As a mathematician, von ...

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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 Stanislaw Ulam

Quotes from the same author

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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 Stanislaw Ulam
Knowing what is big and what is small is more important than being able to solve partial differential equations.
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 Stanislaw Ulam
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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 Stanislaw Ulam
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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 Stanislaw Ulam
I am always amazed how much a certain facility with a special and apparently narrow technique can accomplish.
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 Stanislaw Ulam