What Are the Most Unique Proofs in Mathematics?

[redrzewski]

Life is short, and I know I can never experience all of mathematics. So I want to construct a plan to see as many of the unique proofs (across the various disciplines) as possible. (Independently, I'll also proceed to learn as much as possible in depth as well).

Reading Munkres' discussion of the Urysohn lemma today inspired this. For instance, techniques like Cantor's diagonalization, Godel's incompleteness proof, etc.

The "usefulness" of the result doesn't really matter. Just the cleverness/non-obviousness/insightfulness of the method of proof.

thanks

 

[Gib Z]

Umm...so what's your question? Personally I agree with you, mostly, but I don't see your question...

 

[redrzewski]

My question:

I'd like feedback from other's on what proofs they've encountered with unique/non-obvious techiques in the proof.

Once I have a good list of actual proofs that I should see, then I can construct (on my own) a plan to get the necessary background to at least comprehend the high points of the proof.

 

[StatusX]

I've only started reading about number theory, but so far I don't really like it because every proof is different. There don't seem to be big unifying concepts like there are in other fields, just one result after another, each with a different proof that seems to be pulled out of thin air. So maybe if you just want to see different kinds of proofs, go there. But again, I just started, and I'm guessing there's more to it than that.