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.