Quotes from Jordan Ellenberg

It's not always wrong to be wrong.

In 1931, Kurt Godel proved in his famous second incompleteness theorem that there could be no finitary proof of the consistency of arithmetic. He had killed Hilbert's program with a single stroke. So should you be worried that all of mathematics might collapse tomorrow afternoon? For what it's worth, I'm not. I do believe in infinite sets, and I find the proofs of consistency that use infinite sets to be convincing enough to let me sleep at night.

Don't talk about percentages of numbers when the numbers might be negative.

0.33333. . . . .= 1/3. Multiply both sides by 3 and you'll see 0.99999. . . .= 3/3= 1.

Big Data isn't magic, and it doesn't tell the feds who's a terrorist and who's not. But it doesn't have to be magic to generate long lists of people who are in some ways red-flagged, elevated-risk, "people of interest." Most of the people on those lists will have nothing to do with terrorism. How confident are you that you're not one of them?

You can't write a sonnet if you have to look up the spelling of each word as you go.

Mathematics is common sense.

if he fails, at least fails while daring greatly,

The master group theorist John Conway, upon encountering the lattice in 1968, worked out all its symmetries in a twelve-hour spree of computation on a single giant roll of paper. These symmetries ended up forming some of the final pieces of the general theory of finite symmetry groups that preoccupied algebraists for much of the twentieth century.

People often complain that no one likes facts and numbers and reason and science anymore, but as someone who talks about those things in public, I can tell you that's not true. People love numbers, and are impressed by them, sometimes more than they should be.

To do mathematics is to be, at once, touched by fire and bound by reason.

irrational behavior is as unacceptable to a certain species of economist as the irrational magnitude of the hypotenuse was to the Pythagoreans. It doesn't fit their model of what can be; and yet it is.

In modern terms we would say that the more strongly correlated the measurements, the less information, in Shannon's precise sense, a Bertillon card conveys.

When we say that there's a 5% chance that RED is true, we are making a statement not about the global distribution of biased roulette wheels (how could we know?) but rather about our own mental state. Five percent is the degree to which we believe that a roulette wheel we encounter is weighed toward the red.

But it didn't really happen in the space of a footstep, Poincare explains. That moment of inspiration is the product of weeks of work, both conscious and unconscious, which somehow prepare the mind to make the necessary connection of ideas. Sitting around waiting for inspiration leads to failure, no matter how much of a whiz kid you are.

For one thing, we're doing publishing wrong.

What Secrist's findings really show is that businesses are much more like the cities in Wisconsin. Superior management and business insight play a role, but so does plain luck, in equal measure.

Between Jeans and Pearson comes a notice from one John Butler Burke, who believed he had observed spontaneous generation of microscopic life in a vat of beef bouillon by exposure to the recently discovered element radium.

Why is the second novel by a breakout debut writer, or the second album by an explosively popular band, so seldom as good as the first? It's not, Or not entirely, because most artists only have one thing to say. It's because artistic success is an amalgam of talent and fortune, like everything else in life, and thus subject to regression to the mean.

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 of things that come out a certain way because there is no other way they could possibly be.

If you decide what color jelly beans to eat based just on the papers that get published, you're making the same mistake the army made when they counted the bullet holes on the planes that came back from Germany.

They're running the con on themselves.

Assessing the scale of the p-hacking problem is not so easy—

That's how the Law of Large Numbers works: not by balancing out what's already happened, but by diluting what's already happened with new data, until the past is so proportionally negligible that it can safely be forgotten.