So any theorem that a human can prove is, ipso facto, utterly trivial. -- D Zeilberger, Opinion 36
A complex system that works is invariably found to have evolved from a simple system that worked. -- John Gall
Man muss immer umkehren. -- CGJ Jacobi
Everybody has plans until they get hit. -- M Tyson
Understanding is a poor substitute for convexity. -- NN Taleb, Antifragile
I would rather have today's algorithms on yesterday's computers than vice versa. -- Philippe Toint
u"gyeskedhet, nem fog a macska \ egyszerre kint s bent egeret -- J A, Eszme'let
An economist regarding mathematical research as a product and mathematicians as producers would note that it has a distinctive feature: one's customers are basically the same as one's competitors.
Seeing an astronomer using a telescope to observe a galaxy, no-one will confuse the telescope with the galaxy. Mathematics differs from science in that there is no clear distinction between the tools and the objects of study.
-- David Aldous
I think that it is a relatively good approximation to truth [] that mathematical ideas originate in empirics. [A]s a mathematical discipline travels far from its empirical source it becomes more and more purely aestheticizing, [t]here is a grave danger that the subject will develop along the line of least resistance, that the stream, so far from its source, will separate into a multitude of insignificant branches, and that the discipline will become a disorganized mass of details and complexities. [W]henever this stage is reached, the only remedy seems to me to be the rejuvenating return to the source: the re-injection of more or less directly empirical ideas.
-- John von Neumann
Then there is the other secret. There isn't any symbolism. The sea is the sea. The old man is an old man. The boy is a boy and the fish is a fish. The shark are all sharks no better and no worse.
-- Ernest Hemingway
In recent decades, many investigators published a great number of mathematical works. Whereas the classics of mathematics regarded the science of mathematics as an objective reflection of reality, many of the new investigators do not share this opinion.
-- A Karatsuba