Some mathematicians work on fundamental questions in areas like algebra, geometry, probability, or logic purely to extend what's known, while others apply established mathematical techniques to practical problems in industries like finance or engineering. Either way, the work involves building mathematical or statistical models to represent some real phenomenon, then using those models for analysis or simulation. Because progress in the field depends on shared knowledge, mathematicians also spend real time writing up and publishing their research, and staying current by reading journals and talking shop with other mathematicians at conferences.
Pros
Very high upside earning potential, with top pay reaching $195k
Intellectually rich work applying deep theory to real problems across many fields
Comfortable, climate-controlled office setting with a desk-based routine
Cons
Extremely small field, with only about 100 openings and a shrinking outlook (-0.7%)
Requires a master's degree at minimum, and a PhD for most research roles
Above-average hours, often exceeding a standard 40-hour work week
A typical day
The whiteboard holds yesterday's failure, which is normal: the conjecture's third case still resists, and the morning's deep work session attacks it fresh — two hours of the profession's true labor, thinking hard with paper, coffee, and no notifications, testing an approach borrowed from a different field entirely. It collapses instructively at 11 (the collapse reveals a structure worth its own note). The applied half of the day follows at the lab where the mathematician consults: a fluid dynamics team needs their simulation's instability diagnosed, and it falls to an eigenvalue analysis the mathematician sketches before lunch ends. The afternoon holds a collaboration video call across three time zones — mathematics is a conversation, and coauthors argue warmly over a shared virtual whiteboard — then referee work on a submitted paper, checked line by line because the literature's integrity is peer-maintained. The evening habit: a problem carried in the head's background, where solutions have a history of arriving unannounced. Progress is nonlinear; the profession's skill is persisting anyway.
Tasks at the job
Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.
Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
Workplace & working conditions
Work happens indoors in a climate-controlled setting, and most of the day is spent sitting at a desk.
You're expected to exercise significant independent judgment day to day. Precision and accuracy are essential to the work, and the work is highly structured, following set procedures.
Education necessary or common
Master's degree for applied roles; a PhD is standard for research positions
Common college majors
MathematicsApplied MathematicsMathematics with a minor in the application field of interestStatistics
Licenses & certifications
MS for many applied roles; PhD for research — the degrees are the path
Actuarial exams as an alternative professional track
Security clearance for government roles (the NSA is the country's largest employer of mathematicians)