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

— How not to be wrong: the power of mathematical thinking by Jordan Ellenberg

Proving by day and disproving by night is not just for mathematics. I find it’s a good habit to put pressure on all your beliefs, social, political, scientific, and philosophical. Believe whatever you believe by day; but at night, argue against the propositions you hold most dear.

— How not to be wrong: the power of mathematical thinking by Jordan Ellenberg

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.”

— How not to be wrong: the power of mathematical thinking by Jordan Ellenberg

Gödel’s friends Albert Einstein and Oskar Morgenstern begged him to avoid this matter in his exam, but, as Morgenstern recalls it, the conversation ended up going like this: The examiner: Now, Mr. Gödel, where do you come from? Gödel: Where I come from? Austria. The examiner: What kind of government did you have in Austria? Gödel: It was a republic, but the constitution was such that it finally was changed into a dictatorship. The examiner: Oh! This is very bad. This could not happen in this country. Gödel: Oh, yes, I can prove it.

— How not to be wrong: the power of mathematical thinking by Jordan Ellenberg

“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.”

— How not to be wrong: the power of mathematical thinking by Jordan Ellenberg

I once met a historian of German culture in Columbus, Ohio, who told me that Hilbert’s predilection for wearing sandals with socks is the reason that fashion choice is still noticeably popular among mathematicians today. I could find no evidence this was actually true, but it suits me to believe it, and it gives a correct impression of the length of Hilbert’s shadow.

— How not to be wrong: the power of mathematical thinking by Jordan Ellenberg

If you never give advice until you’re sure it’s right, you’re not giving enough advice.

— How not to be wrong: the power of mathematical thinking by Jordan Ellenberg

“To my surprise, I found extremely well-written and cogent papers that might have become textbook classics for their impeccable logic and clear exposition of data and argument if only the authors had been on the right side.”

— How not to be wrong: the power of mathematical thinking by Jordan Ellenberg

Undecided voters, by and large, aren’t undecided because they’re carefully weighing the merits of each candidate, unprejudiced by political dogma. They’re undecided because they’re barely paying attention.

— How not to be wrong: the power of mathematical thinking by Jordan Ellenberg

if you’re down a million bucks, it’s your problem; but if you’re down five billion bucks, it’s the government’s problem.

— How not to be wrong: the power of mathematical thinking by Jordan Ellenberg

The desperate, newly sober White Flaggers are always encouraged to invoke and pay empty lip-service to slogans they don’t yet understand or believe—e.g. “Easy Does It!” and “Turn It Over!” and “One Day at a Time!” It’s called “Fake It Till You Make It,” itself an oft-invoked slogan. Everyone on a Commitment who gets up publicly to speak starts out saying he’s an alcoholic, says it whether he believes he is yet or not; then everybody up there says how Grateful he is to be sober today and how great it is to be Active and out on a Commitment with his Group, even if he’s not grateful or pleased about it at all. You’re encouraged to keep saying stuff like this until you start to believe it, just like if you ask somebody with serious sober time how long you’ll have to keep schlepping to all these goddamn meetings he’ll smile that infuriating smile and tell you just until you start to want to go to all these goddamn meetings.

— How not to be wrong: the power of mathematical thinking by Jordan Ellenberg