Finding better models and understanding things at a deeper level is never a lost cause and even if we know that we can't find a complete set of axioms for all e

Finding better models and understanding things at a deeper level is never a lost cause and even if we know that we can't find a complete set of axioms for all existing math theories, we still try to understand math better. For example, the string theory people are trying to find an answer for everything (and it seems to be much more complex than 42 :-p). In this context, David Hilber tried to do the same for math (namely find a set of axioms for all existing theories) and Gödel proved that this was a lost cause. Does Gödel's incompleteness theorem apply to physics as well? I can't really grasp it, but my intuition says it does - because why would the formal system of TEO have more simple properties than the formal systems for arithmetic or Turing machines...?