No I don't think this is quite right. The romantic artistic image of the mathematician is a prevalent one now, and we choose to see examples to fit the type. But it hasn't always been this way. Before the early 1800s the mathematician was scene as a pragmatic, man of the world sort. Or so Amir Alexander argues in his book Dual at Dawn: http://www.amazon.co.uk/Duel-Dawn-Mathematics-Histories-Tech...

I agree with you that sensitivity and complexity are not isolated to artists, and a agree to some extent that mathematics is an art form, just wanted to point out that 'mathematician as tortured artist' is a relatively modern trope.

It's hard for a "man of the world" to make time in the 21st century to learn enough about mathematics to make meaningful contributions to the field which still doing the other things being a "man of the world" requires, except perhaps in a few isolated places that happen to overlap something practical. Or, in other words, we programmers probably overestimate the ability for non-mathematicians to contribute to the field because we happen to be sitting in the very best such place already.

Same reason we don't get true renaissance people anymore; one can not even know everything about genetics, to say nothing of biology, let alone half-a-dozen other disciplines.

Are these traits truly associated with "artistry" and "creativity", or are we simply in a place where we've done so much than moving things forward requires monomania?

Yes, no one is a renaissance person any more. But I don't think that there were as many renaissance people in the past as we think. Admittedly I don't have much evidence for this. In the case of maths, I think our idea that many more mathematicians used to be polymaths in the past is slightly skewed dues to the fact that until about 2 centuries ago, 'mathematician' and 'physicist' were not distinct categories. We think of Gauss and Euler as polymaths, but Euler was by all accounts a terrible philosopher.

EDIT: I just remembered that Gauss was an extremely competent philologist, so maybe the above is no longer valid.

Fair enough. I like to think of math as an art form, and I think on some levels it certainly is (as much as I'd also consider Einstein an artist in many ways). The end product is different than an "artist" but I think a lot of the thought processes overlap and cause similar perspectives.