Depending on scale, there are three different Kepler problems: the Hydrogen atom, the Newtonian Kepler problem as well as the binary Blackhole problem. The question whether there is a unifying model which covers all of them is part of the quest of finding a quantum theory of gravity.
As Goedel has shown, mathematics can not tame the danger that some inconsistency develops within the system. One can build bunkers but never will be safe. But the danger is not as big as history has shown. Any crisis which developed has been very fruitful and led to new mathematics. (Zeno paradox->calculus, Epimenids paradox ->Goedel, irrationality crisis ->number fields etc.
The history of the developent of energy and entropy is illustrated. This page is a picture book featuring some of the people involved shaping the concept of energy.
A rather unfamiliar picture of a famous mathematician/physisist.