John von Neumann Quotes

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.

Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealization of common sense.

You don't learn algebra with your blessed soul. Can't you look at it with your clear simple wits?

Let's face it; by and large math is not easy, but that's what makes it so rewarding when you conquer a problem, and reach new heights of understanding.

I don't care much for equations myself. This is partly because it is difficult for me to write them down, but mainly because I don't have an intuitive feeling for equations.

If I can bring some light to bear on problems like that, I feel that people will be enlightened not only on the question but also on a way of approaching such questions.

I tried to fit it in with some previous broad conceptual understanding of some part of mathematics that would clarify the particular problem I was thinking about.

Maths should be more practical and more conceptual, but less mechanical.

The story of pi has been extensively told, no doubt because its history goes back to ancient times, but also because much of it can be grasped without a knowledge of advanced mathematics.

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.

Indeed, the most important part of engineering work-and also of other scientific work-is the determination of the method of attacking the problem, whatever it may be, whether an experimental investigation, or a theoretical calculation. ... It is by the choice of a suitable method of attack, that intricate problems are reduced to simple phenomena, and then easily solved.

I approach cooking from a science angle because I need to understand how things work. If I understand the egg, I can scramble it better. It's a simple as that.

The math helps you have better understanding and helps you have more creative ideas, but you can't replace the creative ideas

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.

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.

I consider that I understand an equation when I can predict the properties of its solutions, without actually solving it.

How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.

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.

It is always the case, with mathematics, that a little direct experience of thinking over things on your own can provide a much deeper understanding than merely reading about them.

Some people are aware of another sort of thinking which... leads to those simple ideas that are obvious only after they have been thought of... the term 'lateral thinking' has been coined to describe this orther sort of thinking; 'vertical thinking' is used to denote the conventional logical process.

How can you shorten the subject? That stern struggle with the multiplication table, for many people not yet ended in victory, how can you make it less? Square root, as obdurate as a hardwood stump in a pasturenothing but years of effort can extract it. You can't hurry the process. Or pass from arithmetic to algebra; you can't shoulder your way past quadratic equations or ripple through the binomial theorem. Instead, the other way; your feet are impeded in the tangled growth, your pace slackens, you sink and fall somewhere near the binomial theorem with the calculus in sight on the horizon.

The important thing to remember about mathematics is not to be frightened

A problem thoroughly understood is always fairly simple. Found your opinions on facts, not prejudices. We know too many things that are not true.

From somewhere, back in my youth, heard Prof say, 'Manuel, when faced with a problem you do not understand, do any part of it you do understand, then look at it again.' He had been teaching me something he himself did not understand very well—something in math—but had taught me something far more important, a basic principle.

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.