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.