John von Neumann Quotes

When I was in school, my favorite subject was math. I took algebra and calculus. At an early age I grasped it and understood it quickly. I just enjoyed breaking the codes and solving problems.

I'm really terrible at math, so I won't even attempt to do ratios and percentages, but all I know is that there's a lot of new songs that no-one has heard yet, and that there's a lot of old songs that some very, very super hardcore fans have heard for sure - there are people that have been coming and seeing me play in bars in like 2002, and there are songs that those people heard.

Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of constraint and freedom that is the very essence of human nature.

Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.

I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense.

Neumann, to a physicist seeking help with a difficult problem: Simple. This can be solved by using the method of characteristics. Physicist: I'm afraid I don't understand the method of characteristics. Neumann: In mathematics you don't understand things. You just get used to them.

Just as I had long suspected, a person didn't really need math for anything anyway. Maybe some people did. Some limited people.

Yes, but you need to learn your maths." "I don't need to, really. I already know how to count to a hundred. And I'm sure I'll never need ore than a hundred of anything.

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

Mathematics would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude.

By keenly confronting the enigmas that surround us, and by considering and analyzing the observations that I had made, I ended up in the domain of mathematics. Although I am absolutely without training in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists.

Geometry enlightlens the intellect and sets one's mind right

Mathematics is not merely an idle art form, it is an essential part of our society.

The study of mathematics is apt to commence in disappointment.

Mathematicians may flatter themselves that they possess new ideas which mere human language is as yet unable to express. Let them make the effort to express these ideas in appropriate words without the aid of symbols, and if they succeed they will not only lay us laymen under a lasting obligation, but, we venture to say, they will find themselves very much enlightened during the process, and will even be doubtful whether the ideas as expressed in symbols had ever quite found their way out of the equations into their minds.

Without mathematics, we are blind.

For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold.

I have often noticed that when people come to understand a mathematical proposition in some other way than that of the ordinary demonstration, they promptly say, "Oh, I see. That's how it must be." This is a sign that they explain it to themselves from within their own system.

The public does not need to be convinced that there is something in mathematics.

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.

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

There's math, and everything else is debatable!

It is shocking that young people should be addling their brains over mere logical subtleties in Euclid's Elements, trying to understand the proof of one obvious fact in terms of something equally .. obvious.

Mathematics as a science, commenced when first someone, probably a Greek, proved propositions about "any" things or about "some" things, without specifications of definite particular things.

The fools think I am writing algebra but what I am really writing is geometry.