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Let no man who is not a Mathematician read the elements of my work.

 

Leonardo da Vinci

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Mathematics is too arduous and uninviting a field to appeal to those to whom it does not give great rewards. These rewards are of exactly the same character as those of the artist. To see a difficult uncompromising material take living shape and meaning is to be Pygmalion, whether the material is stone or hard, stonelike logic. To see meaning and understanding come where there has been no meaning and no understanding is to share the work of a demiurge. No amount of technical correctness and no amount of labour can replace this creative moment, whether in the life of a mathematician or of a painter or musician. Bound up with it is a judgement of values, quite parallel to the judgement of values that belongs to the painter or the musician. Neither the artist nor the mathematician may be able to tell you what constitutes the difference between a significant piece of work and an inflated trifle; but if he is not able to recognise this in his own heart, he is no artist and no mathematician.

 

Norbert Wiener

 

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.

 

G. H. Hardy

 

What does it take to be [a mathematician]? I think I know the answer: you have to be born right, you must continually strive to become perfect, you must love mathematics more than anything else, you must work at it hard and without stop, and you must never give up.

 

Paul Halmos

 

You'll have received an application from Mr Freeman Dyson to come to work with you as a graduate student. I hope that you will accept him. Although he is only 23 he is in my view the best mathematician in England.

 

Freeman Dyson

 

Robert Motherwell: Would you say that a fair statement of your position is that the "meaning" of a work of art consists of the relations among the elements, and not the elements themselves?
Hofmann: Yes, that I would definitely say. You make a thin line and a thick line. It is the same with geometrical shapes. It is all relationship. Without all these relationships it is not possible to express higher art.

 

Hans Hofmann