Meet Jon Von Neumann :

Von Neumann's ability to instantaneously perform complex operations in his head stunned other mathematicians. Eugene Wigner wrote that, seeing von Neumann's mind at work, "one had the impression of a perfect instrument whose gears were machined to mesh accurately to a thousandth of an inch."

Paul Halmos states that "von Neumann's speed was awe-inspiring."

Israel Halperin said: "Keeping up with him was... impossible. The feeling was you were on a tricycle chasing a racing car." Edward Teller wrote that von Neumann effortlessly outdid anybody he ever met, and said "I never could keep up with him".

Lothar Wolfgang Nordheim described von Neumann as the "fastest mind I ever met", and Jacob Bronowski wrote "He was the cleverest man I ever knew, without exception.He was a genius."

George Pólya, whose lectures at ETH Zurich von Neumann attended as a student, said "Johnny was the only student I was ever afraid of. If in the course of a lecture I stated an unsolved problem, the chances were he'd come to me at the end of the lecture with the complete solution scribbled on a slip of paper."

Halmos recounts a story told by Nicholas Metropolis, concerning the speed of von Neumann's calculations, when somebody asked von Neumann to solve the famous fly puzzle:
Two bicyclists start twenty miles apart and head toward each other, each going at a steady rate of 10 mph. At the same time a fly that travels at a steady 15 mph starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner till he is crushed between the two front wheels. Question: what total distance did the fly cover? The slow way to find the answer is to calculate what distance the fly covers on the first, northbound, leg of the trip, then on the second, southbound, leg, then on the third, etc., etc., and, finally, to sum the infinite series so obtained. The quick way is to observe that the bicycles meet exactly one hour after their start, so that the fly had just an hour for his travels; the answer must therefore be 15 miles.

When the question was put to von Neumann, he solved it in an instant, and thereby disappointed the questioner: "Oh, you must have heard the trick before!" "What trick?" asked von Neumann, "All I did was sum the infinite series."

Von Neumann had a very strong eidetic memory, commonly called 'photographic' memory.Herman Goldstine writes: "One of his remarkable abilities was his power of absolute recall. As far as I could tell, von Neumann was able on once reading a book or article to quote it back verbatim; moreover, he could do it years later without hesitation. He could also translate it at no diminution in speed from its original language into English. On one occasion I tested his ability by asking him to tell me how The Tale of Two Cities started. Whereupon, without any pause, he immediately began to recite the first chapter and continued until asked to stop after about ten or fifteen minutes."

It has been said that von Neumann's intellect was absolutely unmatched. “I always thought Von Neumann’s brain indicated that he was from another species, an evolution beyond man,” said Nobel Laureate Hans A. Bethe of Cornell University. "It seems fair to say that if the influence of a scientist is interpreted broadly enough to include impact on fields beyond science proper, then John von Neumann was probably the most influential mathematician who ever lived," wrote Miklos Redai in "Selected Letters."

Glimm writes "he is regarded as one of the giants of modern mathematics".The mathematician Jean Dieudonné called von Neumann "the last of the great mathematicians", while Peter Lax described him as possessing the "most scintillating intellect of this century", and Hans Bethe stated "I have sometimes wondered whether a brain like von Neumann's does not indicate a species superior to that of man".