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.

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.

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.

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

Thoughts are steered in different ways.

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.

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.

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.

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

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

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.

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.

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.

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

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

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.

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

In mathematics, as in physics, so much depends on chance, on a propitious moment.

... there's nothing new under the sun - everything can be traced back to Archimedes or even earlier.

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.

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.

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