Mathematics quotes

Pure mathematics is, in its way, the poetry of logical ideas. As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is. Young man, in mathematics you don't understand things. You just get used to them.

Many who have had an opportunity of knowing any more about mathematics confuse it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination. It is impossible to be a mathematician without being a poet in soul.

Beauty is the first test: there is no permanent place in the world for ugly mathematics. A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. I am interested in mathematics only as a creative art. Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics. Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game. In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy. The fact is that there are few more "popular" subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances may suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity. Real mathematics must be justified as art if it can be justified at all.

It would be better for the true physics if there were no mathematicians on earth. There is no philosophy which is not founded upon knowledge of the phenomena, but to get any profit from this knowledge it is absolutely necessary to be a mathematician.

I think math is a hugely creative field, because there are some very well-defined operations that you have to work within.
You are, in a sense, straightjacketed by the rules of the mathematics. But within that constrained environment, it's up to you what you do with the symbols. In my own research when I'm working with equations, I never feel like I really understand what I'm doing if I'm solely relying on the mathematics for my understanding. I need to have a visual picture in my mind. I'm constantly translating from the math to some intuitive mind's-eye picture. Over the centuries, monumental upheavals in science have emerged time and again from following the leads set out by mathematics. Physicists are more like avant-garde composers, willing to bend traditional rules... Mathematicians are more like classical composers. All mathematics is is a language that is well tuned, finely honed, to describe patterns; be it patterns in a star, which has five points that are regularly arranged, be it patterns in numbers like 2, 4, 6, 8, 10 that follow very regular progression.