In 2010, a startling rumor filtered through the number theory community and reached Jared Weinstein. Apparently, some graduate student at the University of Bonn in Germany had written a paper that redid “Harris-Taylor”—a 288-page book dedicated to a single impenetrable proof in number theory—in only 37 pages. The 22-year-old student, Peter Scholze, had found a way to sidestep one of the most complicated parts of the proof, which deals with a sweeping connection between number theory and geometry.

“It was just so stunning for someone so young to have done something so revolutionary,” said Weinstein, a 34-year-old number theorist now at Boston University. “It was extremely humbling.”

Mathematicians at the University of Bonn, who made Scholze a full professor just two years later, were already aware of his extraordinary mathematical mind. After he posted his Harris-Taylor paper, experts in number theory and geometry started to notice Scholze too.

Since that time, Scholze, now 28, has risen to eminence in the broader mathematics community. Prize citations have called him “already one of the most influential mathematicians in the world” and “a rare talent which only emerges every few decades.” He is spoken of as a heavy favorite for the Fields Medal, one of the highest honors in mathematics.

Scholze’s key innovation—a class of fractal structures he calls perfectoid spaces—is only a few years old, but it already has far-reaching ramifications in the field of arithmetic geometry, where number theory and geometry come together. Scholze’s work has a prescient quality, Weinstein said. “He can see the developments before they even begin.”

Many mathematicians react to Scholze with “a mixture of awe and fear and exhilaration,” said Bhargav Bhatt, a mathematician at the University of Michigan who has written joint papers with Scholze.

That’s not because of his personality, which colleagues uniformly describe as grounded and generous. “He never makes you feel that he’s, well, somehow so far above you,” said Eugen Hellmann, Scholze’s colleague at the University of Bonn.

Instead, it’s because of his unnerving ability to see deep into the nature of mathematical phenomena. Unlike many mathematicians, he often starts not with a particular problem he wants to solve, but with some elusive concept that he wants to understand for its own sake. But then, said Ana Caraiani, a number theorist at Princeton University who has collaborated with Scholze, the structures he creates “turn out to have applications in a million other directions that weren’t predicted at the time, just because they were the right objects to think about.”

Scholze started teaching himself college-level mathematics at the age of 14, while attending Heinrich Hertz Gymnasium, a Berlin high school specializing in mathematics and science. At Heinrich Hertz, Scholze said, “you were not being an outsider if you were interested in mathematics.”

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*has no nonzero whole-number solutions if

^{n}*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.