Dividing one number by another is mere computation; figuring out what you should divide by what is mathematics.

The lesson about inference: you have to be careful about the universe of theories you consider. Just as there may be more than one solution to a quadratic equation, there may be multiple theories that give rise to the same observation, and if we don’t consider them all, our inferences may lead us badly astray.

You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won’t believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one

(most famously, the Oxford philosopher Nick Bostrom

Math is a science of not being wrong about things, its techniques and habits hammered out by centuries of hard work and argument.

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

false linearity

To paraphrase Clausewitz: Mathematics is the extension of common sense by other means.

the ‘one chance in a million’ will undoubtedly occur, with no less and no more than its appropriate frequency, however surprised we may be that it should occur to us.”