As a long time practitioner I suggest some caution in the premise of your question, something which appears to have been overplayed in the popular press. Keep in mind the [Levy Doob][1] theorem, for instance, and the fact that arbitrage arguments are not the only structure giving rise to useful mathematics, even in the narrowest definition of this field (which I fear amounts to pricing PDEs in the minds of some, and within that the definition of an infinitesimal generator; and within that, a very small class of diffusion operators - you get my point). This has very limited relevance to credit risk, for example. 

  [1]: http://en.wikipedia.org/wiki/Doob%2527s_martingale_convergence_theorems