Brian Hayes in American Scientist:
Here is how proof is supposed to work, as illustrated by an anecdote in John Aubrey’s Brief Lives about the 17th century philosopher Thomas Hobbes:
He was 40 yeares old before he looked on geometry; which happened accidentally. Being in a gentleman’s library in…, Euclid’s Elements lay open, and ’twas the 47 El. libri I. He read the proposition. “By G—,” sayd he (he would now and then sweare, by way of emphasis), “this is impossible!” So he reads the demonstration of it, which referred him back to such a proposition; which proposition he read. That referred him back to another, which he also read. Et sic deinceps, that at last he was demonstratively convinced of that trueth. This made him in love with geometry.
What’s most remarkable about this tale—whether or not there’s any trueth in it—is the way Hobbes is persuaded against his own will. He starts out incredulous, but he can’t resist the force of deductive logic. From proposition 47 (which happens to be the Pythagorean theorem), he is swept backward through the book, from conclusions to their premises and eventually to axioms. Though he searches for a flaw, each step of the argument compels assent. This is the power of pure reason.
For many of us, the first exposure to mathematical proof—typically in a geometry class—is rather different from Hobbes’s middle-age epiphany.