Book:Stephen Hawking/God Created the Integers
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Stephen Hawking: God Created the Integers: The Mathematical Breakthroughs that Changed History
Published $\text {2005}$, 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
- Sections from Euclid's Elements
- 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
- Selections from The Works of Archimedes
- 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
- Selections from Diophantus of Alexandria, A Study in the History of Greek Algebra
- 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
- Selections from Principia
- 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)
- Selection from The Analytical Theory of Heat
- 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
- Selections from Disquisitiones ArithmeticaE (Arithmetic Disquisitions)
- 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)
- A Theory of Functions (Lecture Given in Berlin in 1886, with the Inaugural Academic Speech, Berlin 1857)
- 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 I and II
- Selections from Contributions to the Founding of the Theory of Transfinite Numbers
- 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