Sometimes work in one discipline of pure mathematics has a completely unexpected payoff in another. Some of the famous mathematician Pierre de Fermat’s (1601–1665) work in number theory bears this out ...

19th-century mathematicians thought the “roots of unity” were the key to solving Fermat’s Last Theorem. Then they discovered a fatal flaw. Sometimes the usual numbers aren’t enough to solve a problem.

Prime numbers are all the rage these days. I can tell something’s up when random people start asking me about the randomness of primes—without even knowing that I’m a mathematician! In the past couple ...

Like many math students, I had dreams of mathematical greatness. I thought I was close once. A difficult algebra problem in college kept me working late into the night. After hours of struggle, I felt ...