The Oracle of Arithmetic Works Best Without Writing Down a Thing

In 2010, a startling rumor filtered through the number theory community and reached Jared Weinstein. Quanta Magazine Original story reprinted with permission from Quanta Magazine, an editorially independent division of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences “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. 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. 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.” Learning Arithmetic Nyani Quarmyne for Quanta Magazine 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 xn + yn = zn has no nonzero whole-number solutions if n is greater than two.