There are actually many similarities between mathematics and art. By mathematics I do not mean the applied areas of maths or perhaps more precisely those areas of mathematics which are pursued for practical or applied use alone, but mathematics which flows in the direction of
aesthetics and beauty.
To strike up an analogy we can think of the difference between literature and the study of english for its practical use in a similar way that we think of mathematics and its practical use. Sure literature might involve letters and grammar just as mathematics contains numbers and arithmetic, but those who have studied some amount of literature appreciate that the study of literature is very different to writing a letter or some other practical application of the english language.
I find it most unfortunate that many people don't understand what mathematicians do, they think they do something to do with large number crunching or something like that, rather than something closer to art, which I think it is.