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It seems a lot of impossibility theorems - the type that the ancient Greeks would have understood - can be proven using algebraic topology. Perhaps Sperner's lemma can be seen as an algebraic topology theorem? I don't personally know.

PollardsRho•3h ago

Thanks for sharing this proof! As someone who enjoys math but never got myself through enough Galois theory to finish the standard proof, it's fantastic to see a proof that's more elementary while still giving a sense of why the group structure is important.

xyzzyz•47m ago

Sperner lemma is very much an algebraic topology theorem. The ideas involved in it form the basis for the theory of simplicial homology, which in turn will lead you to general homology and cohomology theories.

bobmcnamara•2h ago

Taaaake it to the limit: N=∞, area=0, job done

akoboldfrying•1h ago

> To show that detM is non-zero, we can show that its 2-adic valuation is nonzero.

I think the last word in that sentence should be "finite"?

Also do I understand correctly that "face" means "maximal line segment"? (I see some other comments discussing this and concluding that "face" means "edge", but to me, an "edge" doesn't permit "intermediate" vertices.)