Quotes from 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.

Cauchy was not interested in the needs of engineers. Cauchy was interested in the truth.

Public opinion doesn't exist. More precisely, it exists sometimes, concerning matters about which there's a clear majority view.

Knowing mathematics is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world. Math is a science of not being wrong about things, its techniques and habits hammered out by centuries of hard work and argument. With the tools of mathematics in hand, you can understand the world in a deeper, sounder, and more meaningful way.

There is real danger that, by strengthening our abilities to analyze some questions mathematically, we acquire a general confidence in our beliefs, which extends unjustifiably to those things we're still wrong about.

The paradox of education: what we most admire we put in a box and make dull.

Nobody ever looks in the mirror and says, "Let's face it, I'm smarter than Gauss." And yet, in the last hundred years, the joined effort of all these dummies-compared-to-Gauss has produced the greatest flowering of mathematical knowledge the world has ever seen.

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.

who spends himself in a worthy cause; who at the best knows in the end the triumph of high achievement, and who at the worst, if he fails, at least fails while daring greatly, so that his place shall never be with those cold and timid souls who neither know victory nor defeat.

Yes, the existence of human life is evidence for the existence of God; but it's much better evidence that our world was programmed by people much smarter than us.

We become like those pious people who, over time, accumulate a sense of their own virtuousness so powerful as to make them believe the bad things they do are virtuous too.

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.

One thing the American defense establishment has traditionally understood very well is that countries don't win wars just by being braver than the other side, or freer, or slightly preferred by God. The winners are usually the guys who get 5% fewer of their planes shot down, or use 5% less fuel, or get 5% more nutrition into their infantry at 95% of the cost.

You can explain it to a Congressman in six minutes and he can talk about it for six months.

The ultimate reason for teaching kids to write a proof is not that the world is full of proofs. It's that the world is full of non-proofs , and grown-ups need to know the difference. It's hard to settle for a non-proof once you've really familiarized yourself with the genuine article.

We tend to teach mathematics as a long list of rules.You learn them in order and you have to obey them, because if you don't obey them you get a C-.This is not mathematics. Mathematics is the study if things that come out a certain way because there is no other way they could possibly be.

If you've ever run an experiment, you know scientific truth doesn't pop out of the clouds blowing a flaming trumpet at you. Data is messy, and inference is hard.

He was unsweaty, undusty, and unbloody, but he was right. He was a critic who counted.

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.

Excellence doesn't persist; time passes, and mediocrity asserts itself.*

Mark Twain is good on this: "It takes a thousand men to invent a telegraph, or a steam engine, or a phonograph, or a telephone or any other important thing—and the last man gets the credit and we forget the others.

we're not actually people at all, but simulations running on an ultracomputer built by other people.

Nowadays, the Abrahamic argument—just look at everything, how could it all be so awesome if there weren't a designer behind it?—has been judged wanting, at least in most scientific circles. But then again, now we have microscopes and telescopes and computers. We are not restricted to gaping at the moon from our cribs. We have data, lots of data, and we have the tools to mess with it.

Mathematics, mostly, is a communal enterprise, each advance the product of a huge network of minds working toward a common purpose, even if we accord special honor to the person who places the last stone in the arch.