I'm not sure about that. The words "homeless drug addict" don't exactly bring "mathematician" to mind, but thats' exactly what Erdos was, and he certainly qualified as one of the best mathematicians of the 20th century.
EDIT: Oops, it wasn't methamphetamine; it was dl-amphetamine and methylphenidate. Somehow my brain squished those two together.
Erdos was a drug user, not a drug addict. He famously quit drugs for a month just to show that he was not an addict. And though he was technically homeless, he was not what most people imagine when they hear this word. He merely preferred to spend his life traveling, and had many friends everywhere (which comes with the territory if you're eminent).
His most salient characteristics--eccentricity and lack of concern for non-mathematical things--are common to most mathematicians.
Oops, I mentally squished methylphenidate and dl-amphatamine together (Erdos took both) into methamphetamine. You're right, Erdos didn't take methamphetamine.
It's always true in any field where success is relative, and one's success is based on being "better" than others. For example in rowing, if you're on the same training program as everyone else then your chance of winning is basically flip-a-coin. Similarly, if you paint in the same style as others then your chances of being recognized as the best painter are basically flip-a-coin as well. Math, however, is different because you work at uncovering the properties of mathematical objects whatever they might be (so success is absolute), and you don't get credit for doing stuff that's already been done. Because of this everyone can do math the same way and still win, because how much stuff you discover is a function of you and what you're working on and not your methods.
If I had to come up with a general law on the spot, I'd say that the pressure to create new methodology is directly proportional to the similarity of recent winning outcomes in the past. I haven't fully tried to break this yet, but I'm guessing I'm pretty close to having found a natural law since it is consistent with evolution running in S-Curves.
The trouble with math is that the exceptional mathematicians (including theoretical physics/computer science) are the stereotype, and the regular mathematicians are actually quite different from that. So in fact it's the stereotype that's wrong, not the claim that exceptional mathematicians are not very mathematician-like.
Maybe it depends on whether a field has a lot of fakers. Painting and VC both do. Math has few to none (I can't judge well enough to say for sure).