Curtis’s conjecture at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Curtis’s conjecture

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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If this game doesn't work on your computer, we can't help you. No Lean version yet. Some unformalized games could have issues!

expertly designed by an internal OpenAI model

Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	donuts, coffee cups	Levels:	1
Category:	Topology	Lean version:	not yet
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Curtis’s conjecture. Proves Curtis’s conjecture: the positive-degree mod-two stable Hurewicz image of the sphere is spanned by the images of the Hopf-invariant-one classes η, ν, σ and the Kervaire-invariant-one classes that exist.

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LEVEL 1 The Stable Hurewicz Image of the Sphere at Two

released 2026-09-25 | 1 theorem · 21 lemmas · 30 proofs · 16,733 words | PLAY LEVEL 1 » (pdf)

We prove Curtis's conjecture: in every positive degree, the mod-two stable Hurewicz image of the sphere is spanned by the images of η, ν, σ and the Kervaire-invariant-one classes that exist. Consequently, Eccles's conjecture holds for every sphere Sⁿ with n > 0.

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