The infinite we shall do right away. The finite may take a little longer.

Whatever is worth saying, can be stated in fifty words or less.

The mathematicians know a great deal about very little and the physicists very little about a great deal.

Knowing what is big and what is small is more important than being able to solve partial differential equations.

I am turned off when I see only formulas and symbols, and little text.

It is most important in creative science not to give up. If you are an optimist you will be willing to "try" more than if you are a pessimist.

Thoughts are steered in different ways.

It is still an unending source of surprise for me how a few scribbles on a blackboard or on a piece of paper can change the course of human affairs.

What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else.

One conversation centered on the ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue.

I'm an agnostic. Sometimes I muse deeply on the forces that are for me invisible. When I am almost close to the idea of God, I feel immediately estranged by the horrors of this world, which he seems to tolerate.

In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug.

Do not lose your faith. A mighty fortress is our mathematics. Mathematics will rise to the challenge, as it always has.

Very soon I discovered that if one gets a feeling for no more than a dozen other radiation and nuclear constants, one can imagine the subatomic world almost tangibly, and manipulate the picture dimensionally and qualitatively, before calculating more precise relationships.

It is not so much whether a theorem is useful that matters, but how elegant it is.

What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else. Roughly speaking, people know that it deals with numbers, figures, with relations, operations, and that its formal procedures involving axioms, proofs, lemmas, theorems have not changed since the time of Archimedes.

It was not so much that I was doing mathematics, but rather that mathematics had taken possession of me.

He [John von Neumann] had the invaluable faculty of being able to take the most difficult problem and separate it into its components, whereupon everything looked brlliantly simple.

Mathematics may be a way of developing physically, that is anatomically, new connections in the brain.

Sometimes I feel that a more rational explanation for all that has happened during my lifetime is that I am still only thirteen years old, reading Jules Verne or H. G. Wells, and have fallen asleep.

Ada came from Lwów. She was a very good looking girl who was studying mathematics at the University of Geneva. For a few years I had an off-and-on romance with her.

In its evolution from a more primitive nervous system, the brain, as an organ with ten or more billion neurons and many more connections between them must have changed and grown as a result of many accidents.

I am always amazed how much a certain facility with a special and apparently narrow technique can accomplish.

As a mathematician, von Neumann was quick, brilliant, efficient, and enormously broad in scientific interests beyond mathematics itself. He knew his technical abilities; his virtuosity in following complicated reasoning and his insights were supreme; yet he lacked absolute self confidence.

Thinking very hard about the same problem for several hours can produce a severe fatigue, close to a breakdown. I never really experienced a breakdown, but have felt "strange inside" two or three times during my life.

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