Quotes from Jordan Ellenberg

Data is messy, and inference is hard.

The significance test is the detective, not the judge.

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.

if we now feel comfortable rejecting the conclusions of the Witztum study, what does that say about the reliability of our standard statistical tests?

scientists and statisticians have already been worrying about them for quite some time.

probabilities of uncertain events can be mathematically described and manipulated—but are in fact not obvious at all. If they were, they would not have arrived so late in the history of human thought.

Mathematics is not just a sequence of computations to be carried out by rote until your patience or stamina runs out—although it might seem that way from what you've been taught in courses called mathematics.

the mathematical approach is a formalized version of our natural mental reckonings, an extension of common sense by other means.

What is best in mathematics deserves not merely to be learnt as a task, but to be assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement." —BERTRAND RUSSELL, "The Study of Mathematics" (1902)

That's the dirty little secret of advanced geometry. It may sound impressive that we can do geometry in ten dimensions (or a hundred, or a million...), but the mental pictures we keep in our mind are two-or at most three-dimensional. That's all our brains can handle. Fortunately, this impoverished vision is usually enough.

Democracy is a mess—but it kind of works.

Aristotle observes that eating either too much or too little is troubling to the constitution.

impossible to walk across the street,

When you're trying to draw reliable inferences from improbable events, wiggle room is the enemy.

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.

I came into the Big Money making pictures during World War II," [Reagan] would always say. At that time the wartime income surtax hit 90 percent. "You could only make four pictures and then you were in the top bracket," he would continue. "So we all quit working after about four pictures and went off to the country." High tax rates caused less work. Low tax rates caused more. His experience proved it. These

Frederick Mosteller, who would later found Harvard's statistics department, was there. So was Leonard Jimmie Savage, the pioneer of decision theory and great advocate of the field that came to be called Bayesian statistics.* Norbert Wiener, the MIT mathematician and the creator of cybernetics, dropped by from time to time. This was a group where Milton Friedman, the future Nobelist in economics, was often the

The human body is an immensely complex system, and there are only a few of its features we can measure, let alone manipulate. Based on the correlations we can observe, there are lots of drugs that might plausibly have a desired health effect. And so you try them out in experiments, and most of them fail dismally. To work in drug development requires a resilient psyche, not to mention a vast pool of capital.

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

the interesting thing about the slime mold is that it makes pretty good decisions.

it is probable that improbable things will happen. Granted this, one might argue that what is improbable is probable.

a group of MIT undergrads won millions of dollars by understanding the guts of the Massachusetts state lottery.

not every curve is a line.

There is a proper measure in things. There are, finally, certain boundaries short of and beyond which what is right cannot exist").