In recent days, multiple Erdős problems have been solved by GPT-5.2 Pro, with solutions accepted by Terence Tao. This is not a gimmick—it's a qualitative shift. Erdős problems lie at the core of additive combinatorics, extremal graph theory, and probabilistic methods—problems that resist brute force and demand structural insight.... Many have endured decades of expert scrutiny. Acceptance matters more than authorship. Tao doesn't rubber-stamp ideas; he rigorously tests logic, generality, and novelty. If a proof clears that hurdle, the system didn't merely recombine known lemmas—it explored a true mathematical search space. This means AI has crossed a threshold: from assisting mathematics to participating in it by proposing nontrivial arguments, uncovering hidden structures, and resolving problems humans value—without a predefined solution path. Importantly, this doesn't diminish human mathematicians. It reshapes the field's topology. Just as symbolic algebra systems amplified rather than replaced math, AI now seems poised to expand the frontier itself. If these claims hold, recent days may mark the lift-off for AI-driven science: not flashy demos, but quiet validation by the world's toughest referees. We should remain skeptical, careful, and precise—yet honest about the implications. Something fundamental may have changed. Here's a five-minute video with Terry explaining these problems and meeting the man himself:show more

Prof. Brian Keating

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