Historical Encyclopedia of Natural and Mathematical Sciences

Bearbeitet vonAri Ben-Menahem

1. Auflage 2009. Buch. clxii, 5983 S. HardcoverISBN 978 3 540 68831 0

Format (B x L): 20,3 x 27,6 cm

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Contents

Part I

Pre-Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1. Origins – Splendor of the Simple

(4200 bce–529 ce) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

• Calendars, or the Conquest of Time

• Wheels and Numerals

• Papyri and Clay

• Birth of Science in Ionia

• Blossom in Alexandria

General Bibliography

Name Index

Subject Index

2. Slumber and Awakening (529–1583) . . . . . . . . . . . 497

• In the Womb of Asia

• Diffusion of Greco-Hindu Lore into Western Europe

• Rise of the Universities

• Renaissance

• The Scientific Revolution

• Voyagers and Explorers

General Bibliography

Name Index

Subject Index

xx Contents

Part II

3. The Clockwork Universe (1583–1819) . . . . . . . . . . 911

• Beyond the Greeks

• Infinitesimals and Infinities

• Rise of Mechanics

• The New Astronomy

• Enlightenment

• Social Revolutions and Industrialization

• Algebraization of Geometry and Exploitation of the

Calculus:

Analytic and Projective GeometryAnalytical MechanicsPartial Differential EquationsThe Calculus of Variations

• Emergence of the Theories of Numbers, Probability and

Statistics

• From Alchemy to Chemistry

• Evolution of the Steam Engine

General Bibliography

Name Index

Subject Index

4. Abstraction and Unification (1820–1894) . . . . 1733

• Emergence of Algebraic Structures and the Rise of Ab-

stract Algebras:

Fields, Groups, Matrices, Vectors, QuaternionsInvariants and Quadratic FormsSymbolic Algebra

• Breakaway from Euclidean Geometry

Non-Euclidean GeometriesDifferential Geometry of Surfaces; Riemannian Geometry

Contents xxi

Topology; Algebraic GeometryTensor Calculus

• The Arithmetization of Analysis:

Limits and Convergence of Infinite Series; Fourier SeriesRigorization of the Real Number System; Set Theory

• Complex Analysis; Differential and Integral Equations

• Advent of Electromagnetism: Unification of Optics,

Electricity and Magnetism

• Quantification of Thermal Phenomena: Thermodynam-

ics and Statistical Physics

• The Periodic Table of the Elements

• Organic Chemistry and Cell Theory

• The Theory of Biological Evolution

• Alternating Current Technology; Discovery of Photo-

conductivity

• Oceanography – The Conquest of Inner Space

• Emergence of World Communication: Telephone, Tele-

graph, Facsimile

General Bibliography

Name Index

Subject Index

Part III

5. Demise of the Dogmatic Universe

(1895–1950) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2801

• Maturation of Abstract Algebra and the Grand Fusion

of Geometry, Algebra, Arithmetic and Topology:

Lie Groups and Algebras; Modular Groups: Noether RingsTopological SpacesSpinors; Fiber Bundles; CategoriesModular Functions and Analytic Number Theory

xxii Contents

Exterior Calculus, Homology, and Genera

• Logic, Set Theory, Foundations of Mathematics and the

Genesis of Computer Science

• Modern Analysis:

Functional Analysis and Infinite-Dimensional SpacesNon-Archimedean Analysis (p-adics)

• Electrons, Atoms, Nuclei and Quanta

• Einstein’s Relativity and the Geometrization of Grav-

ity; The Expanding Universe

• Preliminary Attempts to Geometrize Non-Gravitational

Interactions; Kaluza – Klein Models With Compactified

Dimensions

• Subatomic Physics: Quantum Mechanics and Quantum

Electrodynamics; Nuclear and Particle Physics

• Reduction of Chemistry to Physics; Condensed Matter

Physics; The 4th

State of Matter

• The Conquest of Distance by Automobile, Aircraft and

Wireless Communications; Cinematography

• The ‘Flaming Sword’: Antibiotics and Nuclear Weapons

• Unfolding Basic Biostructures: Chromosomes, Genes,

Hormones, Enzymes and Viruses; Proteins and Amino

Acids

• Electromagnetic Technology: Early Laser Theory;

Holography; Magnetic Recording and Vacuum Tubes; In-

vention of the Transistor

• ‘Big Science’: Accelerators; The Manhattan Project

General Bibliography

Name Index

Subject Index

6. Deep Principles – Complex Structures

(1950–2008) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5081

• Continuation of Abstraction and Unification of Pure

Mathematics

Contents xxiii

• Discrete Mathematics and the Ubiquitous Algorithm;

Computation Beyond Algorithms

• Nonlinearity, Stochasticity and the Science of Com-

plexity; Adding Noise to Deterministic Evolution

• Mathematization of the Biological, Environmental and

Social Sciences

• Abstract Algebra and Group Theory in Modern Theo-

retical Physics

• Particle Physics and the Coming of Gauge

• The New Cosmology: Whence, Whither and Why?

• General Relativity meets Quantum Mechanics and Par-

ticle Physics

• Quantum Technology

• RF Engineering and Particle-Accelerator Technology

• Worldwide Communications and Information Technol-

ogy

• Modern Microscopy and Telescopy

• Material Science

• Computer Technology; Computer Simulation – the

Third mode of Science

• Molecular Biology, Genetics and Biochemistry

• Biotechnology of Nature and Man

• Big Science

Appendices

Bibliography

Name Index