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 ...

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.

A 300-billion-digit number is the biggest known pseudoprime, a number which looks like a prime but isn’t. The techniques used to find this behemoth could help keep online transactions secure. The ...