Quotes from Jordan Ellenberg

Nonlinear thinking means which way you should go depends on where you already are. This insight isn't new.

Often people think of developments in computation as arising when we make our computers more blazingly fast, so they can compute more stuff , bigger data . It's actually just as important to prune away big parts of the data that aren't relevant to the problem at hand! The fastest computation is the one you don't do.

It comes back to his math-trained habits of thought. A mathematician is always asking, "What assumptions are you making?

Improbability, as described here, is a relative notion, not an absolute one; when we say an outcome is improbable, we are always saying, explicitly or not, that it is improbable under some set of hypotheses we've made about the underlying mechanisms of the world.

Improbability, as described here, is a relative notion, not an absolute one; when we say an outcome is improbable, we are always saying, explicitly or not, that it is improbable under some set of hypotheses we've made about the underling mechanisms of the world.

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.

Geometry is the cilantro of math.

Math is a science of not being wrong about things,

Usually, when someone announces they're a "nonlinear thinker" they're about to apologize for losing something you lent them.

Virahanka sequence,

numerically flavored advice.

the crazy theory is designed to survive this winnowing process. That's how conspiracy theories work.

All mathematical writing is creative writing.

smaller populations are inherently more variable.

You can do linear regression without thinking about whether the phenomenon you're modeling is actually close to linear. But you shouldn't.

Math is a science of not being wrong about things, its techniques and habits hammered out by centuries of hard work and argument.

The lessons of mathematics are simple ones and there are no numbers in them: that there is structure in the world; that we can hope to understand some of it and not just gape at what our senses present to us; that our intuition is stronger with a formal exoskeleton than without one. And that mathematical certainity is one thing, the softer convictions we find attached to us in everyday life another, and we should keep track of the difference if we can.

In the British statistician R. A. Fisher's famous formulation, "the 'one chance in a million' will undoubtedly occur, with no less and no more than its appropriate frequency, however surprised we may be that it should occur to us.

if your government isn't wasteful, you're spending too much time fighting government waste.

Inference is a hard thing, maybe the hardest thing. From the shape of the clouds and the way they move we struggle to go backward, to solve for x, the system that made them.

if you want an honest view of what's going on, you also have to consider the planes that didn't come back.

Risky strategies can be analyzed numerically; uncertain strategies, Ellsberg suggested, were beyond the bounds of formal mathematical analysis

Revised Sherlock Holmes quote) 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.

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. That's not the stuff war movies are made of, but it's the stuff wars are made of. And there's math every step of the way. —