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The total subject of mathematics is clearly too broad for any of us. i do not think that any mathematician since gauss has covered it uniformly and fully; even hilbert did not and all of us are of considerably lesser width quite apart from the question of depth than hilbert.
-John Von Neumann
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The Total Subject Of Mathematics Is Clearly

John Von Neumann
The total subject of mathematics is clearly too broad for any of us. i do not think that any mathematician since gauss has covered it uniformly and fully; even hilbert did not and all of us are of considerably lesser width quite apart from the question of depth than hilbert.
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Thinking Depth Mathematics

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When the world is mad, a mathematician may find in mathematics an incomparable anodyne. for mathematics is, of all the arts and sciences, the most austere and the most remote, and a mathematician should be of all men the one who can most easily take refuge where, as bertrand russell says, "one at least of our nobler impulses can best escape from the dreary exile of the actual world."
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It is a melancholy experience for a professional mathematician to find himself writing about mathematics. the function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done. statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. exposition, criticism, appreciation, is work for second-rate minds.
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Srinivasa ramanujan was the strangest man in all of mathematics, probably in the entire history of science. he has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33, like riemann before him. working in total isolation from the main currents of his field, he was able to rederive 100 years' worth of western mathematics on his own. the tragedy of his life is that much of his work was wasted rediscovering known mathematics.
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Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. appearances suggest the contrary, but there are easy explanations. music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity
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Everything that comes together falls apart. everything. the chair i’m sitting on. it was built, and so it will fall apart. i’m gonna fall apart, probably before this chair. and you’re gonna fall apart. the cells and organs and systems that make you you—they came together, grew together, and so must fall apart. the buddha knew one thing science didn’t prove for millennia after his death: entropy increases. things fall apart.
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No mathematician should ever allow him to forget that mathematics, more than any other art or science, is a young man's game. ... galois died at twenty-one, abel at twenty-seven, ramanujan at thirty-three, riemann at forty. there have been men who have done great work later; ... [but] i do not know of a single instance of a major mathematical advance initiated by a man past fifty. ... a mathematician may still be competent enough at sixty, but it is useless to expect him to have original ideas.
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