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I had a professor who liked to talk about how "elementary" did not mean easy, it just means "uses only the foundations." This proof is a perfect example of tha
by tnecniv 10y ago
I had a professor who liked to talk about how "elementary" did not mean easy, it just means "uses only the foundations."
This proof is a perfect example of that statement. Formulating the problem the right way -- which is most often the hardest part -- was the real challenge here, not the mechanisms needed to do the formulation or the proof.
- huhtenberg 10y agoNot sure why, but this reminds me how we had a professor that would say Let y(x) = a*x^4 + b*x^3 + c*x^2 + d*x + e, whereby e is not _necessarily_ the base of natural logarithm
- cperciva 10y agoMy favourite along those lines was "let epsilon be a small number which is not necessarily greater than zero". Everybody who spent the preceding year on epsilon-delta proofs did a double-take at that.
- FabHK 10y agoThere's a wonderful book, by the way, Proofs from THE BOOK, of, well, simple beautiful proofs. The book is named after > mathematician Paul Erdős, who often referred to "The Book" in which God keeps the most elegant proof of each mathematical theorem. During a lecture in 1985, Erdős said, "You don't have to believe in God, but you should believe in The Book." https://en.wikipedia.org/wiki/Proofs_from_THE_BOOK https://en.wikipedia.org/wiki/Proofs_from_THE_BOOK