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.
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. Through much of the 20th
century, questions of mathematical rigour were passed off to
logicians and philosophers—working mathematicians have been, for
the most part, content to work with an intuitive definition of
proof. This notion works when each step of a proof is
transparent, and can be examined b