The Monster That Lurks

Not sure which I love more about this Numberphile offering... Tim Burness's step-by-step explanation of the "Monster Group" (with it's almost 200,000 dimensions) or John Conway's sheer astonishment that it exists at all:

15,000 Pages of Calculations...

Michael Aschbacher of Caltech will be receiving the $75,000 Rolf Schock Prize for his part, among dozens of mathematicians who contributed, in the solution to the largest mathematical proof EVUH(!) involving the "Classification Theorem of Finite Simple Groups" (also, simply and appropriately known as "The Enormous Theorem").
Read all about it:

http://www.newscientist.com/article/dn20893-prize-awarded-for-largest-mathematical-proof.html