Book:Stephen Hawking/God Created the Integers

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