Henri Poincare Quotes

... 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.

Nonmathematical people sometimes ask me, “You know math, huh? Tell me something I’ve always wondered, What is infinity divided by infinity?” I can only reply, “The words you just uttered do not make sense. That was not a mathematical sentence. You spoke of ‘infinity’ as if it were a number. It’s not. You may as well ask, 'What is truth divided by beauty?’ I have no clue. I only know how to divide numbers. ‘Infinity,’ ‘truth,’ ‘beauty’—those are not numbers.

Odd numbers are masculine while the even numbers are feminine.

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...?

By an object, I mean anything that we can think, i.e. anything we can talk about.

The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. ... Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.

Imaginary numbers are a fine and wonderful refuge of the divine spirit almost an amphibian between being and non-being.

To be an abstraction does not mean that an entity is nothing. It merely means that its existence is only a factor of a more concrete element of nature.

Just as the introduction of the irrational numbers ... is a convenient myth [which] simplifies the laws of arithmetic ... so physical objects are postulated entities which round out and simplify our account of the flux of existence... The conceptional scheme of physical objects is [likewise] a convenient myth, simpler than the literal truth and yet containing that literal truth as a scattered part.

I believe that numbers and functions of Analysis are not the arbitrary result of our minds; I think that they exist outside of us, with the same character of necessity as the things of objective reality, and we meet them or discover them, and study them, as do the physicists, the chemists and the zoologists.

"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?"

If equations are trains threading the landscape of numbers, then no train stops at pi.

The method of differences is, in fact, a method of additions; and as it includes within its means a larger number of results attainable by addition simply, than any other mathematical principle, it was very appropriately selected as the basis on which to construct an Adding Machine, so as to give to the powers of such a machine the widest possible range.

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.

What I assert and believe to have demonstrated in this and earlier works is that following the finite there is a transfinite (which one could also call the supra-finite), that is an unbounded ascending lader of definite modes, which by their nature are not finite but infinite, but which just like the finite can be determined by well-defined and distinguishable numbers.

Just because something is a metaphor doesn't mean it can't be real.

The mathematical phenomenon always develops out of simple arithmetic, so useful in everyday life, out of numbers, those weapons of the gods: the gods are there, behind the wall, at play with numbers.

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

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

Numbers are the product of counting. Quantities are the product of measurement. This means that numbers can conceivably be accurate because there is a discontinuity between each integer and the next. Between two and three there is a jump. In the case of quantity, there is no such jump; and because jump is missing in the world of quantity, it is impossible for any quantity to be exact. You can have exactly three tomatoes. You can never have exactly three gallons of water. Always quantity is approximate.

The network told me to get rid of Number One, the woman first lieutenant, and also get rid of 'that Martian fellow'... meaning, of course, Spock. I knew I couldn't keep both, so I gave the stoicism of the female officer to Spock, and married the actress who played Number One. Thank God it wasn't the other way around. I mean Leonard's cute, but...

The real truth is, the number of convicts is too overwhelming for the means of proper and effectual punishment. I despair of any remedy but that which I wish I could hope for - a great reduction in the amount of crime.

Mathematics is a body of knowledge, but it contains no truths.

I have tried, with little success, to get some of my friends to understand my amazement that the abstraction of integers for counting is both possible and useful. Is it not remarkable that 6 sheep plus 7 sheep makes 13 sheep; that 6 stones plus 7 stones make 13 stones? Is it not a miracle that the universe is so constructed that such a simple abstraction as a number is possible? To me this is one of the strongest examples of the unreasonable effectiveness of mathematics. Indeed, I find it both strange and unexplainable.

WikiLeaks does not publish from the jurisdiction of Ecuador, from this embassy or in the territory of Ecuador; we publish from France, we publish from, from Germany, we publish from The Netherlands and from a number of other countries, so that the attempted squeeze on WikiLeaks is through my refugee status; and this is, this is really intolerable. [It means] that [they] are trying to get at a publishing organisation; [they] try and prevent it from publishing true information that is of intense interest to the American people and others about an election.