Paul GrahamVerified account

Never underestimate how little history or math people understand. The latter isn't super dangerous except when they need to reason statistically, but the former accounts for a lot of people's strongest political opinions.

Most people never learn any real mathematics. The most important fact of which this leaves them ignorant is that even in a domain in which all terms are precisely defined one can (and indeed frequently does) err spectacularly without realizing it. Truth is exceedingly elusive.

Many of the greatest mathematicians of all time offered proofs of false statements of whose rigor they were quite convinced. The sources of error in their arguments were novel phenomena entirely beyond their ability to imagine. Exposing such phenomena often takes decades.