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Artificial intelligence is mastering the kinds of projects that have long helped to build the careers of young mathematicians. What does that mean for their future? Credit...Illustrations by Yoshi ...

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 ...

In mid-May, OpenAI announced that an internal AI model had disproved the Erdős unit distance conjecture, a famous problem in discrete geometry that had stumped human mathematicians for the last 80 ...

“If you are a mathematician,” one of the world’s leading mathematicians recently wrote, “you may want to make sure you are sitting down before reading further.” And you’ll definitely need to sit down ...

It started almost by accident. At my startup Dwelly, I constantly push the limits of what AI tools can actually do. One day I just typed into a chat: “Can you prove P ≠ NP?”—referring to the problem ...

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 ...

Is America heading toward a national debt crisis? As an economic adviser to President Biden and an economist active in mainly Democratic policy circles since the late 1980s, I’ve spent most of my ...

This package contains a certified proof artifact for a pointwise lower bound in the planar unit-distance problem. It uses Sawin's number-field construction and a prime-ideal microselection ...

For nearly 80 years, mathematicians have struggled to solve a classic geometry puzzle first posed by Paul Erdős in 1946: the planar unit distance problem. The question posed by the legendary Hungarian ...