An OpenAI model solved a famous math problem that stumped humans for 80 years

That might not last. AI systems have been improving at math so rapidly that it’s unclear what role, if any, human mathematicians will play a decade from now. Paul Erdős was one of the most prolific mathematicians in history. He wrote over 1,500 papers in his lifetime, the most ever. One of his greatest talents was coming up with problems that are simple to state but have deep roots. In 1946, he introduced the unit distance problem . Imagine you have some points in a 2D plane and you measure the distance between each pair of points: Credit: Kai Williams / Understanding AI Credit: Kai Williams / Understanding AI In this diagram, there are five points and ten pairs of points. Three pairs happen to be exactly 1 unit apart: AD, BE, and CE. Can we rearrange the points so that more pairs of points are exactly 1 unit apart? Yes. For instance, we could move points A and D to be closer to the B, C, and E cluster. With a bit more work, we could further rearrange the points so that there are seven pairs exactly one unit apart. But that’s the most we can do. We could do the same analysis with 6 points, 7 points, and so on. But as the number of points grows, the problem very quickly becomes too complicated to find the exact answer. The arrangements of 5, 6, 7, 8, and 9 points that have the most pairs of points exactly one unit apart. Figure from the appendix of “The Erdős unit distance problem for small point sets” by Boris Alexeev, Dustin G. …