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 ...

Some mathematical statements feel undeniably true the moment you hear them. Yet proving them can be impossible. This theorem has convinced generations of mathematicians without ever yielding a formal ...

Since the start of the 20th century, the heart of mathematics has been the proof — a rigorous, logical argument for whether a given statement is true or false. Mathematicians’ careers are measured by ...

A mathematician will turn a groundbreaking 100-page proof into computer code. The proof tool, Lean, lets users turn proofs written in prose into rules and logic for testing. Kevin Buzzard already uses ...

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 ...

Turbulence is one of the least understood phenomena of the physical world. Long considered too hard to understand and predict mathematically, turbulence is the reason the Navier-Stokes equations, ...