The Scariest Problem in Math

The most important unsolved mystery in mathematics is nearly 170 years old, and there’s a million-dollar reward for its solution. Why is hardly anyone trying to find it?

- BY JOSEPH HOWLETT ILLUSTRATIONS BY DTAN STUDIO Joseph Howlett

IN OCTOBER 2024 I ATTENDED A WORKSHOP AT HARVARD UNIVERSITY where mathematicians talked through the uses of artificial intelligence in their field. Most were less worried about the future of math than excited about a new tool they might use. During one coffee break, I found myself in a group of participants who all agreed that it made no difference whether a human or a computer solved their favorite open problem. They just wanted to read the proof.

“So you really don’t care whether the Riemann hypothesis gets solved by a human or AI?” I asked. I thought I clocked a slight chill, exchanged smirks, knowing looks. It’s not unusual for me to feel a step behind in these circles.

“An AI that can prove the Riemann hypothesis is not one I’d want to meet,” said Andrew Sutherland, a number theorist at the Massachusetts Institute of Technology. “If that happens, mathematicians having jobs will be the least of our problems.”

I’d merely been tossing out the name of an open question I’d heard of. But I began to wonder: What is this math puzzle that is so complicated only a truly formidable superintelligence could resolve it?

Ever since it was first published, in 1859, Bernhard Riemann’s conjecture about prime numbers has made every list of the most important unsolved mysteries in mathematics. In 1900 mathematician David Hilbert drafted a list of problems to be solved as a blueprint for 20th-century math, and one of them was Riemann’s hypothesis. But at the end of that century the still-open question warranted another wanted poster. In 2000 the Clay Mathematics Institute promised a million-dollar bounty to anyone who solved the Riemann hypothesis, making it one of its seven “Millennium Problems”—the 21st century’s own aspirational to-do list.