You enter a cave. At the end of a dark corridor, you encounter a pair of sealed chambers. Inside each chamber is an all-knowing wizard. The prophecy says that with these oracles’ help, you can learn ...

If pure math can teach us anything, it’s this: occasionally, your special interest might just change the world. For Joshua Zahl and Hong Wang, that special interest was the Kakeya conjecture. “I read ...

Dmitri Krioukov, a UC San Diego physicist, was recently given a ticket for running a stop sign. He went to court to argue the ticket, armed with a scientific paper that mathematically demonstrated ...

Peter Scholze wants to rebuild much of modern mathematics, starting from one of its cornerstones. Now, he has received validation for a proof at the heart of his quest from an unlikely source: a ...

The Langlands program has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore One of the biggest stories in science has been ...

The same branch of mathematics that helped Einstein to formulate his theory of general relativity could now allow scientists to peer with unprecedented accuracy into impenetrable objects—such as the ...

The decades-old Sullivan’s conjecture, about the best way to minimize the surface area of a bubble cluster, was thought to be out of reach for three bubbles and up — until a new breakthrough result.

Marijn Heule turns mathematical statements into something like Sudoku puzzles, then has computers go to work on them. His proofs have been called “disgusting,” but they go beyond what any human can do ...

Despite multiple conferences dedicated to explicating Mochizuki’s proof, number theorists have struggled to come to grips with its underlying ideas. His series of papers, which total more than 500 ...