Maths as a Creative Art

There is far more to mathematics than the rigid application of formal rules to meaningless systems of symbols. For some, it is creative, imaginative, deeply satisfying and in some ways similar to those disciplines sometimes considered diametrically opposed to mathematics, the arts.

“...it is certain that the real function of art is to increase our self-consciousness; to make us more aware of what we are, and therefore of whar the Universe in which we live really is. And since mathematice, in its own way, also performs this function, it is not only aesthetically charming but profoundly significant. It is an art, and a great art.“

John W. N. Sullivan.

“I am interested in mathematics only as a creative art.“
G. H. Hardy.

“I have never done anything ‘useful’. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world… Judged by all practical standards, the value of my mathematical life is nil; ... I have just one chance of escaping a verdict of complete triviality, that I may be judged to have created something worth creating. And that I have created something is undeniable: the question is about its value.
The case for my life ... is that I have added something to knowledge ... and that this has a value which differs in degree only, and not in kind, from the creations of the great mathematicians, or any of the other artists, great of small, who have left some kind of memorial behind them. “
G. H. Hardy.

(thanks to Anna Luise Wagner)

“It is also an art—the most intellectual and classical of the arts. And almost no one is capable of doing significant mathematics. There are no acceptably good mathematicians. Each generation has ist few great mathematicians, and mathematics would not even notice the absence of the others. They are useful as teachers, and their research harms no one, but it is of no importance at all. A mathematician is great or he is nothing. Perhaps that is where the purity of the discipline begins.“

Alfred Adler, 1972

“A mathematician, like a painter, is a maker of patterns. If his patterns are more permanent, it is because they are made with ideas. A painter makes pattern with shapes and colours. A mathematician has no material to work with but ideas, and so his patterns are likely to last longer , since ideas wear less than words. The mathematitian’s patterns, like the painter’s, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place for ugly mathematics.“
G. H. Hardy.

“Mathematics, rightly viewed, possesses not only thruth, but supreme beauty—a beauty cold and austere, like that of a sculpture.“
Bertrand Russell.