705 Quotes About Mathematics

Instead of concentrating just on finding good answers to questions, it's more important to learn how to find good questions!

The impulse to all movement and all form is given by [the golden ratio], since it is the proportion that summarizes in itself the additive and the geometric, or logarithmic, series.

Daniel Bernoulli: "Then this distinguished scholar informed me that the celebrated mathematician, Cramer, had developed a theory on the same subject several years before I produced my paper. Indeed I have found his theory so similar to mine that it seems miraculous that we independently reached sch close agreement on this sort of subject.

Mathematics consists in proving the most obvious thing in the least obvious way.

Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room and it's dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly, it's all illuminated and you can see exactly where you were. Then you enter the next dark room...

Abstraction is the cost of generalization.

Mathemata mathematicis scribuntur.

A mathematician tells you that the wall of warped space prevents the Moon from flying out of its orbit yet can't tell you why an astronaut can go back and forth across that same space.

[...] a decade as notable for its supreme faith in human rationality as for its dark anxieties about mankind’s survival [...]