Stanisław Ulam

1909–1984 · Polish-American mathematician

Topics: mathematics, learning, simplicity, creativity

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

  — Stanisław Ulam

• 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.

  — Stanisław Ulam

• It is still an unending source of surprise for me to see how a few scribbles on a blackboard or on a sheet of paper could change the course of human affairs.

  — Stanisław Ulam

• 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.

  — Stanisław Ulam

• 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.

  — Stanisław Ulam

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

  — Stanisław Ulam

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

  — Stanisław Ulam

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

  — Stanisław Ulam

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

  — Stanisław Ulam

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

  — Stanisław Ulam

• 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?

  — Stanisław Ulam

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

  — Stanisław Ulam

• 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.

  — Stanisław Ulam

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

  — Stanisław Ulam

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

  — Stanisław Ulam

• 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.

  — Stanisław Ulam