[cperciva]

You just need to understand the language.

"Trivial" = "regularly covered in undergraduate courses"

"Easy" = "a good topic for an undergraduate honour's thesis"

"Non-trivial" = "a good PhD thesis topic"

"Distinctly non-trivial" = "a groundbreaking result which will establish a professor's reputation in the field"

[tnecniv]

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]

Not 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]

My 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]

There'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

[MaysonL]

And of course, those change over time.

I had an undergraduate course my freshman year where we went through a circular proof of the equivalence of twelve or thirteen formulations of the axiom of choice. A hundred years ago, proving many of the steps of that proof might well have been non-trivial, perhaps even distinctly so.

[sacheendra]

This made my day!