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“There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn’t say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann.”
― George Pólya

“The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.”
― George Pólya, Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving, Volume I

“The seriousness of a theorem, of course, does not lie in its consequences, which are merely the evidence for its seriousness.”
― G.H. Hardy, A Mathematician's Apology

“It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.”
― Mark Kac, Statistical Independence in Probability, Analysis, and Number Theory

“I carried this problem around in my head basically the whole time. I would wake up with it first thing in the morning, I would be thinking about it all day, and I would be thinking about it when I went to sleep. Without distraction I would have the same thing going round and round in my mind.

(Recalling the degree of focus and determination that eventually yielded the proof of Fermat's Last Theorem.)”
― Andrew John Wiles

“One may characterize physics as the doctrine of the repeatable, be it a succession in time or the co-existence in space. The validity of physical theorems is founded on this repeatability.”
― Friedrich Hund

“The beauty of a mathematical theorem depends a great deal on its seriousness, as even in poetry the beauty of a line may depend to some extent on the significance of the ideas which it contains.”
― G.H. Hardy, A Mathematician's Apology

“There are no proofs. There are only agreements”
― Paul W. Silver

“This skipping is another important point. It should be done whenever a proof seems too hard or whenever a theorem or a whole paragraph does not appeal to the reader. In most cases he will be able to go on and later he may return to the parts which he skipped.”
― Emil Artin

“It was not a friendly picture, but to Conway, as he surveyed, there came a queer perception of fineness in it, of something that had no romantic appeal at all, but a steely, almost an intellectual quality. The white pyramid in the distance compelled the mind's assent as passionlessly as a Euclidean theorem, and when at last the sun rose into a sky of deep delphinium blue, he felt only a little less than comfortable again.”
― James Hilton, Lost Horizon

“Ronald, remember our deal? Keep feeding me the children. You'll stay rich while I stay full.”
― A.K. Kuykendall

“A theory, a theorem and a hypothesis walk into a bar, but leave as soon as the bartender asks them for proofs.”
― Rajesh`