Recently, in math class, I learnt about the four colour theorem. Our teacher described it as quite an "ugly" proof, and I can see why. However, in the history of mathematics, this proof is quite recent, and so if this is one of the oldest "ugly" proofs, then would it be safe to say we will probably have an elegant way to prove it eventually? My question is: what is the oldest "ugly" proof? Also, is there a way of proving that something can't have an elegant proof?
2026-04-08 09:03:11.1775638991
Oldest "Ugly" Proof
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The proof of the existence of only five platonic solids is ugly, and very old:
https://en.wikipedia.org/wiki/Platonic_solid#Geometric_proof
It seems that a problem with many constrainst leads often to enumeration, and that's ugly.