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Atiyah and Singer to Share the 2004 Abel Prize
sbar writes "The 2004 Abel prize-winners have been announced.From the website: 'The Atiyah-Singer index theorem is one of the great landmarks of twentieth century mathematics, influencing profoundly many of the most important later developments in topology, differential geometry and quantum field theory. Its authors, both jointly and individually, have been instrumental in repairing a rift between the worlds of pure mathematics and theoretical particle physics, initiating a cross-fertilization which has been one of the most exciting developments of the last decades.'"
First of all, I'm surprised to see this mentioned in this list. Not because it isn't an essential and relevant result, but because most people here simply don't have a clue about abstract mathematics.
As many people have experienced, studying the higher mathematics is incrediby rewarding, intellectually, especially the parts that have nothing to do with numbers (ie. most). Even if you don't get into the intricacies of stringent proofs of theorems, it is still a world of such incredible wonder. Are you fascinated by science fiction and fantasy? Then mathematics should be able to captivate you; personally I can't think of anything more mindblowing than such things as topology, geometry and algebra.
For all those not initiated to deeper mathematics, there's a simpler online proof that uses the heat equation instead to prove the Atiyah-Singer Index Theorem.
Of course, the first chapter alone is over 80 pages of functional analysis, but still...