applied Mathematics 60 colleges
- Mathematics and Statistics, Other 52 colleges
- Mathematical Statistics and Probability 23 colleges
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Source: O*NET 31.0 Database (USDOL/ETA), occupation 15-2021.00, used under CC BY 4.0 and modified by Whittle. Pay: BLS Occupational Employment and Wage Statistics (May 2025), SOC 15-2021. Outlook and entry education: BLS Employment Projections 2025–35. Program links: NCES CIP 2020 to SOC 2018 crosswalk. How we build these pages.