Stingray, thanks for the post.
Actually, I am really aware of what you speak of. I never heard of the guy from Princeton, but I looked him up - I really like his work. I started to read his philosophical paper on PDE's, but I decided I would reply real quick.
But a few notes. Ed Witten is well known at my school, he's done a few seminars with us, and Mathematical Physics is one of our biggest areas; Topology/ Geometry and Dynamics may be bigger.
So, Mr. Witten, while he has lead to deep insights in mathematics, is not a mathematician I am told, by quite a few mathematicians. Shame he doesn't do both, since he has that piercing mind.
And, the Princeton guy appears to be the same, he does the rigour behind physics (which is awesome) but does not do theoretical physics.
Here is a guy you may know, Albert Schwarz,
http://www.math.ucdavis.edu/research/profiles/schwarz
His work has turned out, it appears to be the closest I can find of a mathematician doing both.
I understand the argument of time, I do, and I don't think it applies to everyone. I know professors who have 3 and 4 areas of research. I was just wondering had anyone split those between mathematics and physics.
I agree with just learning what you need to. But most people need the path to a ph.d b/c 1) helps get a job 2) it's probably quicker to learn all that material in school vice self-teaching. But, I guess both of those are questionable too.
Please drop more names if you have the time. I'd love to look them up and see what they're doing.