On Theorems I (Unsourced)

“To state a theorem and then to show examples of it is literally to teach backwards." (E. Kim Nebeuts)

"Young men should prove theorems, old men should write books." (Godfrey H Hardy)

“We often hear that mathematics consists mainly of proving theorems. Is a writer's job mainly that of writing sentences?" (Gian-Carlo Rota)

“The product of mathematics is clarity and understanding. Not theorems, by themselves.” (Bill Thurston)

"Old theorems never die; they turn into definitions." (Edwin Hewitt)

“[…] a serious mathematical theorem, a theorem which connects significant ideas, is likely to lead to important advances in mathematics itself and even in other sciences." (Godfrey H Hardy)

“I compare arithmetic with a tree that unfolds upwards in a multitude of techniques and theorems while the root drives into the depths.” (Friedrich L G Frege)

“Ah, there’s no excitement to beat the excitement of proving a theorem! Until you find out the next day that it’s wrong.” (Cathleen S Morawetz)

“It always seems to me absurd to speak of a complete proof, or of a theorem being rigorously demonstrated. An incomplete proof is no proof, and a mathematical truth not rigorously demonstrated is not demonstrated at all.” (James J Sylvester)

“I think that science may be styled the knowledge of universals, or abstract wisdom; and art is science reduced to practice - or science is reason, and art the mechanism of it - and may be called practical science. Science, in fine, is the theorem, and art the problem.” (Laurence Sterne)