Proof and beauty

"Just what does it mean to prove something?"

Quod erat demonstrandum. These three words of Latin, meaning, "which was to be shown", traditionally mark the end of a mathematical proof. And, for centuries, a proof was exactly that: showing something by breaking it down into readily agreed-upon steps. ...

... However, if a computer is used to make this reduction, then the number of small, obvious steps can be in the hundreds of thousands-impractical even for the most diligent mathematician to check by hand.

The Economist, March 31, 2005
(via Arts & Letters Daily)