Kevin Hartnett

Every four years, the math world’s preeminent awards are given to the finest minds of a generation. The young winners — all under 40 on the first day of the year — have reshaped mathematics and theoretical computer science. Here are their stories.

Determination and effort propelled Jacob Tsimerman to the top of the math world. But now that he’s won a Fields Medal, he worries that the field is in jeopardy.

With automated proof-checkers, a problem can be broken up into small chunks, solved bit-by-bit, then reassembled with confidence that every piece is correct. For some, this heralds a new area in mathematical research.

Do we need quantum computers to fully understand complex chemical reactions? A new result, decades in the making, shows the surprising power of ordinary “classical” machines.

The amplituhedron, a shape at the heart of particle physics, appears to be deeply connected to the mathematics of paper folding.

After finding the homeschooling life confining, the teen petitioned her way into a graduate class at Berkeley, where she ended up disproving a 40-year-old conjecture.

A simple, widely used mathematical technique can finally be applied to boundlessly complex problems.

In 1940 André Weil wrote a letter to his sister, Simone, outlining his vision for translating between three distinct areas of mathematics. Eighty years later, it still animates many of the most exciting developments in the field.

This past October, dozens of mathematicians gathered in Pasadena to create the third version of “Kirby’s list” — a compendium of the most important unsolved problems in the field.