On Life in General

A great offense starts with solid defense. — Steve Kerr, as a commentator inside the video game NBA Live 07

We are what we repeatedly do. Excellence, then, is not an act but a habit. — Will Durant in The Story of Philosophy

When pressure rises, you don’t rise up to the occasion but instead fall back to your best preparations. — Chris Voss in Never Split the Difference


On Mathematics

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. `Immortality’ may be a silly word, but probably a mathematician has the best chance of whatever it may mean. — G.H. Hardy in A Mathematician’s Apology

[Euclid’s proof that there are infinitely many prime numbers] is [demonstrated] by reductio ad absurdum, and reductio ad absurdum, which Euclid loved so much,  is one of a mathematician’s finest weapons. It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game. — G.H. Hardy in A Mathematician’s Apology

God made the integers, all the rest is work of man. — Leopold Kronecker

Don’t remember it. Know it. — Edward Perry, Department of Mathematics, University of Connecticut

Don’t just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis? — Paul Halmos

Understand it so well as if you might have discovered it yourself. — Donald Sheehy told me.

A good idea has a way of becoming simpler and solving problems other than
that for which it was intended. — Robert Endre Tarjan

The magic of mathematics and theoretical computer science is all the unexpected connections. You start looking for general principles and then mysterious connections emerge. — Robert Endre Tarjan

For us, there is no ignorabimus (Latin, meaning “we will not know”), and in my opinion none whatever in natural science. In opposition to the foolish ignorabimus our slogan shall be: Wir müssen wissen — wir werden wissen. (German, meaning “we must know – we will know.”) — David Hilbert


On Topics in Computer Science and Mathematics

We start with a simplified definition of a martingale. No assumptions are made about the independence or the precise distributions of the random variables in the definition. In fact, this is just the reason why martingales are so powerful!

… It may seem a bit surprising at first that such a sharp concentration result can be proved without even determining the expected value, but such is the power of martingale arguments. — Motwani and Raghavan, “Randomized Algorithms”, Section 4.4.


Makes You Think

[Wittgenstein] once greeted me with the question: ‘Why do people say that it was natural to think that the sun went round the earth rather than that the earth turned on its axis?

I replied: “I suppose, because it looked as if the sun went round the earth.”

“Well,” he asked, “what would it have looked like if it had looked as if the earth turned on its axis?” — G. E. M. Anscombe in “An Introduction to Wittgenstein’s Tractatus.”


A key turning point in my own career came after my oral qualifying exams, in which I very nearly failed due to my overconfidence and lack of preparation, particularly in my chosen specialty of harmonic analysis. After the exam, he (Elias Stein, Tao’s Ph.D. adviser) sat down with me and told me, as gently and diplomatically as possible, that my performance was a disappointment, and that I seriously needed to solidify my mathematical knowledge. This turned out to be exactly what I needed to hear; I got motivated to actually work properly so as not to disappoint my advisor again. — Terry Tao on his Ph.D. proposal oral exam


In 1922, Thomas Edison came to visit Steinmetz. By then, Edison was nearly deaf, and Steinmetz tapped out a message on Edison’s knee in Morse Code. Edison beamed, and the two continued their silent conversation in front of bewildered reporters.


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