"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is" - John von Neumann

“Young man, in mathematics you don't understand things. You just get used to them.” John von Neumann

"As a mathematical discipline travels far from its empirical source, or still more, if it is a second or third generation only indirectly inspired by ideas coming from "reality", it is beset with very grave dangers. It becomes more and more purely aestheticizing, more and more purely l’art pour l’art. This need not be bad, if the field is surrounded by correlated subjects, which still have closer empirical connections, or if the discipline is under the influence of men with an exceptionally well-developed taste. But there 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. In other words, at a great distance from its empirical source, or after much “abstract” inbreeding, a mathematical subject is in danger of degeneration." - John von Neumann

"We need heuristic reasoning when we construct a strict proof as we need scaffolding when we erect a building" - George Pólya

"To teach mathematics well, one must also know how to misunderstand it at least to the extent ones students do" - George Pólya

"Mathematics is not a spectator sport" - George Polya

"Mathematics requires a small dose, not of genius, but of an imaginative freedom which, in a larger dose, would be insanity. And if mathematicians tend to burn out early in their careers, it is probably because life has forced them to acquire too much common sense, thereby rendering them too sane to work. But by then they are sane enough to teach, so a use can still be found for them." - Angus K. Rodgers

"I was unable to find flaws in my "proof" for quite a while, even though the error is very obvious. It was a psychological problem, a blindness, an excitement, an inhibition of reasoning by an underlying fear of being wrong. Techniques leading to the abandonment of such inhibitions should be cultivated by every honest mathematician." - from How Not to Prove the Poincare Conjecture, by John Stallings

"In so far as theories of mathematics speak about reality, they are not certain, and in so far as they are certain, they do not speak about reality." - Albert Einstein

“If the transcendental is accessible to us only through the medium of images and symbols, let the symbols at least be as distinct and unambiguous as mathematics will permit.” - Hermann Weyl

"It is impossible to be a mathematician without being a poet in soul." - Sofia Kovalevskaya

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry." - Bertrand Russel

"A good stack of examples, as large as possible, is indispensable for a thorough understanding of any concept, and when I want to learn something new, I make it my first job to build one." - Paul Halmos

"Statisticians, like artists, have the bad habit of falling in love with their models." - George Box

"There are three kinds of lies: lies, damned lies, and statistics." - Benjamin Disraeli

"If you torture the data enough, nature will always confess." - Ronald Coase

"Statistical thinking will one day be as necessary a qualification for efficient citizenship as the ability to read and write." -H.G. Wells

"There are no routine statistical questions, only questionable statistical routines." - D.R. Cox

"The essence of mathematics lies precisely in its freedom." - Georg Cantor

"Once you have experienced flight in mathematical skies, you will forever walk the Earth with your eyes turned skyward, for there you have been, and there you will always long to return." - Bill Dubuque

"Mathematics is commonly explained and recorded in symbolic and concrete forms that are easy to communicate, rather than in conceptual forms that are easy to understand once communicated." - Bill Thurston

"Math is more than a language, it's a system of reasoning. The symbolic operations that transform equations is equivalent to constructing long chains of logical inference, building arguments too intricate to hold in our heads." - Strogatz

"Mathematicians are guided by the notion (an idea of an object that we wish to represent formally) but they work with the definition."  - Asaf Karagila

"A mathematician tries to ‘see through’ a complex system’s accidental complexity up to a simpler, more abstract, more true version which can be understood & manipulated - but for the hacker, all complexity is essential, and they are instead trying to unsee the simple abstract system down to the more complex less abstract (but also more true) version" - gwern

"The beauty of mathematics only shows itself to more patient followers." - Maryam Mirzakhani

“While the other sciences search for the rules that God has chosen for this Universe, we mathematicians search for the rules that even God has to obey.” - Jean-Pierre Serre