Stefan Banach Quotes

Mathematicians may flatter themselves that they possess new ideas which mere human language is as yet unable to express.

It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress.

To me, mathematics, computer science, and the arts are insanely related. They're all creative expressions.

Dull minds are never either intuitive or mathematical.

Before he has seen the whole, how unusually perceptive and imaginative the person must be to evolve the entire sequence by meditating on its single, pair or triplet of essential images.

Creativity is just connecting things. When you ask creative people how they did something, they feel a little guilty because they didn't really do it, they just saw something. It seemed obvious to them after a while. That's because they were able to connect experiences they've had and synthesize new things.

The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law.

Mathematics is the art of giving the same name to different things.

One of the most amazing things about mathematics is the people who do math aren't usually interested in application, because mathematics itself is truly a beautiful art form. It's structures and patterns, and that's what we love, and that's what we get off on.

Artists realise that mathematicians have a way of looking at the world that can make them see things differently.

Mathematics are the result of mysterious powers which no one understands, and which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty's sake and pulls it down to earth.

The first type of abstraction from objects I shall refer to as simple abstraction, but the second type I shall call reflective abstraction, using this term in a double sense.

Prediction by analogy -creativity - is so pervasive we normally don't notice it.

One of the pleasures of looking at the world through mathematical eyes is that you can see certain patterns that would otherwise be hidden.

I guess I'm a very keen observer, and I'd like to think I have a good imagination.

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.

Imagination is a poor matter when it has to part company with understanding.

It is impossible to be a mathematician without being a poet in soul.

A lot of people think that persuasion is all about values and aligning values. I largely disagree. I think persuasion generally, and political persuasion more particularly, has much more to do with explaining in new ways and connecting dots in new ways than just invoking emotions and values.

The art of doing mathematics consists in finding that special case which contains all the germs of generality.

Pure mathematics is, in its way, the poetry of logical ideas.

Logicians may reason about abstractions. But the great mass of men must have images.

Mathematics seems to endow one with something like a new sense.

I listen to things that are popular and try to think about it in a mathematical way.

My dad is a mathematician; I think we both have that problem-solving, looking-for-patterns way of thinking.