Stanisław Ulam Quotes

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

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.

Even the simplest calculation in the purest mathematics can have terrible consequences. Without the invention of the infinitesimal calculus most of our technology would have been impossible. Should we say therefore that calculus is bad?

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

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

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

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.

Thoughts are steered in different ways.

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...

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

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

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

As one sharpens a knife on a whetstone, the brain can be sharpened on dull objects of thought. Every form of assiduous thinking has its value.