Everyone knows that arithmetic is true: 2 + 2 = 4. But surprisingly, we don’t know why it’s true. By stepping outside the box of our usual way of thinking about numbers, my colleagues and I have ...

A year after he started his Ph.D. in mathematics at McGill University, Matt Bowen had a problem. “I took my qualifying exams and did absolutely horribly on them,” he said. Bowen was sure that his ...

AN excellent way to see one’s own country, or one’s own century, is to visit another. While I was making just such a mental pilgrimage to the eighth century, a recent interest in unconventional ...

The 30-year-old math sensation Peter Scholze is now one of the youngest Fields medalists for “the revolution that he launched in arithmetic geometry.” In the run-up to the presentation of the Fields ...

You may never have heard of modular arithmetic, but you use it every day without the slightest difficulty. In this system, numbers wrap around when they reach a certain size called the modulus; it is ...