Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don’t look alike are really the same. That is one of their innermost Freudian motivations. In fact,...

Can I just say that I don’t care if two planes or trains or whatever take off from different locations at different times and travel at different speeds. I am not traffic control, so why...

[Regarding mathematics,] there are now few studies more generally recognized, for good reasons or bad, as profitable and praiseworthy. This may be true; indeed it is probable, since the sensational triumphs of Einstein, that stellar...

And what he meant was that maths wasn’t like life because in life there are no straightforward answers in the end

Oh, figures!’ answered Ned. ‘You can make figures do whatever you want.

Done any exciting sums lately?””I don’t just do sums,” Miles told her. “There’s much more to my life than that.””Is there?” Alicia asked, trying to sound interested.”Yes,” said Miles. “Sometimes I draw graphs.

Why don’t we want our children to learn to do mathematics? Is it that we don’t trust them, that we think it’s too hard? We seem to feel that they are capable of making arguments...

I’ll tell you once,and I’ll tell you again.There’s always a primebetween n and 2n.

Life is complex. It has real and imaginary parts.

As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of a useful course is to begin with arithmetic, and then not Euclid but algebra....

Hal Incandenza has an almost obsessive dislike for deLint, whom he tells Mario he sometimes cannot quite believe is even real, and tries to get to the side of, to see whether deLint has a...

There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it...

Everybody believes in the exponential law of errors: the experimenters, because they think it can be proved by mathematics; and the mathematicians, because they believe it has been established by observation.

Turing attended Wittgenstein’s lectures on the philosophy of mathematics in Cambridge in 1939 and disagreed strongly with a line of argument that Wittgenstein was pursuing which wanted to allow contradictions to exist in mathematical systems....

If there is anything that can bind the mind of man to this dreary exile of our earthly home and can reconcile us with our fate so that one can enjoy living,—then it is verily...