What is geometry?

In the context of quantum calculus one is interested in discrete structures like graphs or finite abstract simplicial complexes studied primarily in combinatorics or combinatorial topology. Are they geometry? Are they calculus? What is geometry? In MathE320 I try to use the following definition: Geometry is the science of shape, size and symmetry. The symmetry statement is borrows from Klein’s … ….

Three Kepler Problems

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.

The finitist bunker

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.