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