OpenAI confirmed that its new reasoning model has solved a geometric problem posed by Paul Erdős in 1946. The challenge, known as the Erdős distance problem, had resisted mathematicians for decades. The solution came by applying patterns not based on traditional grids, an approach that no one had thoroughly explored.
How AI Broke the Mold of Classical Geometry 🧠
OpenAI's model analyzed geometric configurations that avoided the grid structure, previously considered the basis for optimal solutions. Through reinforcement learning and non-linear pattern search, the AI identified a point arrangement that maximizes minimum distances. The result not only solves the problem but also provides a verifiable demonstration, something human mathematicians failed to achieve in nearly a century.
Erdős Turns in His Grave (and Asks for a GPU) 🤖
The most curious thing is that Erdős, famous for solving problems with other humans, now receives help from a machine. The Hungarian mathematician used to ask for coffee and amphetamines to work; today he would need access to cloud servers. Meanwhile, living mathematicians debate whether this is an achievement or a sign that they should have played more Minecraft to train their spatial intuition.