Pure Mathematics

What you'll do in college

Pure math is about proofs—rigorously establishing why mathematical statements are true. After calculus and linear algebra, you'll move into abstract subjects like real and complex analysis, abstract algebra, topology, and number theory. Problem sets are usually short but brutal, demanding hours of careful thinking for each question.

There are few labs and no software in many courses—just chalk, paper, and ideas. Math majors often form tight study groups because the material is hard to learn alone.

What you'll do after college

Pure math is unusually flexible. Some grads continue to PhDs and become mathematicians or professors; many others go into quantitative finance, software engineering, data science, cryptography, actuarial science, or teaching.

Employers value math majors for their problem-solving discipline and rigor, even if the specific theorems never come up at work. Pay varies widely, with quant roles among the highest-paid jobs in finance.

Famous graduates

• Katherine Johnson — Legendary NASA mathematician; B.S. in Mathematics and French from West Virginia State University
• John Nash — Nobel laureate whose life inspired ''A Beautiful Mind''; B.S./M.S. in Mathematics from Carnegie Mellon
• David Blackwell — First Black mathematician inducted into the National Academy of Sciences; B.A. in Mathematics from UIUC
• Eric Lander — Led the Human Genome Project; founded the Broad Institute

Selectivity vs. earnings