Architectonics of Constellations : The Constellatory Unfolding Leitmotif in Mathematical Thinking and Its Weaving Screens of Quantum Physical Ontophainetics / Elias Zafiris, Albrecht von Müller.

Format:

Book

Author/Creator:

Zafiris, Elias, Author.

Müller, Albrecht von, Author.

Series:

Chronoi , 2701-1453 ; 17

De Gruyter Contemporary Social Sciences , 2747-5689 ; 4

Dependency and Slavery Studies , 2701-1127 ; 16

De Gruyter STEM

Latin American Literatures in the World / Literaturas Latinoamericanas en el Mundo , 2513-0757 ; 14

Key Concepts in Interreligious Discourses , 2513-1117 ; 13

Applied Virtuality Book Series , 2196-3118 ; 26

Language:

English

Physical Description:

1 online resource (320 p.)

Place of Publication:

LaVergne : Birkhäuser, 2026.

Basel Birkhäuser, [2026]

Language Note:

In English.

Biography/History:

Elias Zafiris , Vienna University of Technology. Albrecht von Müller , Parmenides Foundation, Pullach, Germany

Summary:

Gödel's incompleteness theorems of 1931 challenged the foundations of mathematics - yet many mathematicians still adhere to rigid, Platonic notions. This book opens the door to a different perspective: mathematics as a creative, open system. The authors examine key revolutions of the 20th century and show that a flexible ontology reflects mathematical practice more accurately than traditional Platonism. A compelling contribution for anyone who wants to experience mathematics not as a frozen structure, but as a living, constantly evolving process.

Contents:

Frontmatter

Table of Contents

Foreword / Gregory Chaitin

Constellatory Unfolding in Mathematical Thinking

The Synthetic Act of Representation

Constellatory Unfolding and Chrono-Topological Binding in the Present

Riemann's Vision and Unfolding in Geometric Function Theory: Multiply-Extended Variable Magnitudes and Riemann Surfaces

Galois' Vision and Unfolding in Algebra: Indistinguishability of Roots of Polynomial Equations and Galois Theory

Grothendieck's Vision and Unfolding in Topology: Unification Bond of Riemann's Geometric with Galois' Algebraic Unfolding Paradigms via Topological Covering Spaces and the Fundamental Group as a Galois Group

Poincaré's Vision and unfolding in Geometry: the Natural Intrinsic Geometry of Riemann Surfaces as an Algebraic-Topological Bond

Cayley's Vision and Unfolding in Combinatorial Group Theory: the Algebraic Bond Between the Topological and the Geometric Role of the Non-Commutative Free Group in Two Generators

Klein's Vision and Unfolding in the Geometric Conception of Potential Theory: Uniformization of Riemann Surfaces via the Bond of the Non-Commutative Free Group in Two Generators

Gödel's Vision and Unfolding in Mathematical Logic: Gödel's First Incompleteness Theorem

Cohen's Vision and Unfolding in Set Theory: Boolean-Valued Models of Set Theory and Boolean Topoi

Grassmann's Vision and Unfolding in Lineal Geometric Analysis: Ascending to the Exterior Algebra and Descending Back to its Commutative Shadow via Temporal Orders

Leray's Vision and Unfolding of the Notion of a Topological Space: Sheaves as Models of the Compatible Passage from the Local to the Global and the Articulation of Points

Grothendieck's Vision and Unfolding in the Conception of Geometric Form: Group Sheaves as Locally Variable Coefficient Systems for Cohomology

De Rham's Vision and Unfolding in the Integration of Infinitesimal Variation via Differential Forms: Cohomology of a Differential Complex and the Universal Role of the Constant Sheaf of the Reals

Weyl's Vision and Unfolding in the Conception of Physical Geometry: Local Gauge Symmetry, Interaction Potentials, and the Articulation of Matter

Chern's Vision and Unfolding of Spectra: Gauge Equivalence of Differential Sheaves, Integrality, and Quantization

Steenrod's Vision and Unfolding of the Inertial Structure of Spectra: Integrable Connections and Local Coefficients Systems for Cohomology

Hilbert's Vision and Unfolding of Holonomic Temporal Qualification: Monodromy, Holonomy and the Geometric Phase of Spectra

Weaving Screens of Physical Ontophainetics

Self-Unfolding and Self-Referentiality: Action and Structure from the Viewpoint of Natural Philosophy

Adjunction and Metaphora

Ontophainetics of the Quantum of Action

From Microcosm to Macrocosm: Dark Matter and Dark Energy

Imprint

Notes:

Title from eBook information screen..

This eBook is made available Open Access under a Creative Commons Attribution (CC BY) license: https://creativecommons.org/licenses/by-nc-nd/4.0

Description based on online resource; title from PDF title page (publisher's Web site, viewed July 08 2026)

ISBN:

9783035631050