47 Quotes by Jordan Ellenberg

Mathematicians can be persnickety about logical niceties. We’re the kind of people who think it’s funny, when asked, “Do you want soup or salad with that?” to reply, “Yes.

Mathematics is the extension of common sense by other means.

A reasonable person believes, in short, that each of his beliefs is true and that some of them are false.

A basic rule of mathematical life: if the universe hands you a hard problem, try to solve an easier one instead, and hope the simple version is close enough to the original problem that the universe doesn’t object.

If you do happen to find yourself partially believing a crazy theory, don’t worry – probably the evidence you encounter will be inconsistent with it, driving down your degree of belief in the craziness until your beliefs come into line with everyone else’s. Unless, that is, the crazy theory is designed to survive this winnowing process. That’s how conspiracy theories work.

It’s not wrong to say Hilbert was a genius. But it’s more right to say that what Hilbert accomplished was genius. Genius is a thing that happens, not a kind of person.

Math gives us a way of being unsure in a principled way: not just throwing up our hands and saying “huh,” but rather making a firm assertion: “I’m not sure, this is why I’m not sure, and this is roughly how not-sure I am.” Or even more: “I’m unsure, and you should be too.

Improbable things happen a lot.

Maybe individual people seem irrational because they aren’t really individuals! Each one of us is a little nation-state, doing our best to settle disputes and broker compromises between the squabbling voices that drive us.