Geometrically the irrationality of the square root of 2 means that there is no integer-by-integer square whose area is twice the area of another integer-by-integer square. A visual proof that the square root of 2 is irrational (not found in previous visual proof post.)
posted by Obscure Reference on May 9, 2012 - 38 comments

A thread full of proofs without words at MathOverflow and quite a lot more of them courtesy of Google Books.
posted by Wolfdog on Jul 18, 2011 - 22 comments

New math theories reveal the nature of numbers [1,2] - "We prove that partition numbers are 'fractal' for every prime. These numbers, in a way we make precise, are self-similar in a shocking way. Our 'zooming' procedure resolves several open conjectures, and it will change how mathematicians study partitions." (/.|via) [more inside]
posted by kliuless on Jan 22, 2011 - 45 comments

Futurama has always been a haven for geek humor, but last week's episode "The Prisoner of Benda" pushed things to the next level. First hinted at in an American Physical Society interview with showrunner David X. Cohen (previously), staff writer and mathematics Ph.D. Ken Keeler devised a novel mathematical proof based on group theory to resolve the logic puzzle spawned by the episode's brain-swapping (but no backsies!) conceit. Curious how it works? Read the proof (in the show or in plain text), then see it in action using this handy chart. Too much math for a lazy Sunday? Then entertain your brain with lengthy clips from the episode -- including two of the funniest moments in the series in the span of two minutes.
posted by Rhaomi on Aug 22, 2010 - 130 comments

I am pleased to announce a proof that P is not equal to NP. In this paper, Vinay Deolalikar (HP Labs) proposes a proof to answer the most important problem in its field of mathematics. [more inside]
posted by knz on Aug 8, 2010 - 113 comments

Proofs and Pictures: The Role of Visualization in Mathematical and Scientific Reasoning [video] "The picture is a telescope for looking into Plato's heaven." -- James Brown [cached]
posted by Chuckles on Aug 20, 2006 - 27 comments

Nerdy proof that girls are evil.
posted by betobeto on May 18, 2001 - 13 comments