4 ms·
Haven't read the article. But something about this reminds me of Arnold's topological proof of the unsolvability of the quintic (YouTube form: https://www.youtu
by ogogmad 2y ago
Haven't read the article. But something about this reminds me of Arnold's topological proof of the unsolvability of the quintic (YouTube form: https://www.youtube.com/watch?v=BSHv9Elk1MU https://www.youtube.com/watch?v=BSHv9Elk1MU ; PDF: https://web.williams.edu/Mathematics/lg5/394/ArnoldQuintic.pdf https://web.williams.edu/Mathematics/lg5/394/ArnoldQuintic.p...).
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 2y agoThanks 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 2y agoSperner 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.