The Grand Unification Theory, the Theory of Everything... and the many other names it goes by; the One Rule to rule them all is to many the ultimate forseeable goal of science. A fundamental truth from which all other truths can be predicted, calculated and derived. This, in most interpretations involves the elusive goal of unifying the fundamental forces of reality, namely: gravity, the strong nuclear force, the weak nuclear force and electromagnetism. Gravity is proving to be a problematic child, who doesn't play well with the others. Some very well known scientists have been notedly on the search for this elisive equation, but lets talk about possibly the most well known (and still living) physicist ever to walk the earth, Stephen Hawking.
Mr Hawking is a betting man, and relatively recently conceeded a bet concerning the discovery of a unifying theory. He ran into a philosophical problem such as they occur in physics: philosophy educates exploration - without it you can't easily imagine where to look. This philosophical problem was proven by Kurt Gödel in 1931. Simply put (very simply put):
The whole system can not be accurately and wholly described by a part of that system.
You can now see the issue. The laws of mathematics is only a subset of the laws of physics - and so reality can't be completely circumscribed in mathematical terms. So Mr Hawking changed his mind, he does not believe that a unified theory is achievable.
But what if the nature of the laws of reality is fractal, and that small subset of rules we call mathematics is 'repeated' on each scale of observation? Surely knowing an accurate enough approximation of the whole of mathematics would allow the extrapolation of everything beyond? Like the fronds of a Pine tree predict the shape of the whole organism as viewed from a distance.
This would be nice, but we don't get to view reality from the outside and analyse it on each incremental scale. We're stuck in the bit defined by mathematics, and with no way to completely describe mathematics itself, how do you propose to imagine what might lay beyond. As always with science an old adage never fails to deliever: when you answer one question you are only presented with countless more.
It would seem that there is a limit to what science can achieve; it may yet prove to be a limit so vast that our current limited view of the world prevents us from even beginning to imagine the possibilities.