Heide

An LLM came up with a novel solution to the Erdős unit distance problem. It was unsolved for 80 years.

"And, on May 20, OpenAI shared a solution to the unit distance problem, along with a blog post explaining the work and a companion paper that featured nine world-class mathematicians commenting on the correctness of the proof and the importance of what had been done (as well as presenting a streamlined human version of the result). Mathematicians had generally believed that Erdős’ conjecture — about how many evenly spaced points can be placed on a plane — was correct. To general surprise, OpenAI’s internal model found a counterexample. To do so, it had found a sophisticated way to use tools from an area of math called algebraic number theory. As Jacob Tsimerman of the University of Toronto wrote in the companion article, “This is a really impressive piece of work. … It is definitely an intimidating construction.”

The destruction code: 4321

“Well, the code definitely isn’t 4321”