At 16, Scholze learned that a decade earlier Andrew Wiles had proved the famous 17th-century problem known as Fermat’s Last Theorem, which says that the equation x^n + y^n = z^n has no nonzero whole-number solutions if n is greater than two. Scholze was eager to study the proof, but quickly discovered that despite the problem’s simplicity, its solution uses some of the most cutting-edge mathematics around. I understood nothing, but it was really fascinating, he said.

So Scholze worked backward, figuring out what he needed to learn to make sense of the proof. To this day, that’s to a large extent how I learn, he said. I never really learned the basic things like linear algebra, actually — I only assimilated it through learning some other stuff.