Mathematical Philosophy Quotes

Odd numbers are masculine while the even numbers are feminine.

How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?

If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper.

God made integers, all else is the work of man.

The Good Lord made all the integers; the rest is man's doing.

I don’t believe in statistics. I believe in calculus.

A geometry implies the heterogeneity of locus, namely that there is a locus of the Other. Regarding this locus of the Other, of one sex as Other, as absolute Other, what does the most recent development in topology allow us to posit?

I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.

For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?

And what are these fluxions? The velocities of evanescent increments. And what are these same evanescent increments? They are neither finite quantities, nor quantities infinitely small, nor yet nothing. May we not call them the ghosts of departed quantities...?

We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.

We come now to the question: what is a priori certain or necessary, respectively in geometry (doctrine of space) or its foundations? Formerly we thought everything; nowadays we think nothing. Already the distance-concept is logically arbitrary; there need be no things that correspond to it, even approximately.

Geometry is knowledge that appears to be produced by human beings, yet whose meaning is totally independent of them.

We have heard much about the poetry of mathematics, but very little of it has as yet been sung. The ancients had a juster notion of their poetic value than we. The most distinct and beautiful statements of any truth must take at last the mathematical form. We might so simplify the rules of moral philosophy, as well as of arithmetic, that one formula would express them both.

I have presented principles of philosophy that are not, however, philosophical but strictly mathematical-that is, those on which the study of philosophy can be based. These principles are the laws and conditions of motions and of forces, which especially relate to philosophy.

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect. . . Geometry should be ranked, not with arithmetic, which is purely aprioristic, but with mechanics.

Some mathematician, I believe, has said that true pleasure lies not in the discovery of truth, but in the search for it.

"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?"

... numbers have neither substance, nor meaning, nor qualities. They are nothing but marks, and all that is in them we have put into them by the simple rule of straight succession.

I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply the notes of our observations.

The pretence that numbers are not the humble creation of man, but are the exacting language of the Universe and therefore possess the secret of all things, is comforting, terrifying and mesmeric.

We have overcome the notion that mathematical truths have an existence independent and apart from our own minds. It is even strange to us that such a notion could ever have existed.

Algebra is the metaphysics of arithmetic.

Philip Kitcher thinks that mathematics is surprisingly like empirical science. Few mathematicians would agree; philosophers too, from Socrates on, have held the opposite opinion.