Terence Tao Quotes

In no other branch of mathematics is it so easy for experts to blunder as in probability theory.

In abstract mathematics, of course operations alter those particular relations which are involved in the considerations of number and space, and the results of operations are those peculiar results which correspond to the nature of the subjects of operation.

Number, place, and combination . . . the three intersecting but distinct spheres of thought to which all mathematical ideas admit of being referred.

I still think in a parallel universe, I became a mathematician.

I've debated many economists who claim to specialize in risk and probability: when one takes them slightly outside their narrow focus, but within the discipline of probability, they fall apart, with the disconsolate face of a gym rat in front of a gangster hit man.

You have this world of mathematics, which is very real and which contains all kinds of wonderful stuff. And then we also have the world of nature, which is real, too.

Skill is a function of chance. It’s an intuitive best-use of chance situations.

If the prior distribution, at which I am frankly guessing, has little or no effect on the result, then why bother; and if it has a large effect, then since I do not know what I am doing how would I dare act on the conclusions drawn?

It is almost as hard to define mathematics as it is to define economics, and one is tempted to fall back on the famous old definition attributed to Jacob Viner, "Economics is what economists do," and say that mathematics is what mathematicians do. A large part of mathematics deals with the formal relations of quantities or numbers.

Only Numbers. Pure math. You have to accustom yourself to thinking that way.

While we can prove that almost all numbers in the continuum are random, we cannot prove that any specific number is indeed random.

Random chance is not sufficient to explain random chance. ~Jubal Harshaw

One may say that mathematics talks about the things which are of no concern to men. Mathematics has the inhuman quality of starlight - brilliant, sharp but cold ... thus we are clearest where knowledge matters least: in mathematics, especially number theory.

I am fully assured, that no general method for the solution of questions in the theory of probabilities can be established which does not explicitly recognize, not only the special numerical bases of the science, but also those universal laws of thought which are the basis of all reasoning, and which, whatever they may be as to their essence, are at least mathematical as to their form.

This branch of mathematics [Probability] is the only one, I believe, in which good writers frequently get results which are entirely erroneous.

I failed math twice, never fully grasping probability theory. I mean, first off, who cares if you pick a black ball or a white ball out of the bag? And second, if you’re bent over about the color, don’t leave it to chance. Look in the damn bag and pick the color you want.

Essentially, there's a universe inside your brain. The number of connections possible inside your brain is limitless. And as people have learned to have more managerial and direct creative access to their brains, they have also developed matrices or networks of people that communicate electronically. There are direct brain/computer link-ups. You can just jack yourself in and pilot your brain around in cyberspace-electronic space.

If one puts an infinite number of monkeys in front of typewriters, and lets them clap away, there is a certainty that one of them will come out with an exact version of the 'Iliad.'

The physicist who states a law of nature with the aid of a mathematical formula is abstracting a real feature of a real material world, even if he has to speak of numbers, vectors, tensors, state-functions, or whatever to make the abstraction.

There is no such thing as luck; there is only adequate or inadequate preparation to cope with a statistical universe.

Number is the Word but is not utterance it is wave and light, though no one sees it it is rhythm and music, though no one hears it. Its variations are limitless and yet it is immutable. Each form of life is a particular reverberation of Number.

The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.

Number theorists are like lotus-eaters -- having once tasted of this food they can never give it up.

"Nought usually comes at the beginning," Ralph said. "Not necessarily," said Sibyl. "It might come anywhere. Nought isn't a number at all. It's the opposite of number." Nancy looked up from the cards. "Got you, aunt," she said. "What about ten? Nought's a number there - it's part of ten." "Well, if you say that any mathematical arrangement of one and nought really makes ten - " Sibyl smiled. "Can it possibly be more than a way of representing ten?"