# Accessible proofs of contemporary results in mathematics

Are there strong results in contemporary mathematical research (last 20 years) which have a proof which every mathematician (holding a PhD) can completely understand within a few days? -- If yes, please give examples. If not, please explain the phenomenon.

• There are some pretty weak PhDs out there, so on those grounds the answer is "no". But if you mean "a good mathematician who is not an expert", then I would say "yes". – Igor Rivin Nov 7 '13 at 13:33
• – Waldemar Nov 7 '13 at 13:41
• Already 3 votes to close ? I think this is an interesting soft question, and not an exact duplicate of the question 129759 : there is a difference between a proof understandable by an undergraduate, and a proof understandable by most active mathematicians. The former supposes a low-level proof (in the sense of not using any sophisticated notion: no manifolds, no Lie Groups, no representations, no complex analysis, etc.) which will be in general, as a matter of compensation, quite technical. Here the OP is asking for nice theorems outside of my field that I could understand quickly... – Joël Nov 7 '13 at 14:44
• Another problem is that it is not clear to me what a "strong result" is. – Deane Yang Nov 7 '13 at 14:45
• Igor, I'm curious about what results you have in mind. – Deane Yang Nov 7 '13 at 14:47

My favorite from the last few years is the proof by Hugo Duminil-Copin and Stanislav Smirnov that the connective constant of the honeycomb lattice is $\sqrt{2+\sqrt{2}}$: http://arxiv.org/abs/1007.0575