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.

..and to think now that great mathematicians find my work interesting because I am able to illustrate their theories. They can not imagine that I was such a bad pupil in mathematics. I don't understand it myself neither. I never could understand why it was necessary to prove something that everyone already sees. I saw it, I knew it, so it is how it is… But yes, you had to prove it. I did overcome it when I realized I can make something else - I thought I was a good-for-nothing. In my family there were no other artists to find.. .I was just a weird duck, right?

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.

The mathematician's sense of tension is intimately related to his sense of beauty, and is what makes mathematics worthwhile doing.

I used to fear I was not made for mathematics and would look for people to tell me I was on the right track. You need to develop a personal conviction that you are a mathematician, and that what you are doing makes sense.

Although there are at present many occupations that require a good deal of skill and training in advanced mathematics, mathematics itself is still often regarded as a curious profession demanding singular talents and a singular personality.

mathematics as an innate ability. You either have “it” or you don’t. But to Schoenfeld, it’s not so much ability as attitude. You master mathematics if you are willing to try. That’s what Schoenfeld attempts to teach his students. Success is a function of persistence and doggedness and the willingness to work hard for twenty-two minutes to make sense of something that most people would give up on after thirty seconds. Put a bunch of Renees in a classroom, and give them the space and time to explore mathematics for themselves,

The mathematician requires tact and good taste at every step of his work, and he has to learn to trust to his own instinct to distinguish between what is really worthy of his efforts and what is not; he must take care not to be the slave of his symbols, but always to have before his mind the realities which they merely serve to express. For these and other reasons it seems to me of the highest importance that a mathematician should be trained in no narrow school; a wide course of reading in the first few years of his mathematical study cannot fail to influence for good the character of the whole of his subsequent work

For the great majority of mathematicians, mathematics is... a whole world of invention and discovery—an art. The construction of a new theorem, the intuition of some new principle, or the creation of a new branch of mathematics is the triumph of the creative imagination of the mathematician, which can be compared to that of a poet, the painter and the sculptor.

That was what drew him to mathematics. Not because it was rarefied, but because it probed to the subtle, deeper reality. People said that mathematicians were unworldly, and yammered on about how Einstein couldn’t make correct change. Nonsense. Einstein just didn’t give a damn. It was the subtle, the beautiful that concerned him.

The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful.

I learned mathematics on my own from textbooks which is perhaps strange given that both my parents were involved in the subject. At the same time, I spent a good deal of time studying art and wanted to follow a career in that direction until I was eventually convinced by my family that I should first work for a mathematics degree to ensure that I could earn a living.

Mathematicians are extremely lucky, they are paid for doing what they would by nature have to do anyway. One should not have a non-teaching fellowship too long, there comes a time when one must make a contribution to society. Great mathematics is achieved by solving difficult problems not by fabricating elaborate theories in search of a problem.

I don’t think that everyone should become a mathematician, but I do believe that many students don’t give mathematics a real chance.