How Not To Be Wrong: The Hidden Maths of Everyday

by Jordan Ellenberg

In Scalia’s view, when judges try to understand what the law intends—its spirit—they’re inevitably bamboozled by their own prejudices and desires. Better to stick to the words of the Constitution and the statutes, treating them as axioms from which judgments can be derived by something like logical deduction.

Judges and justices are servants of the law, not the other way around. Judges are like umpires. Umpires don’t make the rules; they apply them. The role of an umpire and a judge is critical. They make sure everybody plays by the rules. But it is a limited role. Nobody ever went to a ball game to see the umpire.

Sometimes it takes Pascal’s route: if reason does not determine the judgment, make the judgment that seems to have the best consequences.

“A scientist can hardly encounter anything more undesirable than, just as a work is completed, to have its foundation give way.”

The typical working mathematician is a Platonist on weekdays and a formalist on Sundays.”

But the ability to work hard—to keep one’s whole attention and energy focused on a problem, systematically turning it over and over and pushing at everything that looks like a crack, despite the lack of outward signs of progress—is not a skill everybody has. Psychologists nowadays call it “grit,” and it’s impossible to do math without it.

that there’s always somebody ahead of you, whether they’re right there in class with you or not.

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.”

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

It is not the critic who counts; not the man who points out how the strong man stumbles, or where the doer of deeds could have done them better. The credit belongs to the man who is actually in the arena, whose face is marred by dust and sweat and blood; who strives valiantly; who errs, who comes short again and again, because there is no effort without error and shortcoming; but who does actually strive to do the deeds; who knows great enthusiasms, the great devotions; 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.

“The closet philosopher, the refined and cultured individual who from his library tells how men ought to be governed under ideal conditions, is of no use in actual governmental work,”

For this is action, this not being sure!

Sitting on a fence is a man who swings from poll to poll Sitting on a fence is a man who sees both sides of both sides. … But the real problem with this man Is he says he can’t when he can

As the philosopher W. O. V. Quine put it, “To believe something is to believe that it is true; therefore a reasonable person believes each of his beliefs to be true; yet experience has taught him to expect that some of his beliefs, he knows not which, will turn out to be false. A reasonable person believes, in short, that each of his beliefs is true and that some of them are false.”

The difference between judges and mathematicians is that judges have to find a way to pretend we know, while mathematicians are free to tell the truth.

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.”

drop one tiny contradiction anywhere into a formal system and the whole thing goes to hell. Philosophers of a mathematical bent call this brittleness in formal logic ex falso quodlibet, or, among friends, “the principle of explosion.”

As F. Scott Fitzgerald said, “The test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function.”

For if you have really understood what’s keeping you from disproving the theorem, you very likely understand, in a way inaccessible to you before, why the theorem is true.

Samuel Beckett later put it more succinctly: “I can’t go on, I’ll go on.”

Ever tried. Ever failed. No matter. Try again. Fail again. Fail better.

Roosevelt’s view that analytic “book-learning” stands in opposition to virility is expressed more directly by Shakespeare, who in the opening scene of Othello has Iago derisively call his rival Cassio “a great arithmetician … That never set a squadron in a field / Nor the division of a battle knows / more than a spinster.”

“These then were some hazards of the course / Yet though we knew the course was hazards and nothing else”: