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

Stanislaw Ulam

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Stanislaw Ulam
Age: 75 †
Born: 1909
Born: April 13
Died: 1984
Died: May 13
Mathematician
Lemberg
Austria
Stanislaw Ulam
Stanisław Marcin Ulam
Bigs
Able
Important
Differential
Partial
Equations
Solve
Small
Knowing

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What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics it is always something else.
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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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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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Thoughts are steered in different ways.
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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.
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Rota's personality is compatible with mine.
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Mathematics may be a way of developing physically, that is anatomically, new connections in the brain.
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... there's nothing new under the sun - everything can be traced back to Archimedes or even earlier.
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In mathematics, as in physics, so much depends on chance, on a propitious moment.
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There may be such a thing as habitual luck. People who are said to be lucky at cards probably have certain hidden talents for those games in which skill plays a role. It is like hidden parameters in physics, this ability that does not surface and that I like to call habitual luck.
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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.
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It is not so much whether a theorem is useful that matters, but how elegant it is.
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I am always amazed how much a certain facility with a special and apparently narrow technique can accomplish.
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With sixty professors there are roughly eighteen hundred pairs of professors. Out of that many pairs it was not surprising that there were some whose members did not like one another.
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Thanks to my memory, which enabled me to quote Latin and to discuss Greek and Roman civilization, it became obvious to some of my colleagues in other fields that I was interested in things outside mathematics. This lead quickly to very pleasant relationships.
Stanislaw Ulam
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The mathematicians know a great deal about very little and the physicists very little about a great deal.
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Do not lose your faith. A mighty fortress is our mathematics. Mathematics will rise to the challenge, as it always has.
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By an incredible coincidence, Gamow and Edward Condon, who had discovered simultaneously and independently the explanation of radioactivity (one in Russia, the other in this country), came to spend the the last ten years of their lives within a hundred yards of each other in Boulder.
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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.
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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.
Stanislaw Ulam