An Erdős Conjecture Falls & The Compute Squeeze Tightens - AI Week in Review (May 17-23, 2026)

AI proves new math

The Erdős announcement came in two parts. First OpenAI's internal team published the result, with detailed accompanying material on the reasoning approach. Then external mathematicians went through the steps and confirmed the proof is genuine — meaning every transition between propositions is rigorously justified, no skipped cases, no unstated assumptions. The conjecture is in the category sometimes called 'concrete but hard': about distances between points in the plane, the kind of problem that admits no shortcut and resists most known techniques. What makes the result interesting isn't just that AI did math. AI has been doing math for a while, with humans either prompting or verifying. What's different here is that the reasoning model generated the proof end-to-end in a form mathematicians can check at the level of individual steps. That's the threshold where the answer to 'is AI doing real research' stops being a debate. It landed in a week with other quieter signals about how these models actually learn. A new paper from researchers at multiple institutions argued that, with enough compute, the best data-quality filter for pretraining may be no filter at all — that careful curation has been quietly destroying signal at scale. Separately, researchers reported a phenomenon called mode-hopping during pretraining: models abruptly switching between shallow heuristics and actual reasoning, complicating which checkpoints to ship. A Goodfire paper this week argued that sparse autoencoders — the dominant tool for mechanistic interpretability — often capture features in a 'dilution' regime where individual neurons represent fractional concepts, and proposed clustering them to recover the underlying manifold structure. On the efficiency side, Nous Research introduced Lighthouse Attention to attack long-context KV-cache costs, and a DeepMind and Seoul National University collaboration released LiteFrame, a compact video encoder that meaningfully extends long-form video understanding. Taken together: the engineering of these models is moving faster than the science describing them. The Erdős proof is the public moment. The data-filter and interpretability papers are the underground signals that suggest the public moments are about to get more frequent.