QED: Just what does it mean to prove something?

From The Economist:

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. Proving something was a matter of convincing one’s peers that it has indeed been shown—no more, and no less. The rhetorical flourish of a Latin epigram also has served to indicate that the notion of proof is well understood, and commonly agreed. But that notion is now in flux. The use of computers to prove mathematical theorems is forcing mathematicians to re-examine the foundations of their discipline.

More here.

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