A problem formulated in 1946 by mathematician Paul Erdős has been solved by an OpenAI artificial intelligence. The question, known as the unit distance problem, asked how many pairs of points can be at distance 1 when placing n points on a plane. For over eight decades, mathematicians used grids and numbers with many divisors, but only achieved limited progress, with an upper bound barely greater than n.
The AI approach to solving the conjecture 🤖
OpenAI's AI tackled the problem by analyzing geometric configurations not based on square grids. Instead of rescaling with divisible numbers, it explored random distributions and symmetry patterns. The system generated sets of points where the number of pairs at distance 1 exceeded human bounds. The results indicate that the upper bound is n multiplied by a constant, a breakthrough mathematicians failed to achieve in 80 years. The AI validated its findings with automated tests.
Meanwhile, mathematicians kept using their grids 📐
Mathematicians spent 80 years drawing little squares and recounting divisors, like someone looking for keys under a lamppost because that's where the light is. The AI, without biases or coffee breaks, came along and said: why not try something else. And it worked. Now humans can feel proud: they created a tool that solves in hours what they couldn't in decades. Of course, next time someone asks how it was done, the answer will be: I don't know, ask the machine.