On Knots and Cohomology and Dowker
Something about knots and something about topological data analysis and something about the general frame work to do mathematics in a finite setting.
Category: History
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, …
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.
From Affinity over Vis Viva to Energy
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.
