Book:Stephen Hawking/God Created the Integers

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Stephen Hawking: God Created the Integers: The Mathematical Breakthroughs that Changed History

Published $2005$, Penguin

ISBN 978-0-14-101878-2.


Subject Matter

This book consists of an anthology of important mathematical writings from Euclid to Turing, with a commentary by Stephen Hawking himself on each.

The title comes from a quote from Leopold Kronecker:

God created the integers; all else is the work of man.


Contents

Introduction
EUCLID (c.325 BC - 265 BC) His Life and Work
Sections from Euclid's Elements
Book I: Basic Geometry - Definitions, Postulates, Common Notions and Proposition 47 (Leading up to the Pythagorean Theorem)
Book V: The Eudoxian Theory of Proportion - Definitions & Propositions
Book VII: Elementary Number Theory - Definitions & Propositions
Book IX: Proposition 20: The Infinitude of Prime Numbers
Book IX: Proposition 36: Even Perfect Numbers
Book X: Commensurable and Incommensurable Magnitudes
ARCHIMEDES (287 BC - 212 BC) His Life and Work
Selections from The Works of Archimedes
On the Sphere and Cylinder, Book I
On the Sphere and Cylinder, Book II
Measurement of a Circle
The Sand Reckoner
The Methods
DIOPHANTUS (Third Century AD) His Life and Work
Selections from Diophantus of Alexandria, A Study in the History of Greek Algebra
Book II Problems 8-35
Book III Problems 5-21
Book V Problems 1-29
RENÉ DESCARTES (1596-1650) His Life and Work
The Geometry of René Descartes
ISAAC NEWTON (1642-1727) His Life and Work
Selections from Principia
Book I: Of the Motion of Bodies
PIERRE SIMON DE LAPLACE (1749-1827) His Life and Work
A Philosophical Essay on Probabilities
JEAN BAPTISTE JOSEPH FOURIER (1768-1830) His Life and Work
Selection from The Analytical Theory of Heat
Chapter III: Propagation of Heat in an Infinite Rectangular Solid (The Fourier series)
CARL FRIEDRICH GAUSS (1777-1855) His Life and Work
Selections from Disquisitiones ArithmeticaE (Arithmetic Disquisitions)
Section III Residues of Powers
Section IV Congruences of the Second Degree
AUGUSTIN-LOUIS CAUCHY (1789-1857) His Life and Work
Selection from Oeuvres complètes d'Augustin Cauchy
Resume des icons donnees a l'Ecole Royal Polytechnique sur le calcul infinitesimal (1823), series 2, vol. 4
Lessons 3 - 4 on differential calculus
Lessons 21-24 on the integral
GEORGE BOOLE (1815-1864) His Life and work
An Investigation of the Laws of Thought
GEORG FRIEDRICH BERNHARD RIEMANN (1826-1866) His Life and Work
On the Representability of a Function by Means of A Trigonometric Series (Ueber die Darstellbarkeit eider Function durch einer trigonometrische Reihe)
On the Hypotheses which lie at the Bases of Geometry (Ueber die Hypotheses welche der Geometrie zu Grunde liegen)
On the Number of Prime Numbers Less than a Given Quantity (Ueber di Anzahl of Primzahlen unter eine gegeben Grosse)
KARL WEIERSTRASS (1815-1897) His Life and Work
A Theory of Functions (Lecture Given in Berlin in 1886, with the Inaugural Academic Speech, Berlin 1857)
$\S 7$ Uniform Continuity (Gleichmassige Stetigkeit)
RICHARD JULIUS WILHELM DEDEKIND (1831-1916) His Life and Work
Essays on the Theory of Numbers
GEORG CANTOR (1845-1918) His Life and Work'
Selections from Contributions to the Founding of the Theory of Transfinite Numbers
Articles l and 11
HENRI LEBESGUE (1875-1941) His Life and Work
Selections from Integrale, Longueur, Aire (Integral, Length, Area)
KURT GÖDEL (1906-1978) His Life and Work
On Formally Undecidable Propositions of Principia Mathematica and Related Systems
ALAN MATHISON TURING (1912-1954) His Life and Work
On computable numbers with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society