Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946.
For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids.
An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better.
This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.
Terence Tao is answering a fundamental question regarding the safety and reliability of modern AI: "How can we use a tool that is powerful, but unreliable?"
W = ∑(wᵢ ⋅ xᵢ) + b
AI isn’t just about “smart”; it’s about the probability of *looking* right. We’ve built systems where the weights (wᵢ) are optimized for plausibility, not veracity.
This creates a “convincing mirror” that confidently serves dangerous advice in medicine or finance. The gap between “convincing” and “correct” is the most critical variable we need to solve for.