RESEARCH PROGRAM

Research Program

The Concept and Formalization of Constellatory Unfolding as a Cross-Cutting Principle 

 of an Autogenetic Universe

Albrecht von Müller and Elias Zafiris

Second Book Volume 

(In Complete Form: To be Published by Birkhäuser in 2025)

On the Foundations of Mathematical Thinking from the Perspective of Constellatory Unfolding

By consulting the original sources, based on the writings of the mathematical figures in focus that - as universally recognized - have enriched and developed the body of mathematical thinking in novel ways, we explicate in detail the semantic constellatory unfolding processes permeating these genuine advances in the following characteristic instances:

• Riemann's geometric function theory on the complex domain;

• Galois' theory of field extensions via permutation groups;

• Grothendieck's unification of Riemann's and Galois theories in the topological domain of covering spaces and the fundamental group;

• Poincare's uniformization strategy in complex surface geometry;

• Cayley's geometrization of group theory with emphasis on the non-commutative free group on two generators;

• Klein's uniformization strategy of Riemann surfaces based on potential theory and the free group;

• Goedel's first incompleteness theorem in mathematical logic;

• Cohen's method of forcing and the emergence of topoi as non-standard models of set theory;

• Grassmann's extension theory in the context of lineal geometric analysis;

• Leray's topological theory of sheaves and the compatiple passage from the local to the global;

• Grothendieck's theory of sheaves as coefficient systems for cohomology;

• de Rham's theory of differential forms and cohomology;

• Weyl's program of localizing gauge symmetry to articulate matter;

• Chern's theory of bundles with connection and the emergence of integrality;

• Steenrod's theory of integrable connections and local systems;

• Hilbert's program relating the monodromy action of the fundamental group with the theory of differential equations.

Table of Contents and Introduction