Quotes from Jordan Ellenberg

I think we need more math majors who don't become mathematicians. More math major doctors, more math major high school teachers, more math major CEOs, more math major senators. But we won't get there unless we dump the stereotype that math is only worthwhile for kid geniuses.

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.

Knowing mathematics is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world.

Improbable things happen a lot.

Working an integral or performing a linear regression is something a computer can do quite effectively. Understanding whether the result makes sense—or deciding whether the method is the right one to use in the first place—requires a guiding human hand. When we teach mathematics we are supposed to be explaining how to be that guide. A math course that fails to do so is essentially training the student to be a very slow, buggy version of Microsoft Excel.

A mathematician is always asking, "What assumptions are you making? And are they justified?

Dividing one number by another is mere computation ; knowing what to divide by what is mathematics.

if gambling is exciting, you're doing it wrong.

Genius is a thing that happens, not a kind of person.

Nonlinear thinking means which way you should go depends on where you already are.

Mathematics is the extension of common sense by other means.

It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth, unless the truth is a hypothesis it didn't occur to you to consider.

A math teacher's least favorite thing to hear from a student is "I get the concept, but I couldn't do the problems." Though the student doesn't know it, this is shorthand for "I don't get the concept.

The Pythagoreans, you have to remember, were extremely weird. Their philosophy was a chunky stew of things we'd now call mathematics, things we'd now call religion, and things we'd now call mental illness.

One of the great joys of mathematics is the incontrovertible feeling that you've understood something the right way, all the way down to the bottom; it's a feeling I haven't experienced in any other sphere of mental life. And when you know how to do something the right way, it's hard-for some stubborn people, impossible-to make yourself explain it the wrong way.

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

Math, like meditation, puts you in direct contact with the universe, which is bigger than you, was here before you, and will be here after you.

Safety warning: never divide by zero unless a licensed mathematician is present.

Before the work of Georg Cantor in the nineteenth century, the study of the infinite was as much theology as science; now, we understand Cantor's theory of multiple infinities, each one infinitely larger than the last, well enough to teach it to first-year math majors. (To be fair, it does kind of blow their minds.)

When you reason correctly, as Silver does, you find that you always think you're right, but you don't think you're always right.

In the Bayesian framework, how much you believe something after you see the evidence depends not just on what the evidence shows, but on how much you believed it to begin with.

It's not like that, as we've seen. Mathematicians aren't crazy, and we aren't aliens, and we aren't mystics. What's true is that the sensation of mathematical understanding-of suddenly knowing what's going on, with total certainty, all the way to the bottom-is a special thing, attainable in few if any other places in life. You feel you've reached into the universe's guts and put your hand on the wire. It's hard to describe to people who haven't experienced it.

you never miss the plane, you're spending too much time in airports.

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.