AI cracks decades-old maths — OpenAI and DeepMind, days apart

On 20 May, OpenAI said a general reasoning model disproved the planar unit-distance conjecture (Erdős, 1946), using algebraic number theory rather than the long-assumed grid arrangement. The model established a super-linear lower bound — a result, not a retrieval. A day later, Google DeepMind posted that AlphaProof Nexus (Gemini 3.1 Pro + Lean) had solved nine open Erdős problems and 44 conjectures from the integer-sequence encyclopedia — two of the nine open for 56 years — at a few hundred dollars of compute each. Same testbed, different labs, different methods, one week apart.

DeepMind's results are verified step-by-step in the Lean proof assistant — the model proposes, the checker certifies, and a flawed step is simply rejected and fed back. That guards against AI's worst habit: sounding right while being wrong. OpenAI's construction was checked by mathematicians including Fields medallist Timothy Gowers, with formal peer review still to come — credible, but a softer guarantee. Same word, 'solved'; two different levels of proof, and the difference is the story.

What to watch. The durable result isn't any single proof — it's the generate-then-verify loop. If 'AI proposes, a formal checker certifies' spreads beyond maths to other places where claims can be machine-checked, that pipeline, not the nine problems, is the milestone that ages well.