QED

A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between analogies.
Stefan Banach

It is my experience that proofs involving matrices can be shortened by 50% if one throws the matrices out.
Emil Artin, Geometric Algebra, p. 14 (1957)

If a ‘religion’ is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one.
John D. Barrow, The Artful Universe Expanded, p. 250 (2005)

Hans Riesel held a Mersenne record for 14 days in the 50’s, calculated using the first Swedish computer. My old highschool computing teacher had worked as a student on the system and had managed to crush his foot when a byte fell out of its rack and onto him.
Anders Sandberg
Bron: Eliezer Yudkowsky

Mathematics is the science of patterns, and nature exploits just about every pattern that there is.
Ian Stewart, Nature’s Numbers: The Unreal Reality of Mathematical Imagination, p. 18 (1995)

The purpose of computation is insight, not numbers.
Richard Hamming, epigraaf in Numerical Methods for Scientists and Engineers (1962)

When I give this talk to a physics audience, I remove the quotes from my ‘Theorem’.
Brian Greene, in een lezing voor de Joint Mathematics Meetings, Washington DC (19 januari 2000)

Lemmas do the work in mathematics: Theorems, like management, just take the credit.
Paul Taylor, Practical Foundations of Mathematics, p. 192 (1999)

Les mathématiciens n’étudient pas des objets, mais des relations entre les objets ; il leur est donc indifférent de remplacer ces objets par d’autres, pourvu que les relations ne changent pas. La matière ne leur importe pas, la forme seule les intéresse.
Henri Poincaré, La science et l’hypothèse (1902)

Whenever I want to learn a new subject, I announce a graduate course in it, since the best way to learn is by teaching. But even better than teaching humans is teaching computers, i.e. program! Since computers will not let you wave your hands and wing it.
Doron Zeilberger, Opinion 37: Guess What? Programming is Even [...]