Ever thought that we might be fundamentally missing something in our approach to physics?
Maybe its time to try something new such as applying category theory, of all things, to physics (of particular interest to me - the application of topos theory to the foundations of physics). I stumbled across this incipient branch of mathematical physics quite by accident while checking out the "Quantum Information Scientists of the World Unite" group on facebook.
I have yet to get to grips with this subject but it does look highly promising and very exciting. Especially when you consider that "Briefly put, a topos is a category whose structure is so rich that it is capable of modelling any situation which can even be discussed in mathematical terms." Chris Hillman "A Categorical Primer" (1997). Surly this must find great application in physics.
So far I have mostly looked at the work of Bob Coecke and Andreas Doering, you may want to look at their web site: Categories, Logic and Physics
if you are really interested and a bit lost (like me) see: quant-ph/0510032, quant-ph/0506132 and quant-ph/0703060, 62, 64 and 66