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Congratulations to the @HarmonicMath Aristotle team for a spectacular result at the IMO. It's a masterclass in formal proof and problem-solving. ​This marks the AI's coronation as the champion of the known mathematical world. ​But the ultimate benchmark isn't an Olympiad champion; it's a giant who builds new worlds, like Grothendieck. ​The fundamental question this raises: How could a system optimized for finding proofs within a framework make a Grothendieckian Gesture—i.e., invent the concept of 'schemes' by reframing geometry in the language of commutative algebra, a move that was radically outside its conceptual training data? ​Solving problems is one thing. Building the universes where problems dissolve is another.
Replying to @HarmonicMath
Aristotle: IMO Level Automated Theorem Proving - arxiv.org/abs/2510.01346
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