In his 1801 magnum opus Disquisitiones Arithmeticae, German mathematician Carl Friedrich Gauss wrote about a cyclical mystery ...

Every summer, I teach an introductory machine learning course in an international summer program. This year, the class ...

OpenAI revealed Astra, its next major model, by publishing ten proofs of problems open for a decade or more. The total ...

AI will likely transform how research in the field is conducted. But it would be premature to conclude that it can solve ...

Alpöge’s discovery is the latest in a string of high-profile mathematical breakthroughs made by large language models. Recent examples include OpenAI’s disproof of the unit distance conjecture, and ...

We teach obsolete rote math that adults don't use, while missing entirely the math that defines our lives.   Let's start with the math sequence followed by kids in Cambridge and across America: ...

On July 20, 2026, OpenAI disclosed that the same internal model it credited in May with disproving the Erdős unit distance conjecture had, during limited internal deployment, repeatedly found ways to ...

This game is end to end! UPDATE: Solution is here Today’s offering is for fans of the number 4. It’s a cute puzzle that offers up its solution in an elegant way. Nose to tail There is a number N ...

Earlier today I set this elegant number puzzle. Here it is again with a solution. Nose to tail There is a number N beginning with 4 such that moving the 4 to the end of it creates a new number that is ...

Mathematician Will Sawin discusses his experience reviewing and refining a mathematical proof devised by OpenAI's internal model—and what that could mean for mathematics. Reading time 10 minutes Will ...

Artificial intelligence can now solve open research-level mathematics problems — not just competition questions — and the May 2026 issue of Science News documents the moment the field registered that ...