Mathematicians and string theory? Hello,
I'm curious on whether say, a ph.d in mathematics with no experience in physics could pick up a book on String theory (say some intro for mathematicians) and learn it and then do research kinda "quickly"? From what I've understood, string theory is mostly mathematics so I would be interested in knowing.
 A: OK, I'll bite -- although I am not convinced that this is a suitable question for MO.
First of all, it depends what you mean by 'string theory'.  There is mathematics which has been influenced (some deeply, some less so) by physics research billed as string theory:


*

*Mirror symmetry comes to mind as one area where the influence has been crucial.  To the two references in Wadim's comment, you could add the freely available Mirror symmetry (PDF) with contributions by Hori, Katz, Klemm, Pandharipande, Thomas, Vafa, Vakil and Zaslow.

*Stability conditions in derived categories, particularly the work of Tom Bridgeland, taking inspiration from the work by string theorist Michael Douglas and collaborators.

*Vertex operator algebras, conformal field theory,...
However, I would not say that working on mathematics which has been touched by string theory, necessarily implies that you are working on string theory.
If you really want to work on string theory, you have to learn some physics, if only because that is the language which the majority of practitioners still speak.  A good resource (for mathematicians) to get you started are the lectures at the IAS activity Quantum Field Theory in the late 1990s.
One has to wonder, though, whether without any background in physics you really want to go down this path.
A: It is definitely possible to start research in string theory without any background in physics. What is less certain is whether it is easily done by reading a book. The difficulty is to identify a good research problem that can be finished in a finite amount of time. A better strategy perhaps would be to scan the abstracts and articles in the hep-th arxiv, and to focus on papers that use the kind of mathematics that you're interested in. (A fairly recent book that touches on many of the current directions in string theory is "String Theory and M-Theory: A Modern Introduction", by Katrin and Melanie Becker and 
John Schwarz.)
