Mathematics quotes

Mathematics quotes by G. H. Hardy

Also about
Beauty, Science, Art, Ideas, Glory, Creation, Absurd, Music
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.