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 ...

Think about placing dots on a flat surface. You want as many pairs as possible to be separated by the same distance. For any amount of dots, what is the greatest possible number of pairs that can be ...

Place any number of dots on a two-dimensional plane—say, a piece of paper—and measure the distance between each pair. If you rearrange the dots, how many pairs could be positioned exactly the same ...

Last week, OpenAI shocked the mathematical community by revealing that one of its internal artificial intelligence (AI) models had found a counterexample to a famous conjecture made by legendary ...