Historically, there was no such division. Many of the great artists of the past were also mathematicians, engineers, anatomists, etc. Of course, in the past, it was comparatively easy to become an expert in many if not all areas of human knowledge.
Now, it’s difficult to conquer even one area of human knowledge, so we’ve adjusted by developing expertise in ever smaller specialisations.
In my final year at school, I still could not decide between studying science and going to art school. So I tossed a coin. Science won. I was a little sad, but consoled myself that I could always return to art when I retired – it would have been trickier to take up science as a retiree!
So what happened? well, I became a scientist. I became an expert in visual psychophysics, specifically the tiny, tiny specialisation of first and second order integration of spatial and orientational information in the early visual cortex. A lot of my source visual material was… paintings. Art. And now, for relaxation, I use my mathematical expertise to develop my own art.
Art and mathematics are not that different, at least to me. When I plan a painting, I think in terms of geometry, perspective, and other essentially mathematical constructs. When I read a mathematical proof, in my mind, the various parts form a complex ballet or orchestral composition. There’s a false dichotomy between the two, which has been supported – if not promulgated – through education. In truth, good scientists are as creative and radical as any artist, and good artists are as precise and methodical as any scientist.