Life is only good for two things, doing mathematics and teaching it.
If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper.
The real satisfaction from mathematics is in learning from others and sharing with others.
Programming is much much harder than doing mathematics.
People who wish to analyze nature without using mathematics must settle for a reduced understanding.
When we talk about the impact inside mathematics, and applications in the sciences, [Mandelbrot] is one of the most important figures of the last 50 years.
. . . mathematics is absolutely necessary and useful to the other sciences.
The "seriousness" of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects.
On sighting mathematicians poetry should unhook the algebra from their minds and replace it with poetry; on sighting poets it should unhook poetry from their minds and replace it with algebra.
Science advances one funeral at a time.
The standard model gives us an accuracy of ten decimal digits, this is an amazing success that has never been achieved before in science.
. . . though mathematics may teach a man how to build a bridge, it is what the Scotch Universities call the humanities, that teach him to be civil and sweet-tempered.
Nature's great book is written in mathematics.
If all art aspires to the condition of music, all the sciences aspire to the condition of mathematics.
A lot of music is mathematics. It's balance.
The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work-that is, correctly to describe phenomena from a reasonably wide area.
Mathematics is not something that you find lying around in your back yard. It's produced by the human mind. Yet if we ask where mathematics works best, it is in areas like particle physics and astrophysics, areas of fundamental science that are very, very far removed from everyday affairs.
There is something in statistics that makes it very similar to astrology.
The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future.
Mathematics is an interesting intellectual sport but it should not be allowed to stand in the way of obtaining sensible information about physical processes.