God created the integers : the mathematical breakthroughs that changed history / edited, with commentary, by Stephen Hawking.

Introduction -- [pt. 1]. Euclid (c.325 BC-265 BC) : His life and work -- Selections form Euclid's Elements -- Book 1 : Basic geometry - definitions, postulates, common notions and proposition 47 (leading up to the Pythagorean Theorem) -- Book 5 : The Eudoxian theory of proportion - definitions & propositions -- Book 7 : Elementary number theory - definitions & propositions -- Book 9 : Proposition 20 : The infinitude of prime numbers -- Book 10 : Commensurable and incommensurable magnitudes -- [pt. 2]. Archimedes (287 BC-212 BC) : His life and work -- Selections form The Works of Archimedes -- On the sphere and cylinder, book 1-- On the sphere and cylinder, book 2 -- Measurement of a circle -- The sand reckoner -- The methods -- [pt. 3]. Diophantus (third century AD) : His life and work -- Selections from Diophantus of Alexandria, A Study in the History of Greek Algebra -- Book 2 problems 8-35 -- Book 3 problems 5-21 -- Book 5 problems 1-29 --

[pt. 4]. René Descartes (1596-1650) : His life and work -- The geometry of Rene Descartes -- [pt. 5]. Isaac Newton (1642-1727) : His life and work -- Selections from Principia -- Book 1 : Of the motion of bodies -- [pt. 6]. Pierre Simon de Laplace (1749-1827) : His life and work -- A philosophical essay on probabilities -- [pt. 7]. Jean Baptiste Joseph Fourier (1768-1830) : His life and work -- Selection from The Analytical Theory of Heat -- Chapter 3 : Propagation of heat in an infinite rectangular solid (The Fourier series) -- [pt. 8]. Carl Friedrich Gauss (1777-1855) : His life and work -- Selections from Disquisitiones Arithmeticae (Arithmetic Disquisitions) -- Section 3 Residues of powers -- Section 4 Congruences of the second degree -- [pt. 9]. Augustin-Louis Cauchy (1789-1857) : His life and work -- Selection from Oeuvres complètes d'Augustin Cauchy -- Resume des lecons donnees a l'Ecole Royale Polytechnique sur le calcul infinitesimal (1823), series 2, vol. 4 -- Lessons 3-4 on differential calculus -- Lessons 21-24 on the integral --

[pt. 10]. George Boole (1815-1864) : His life and work -- An investigation of the laws of thought -- [pt. 11]. George Friedrich Bernhard Riemann (1826-1866) : His life and work -- On the representability of a function by means of a trigonometric series (Ueber die darstellbarkeit einer function durch einer trigonometrische reihe) -- On the hypotheses which lie at the bases of geometry (Ueber die hypothesen 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) -- [pt. 12]. 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) -- 7 : Uniform continuity (Gleichmässige Stetigkeit) -- [pt. 13]. Richard Julius Wilhelm Dedekind (1831-1916) : His life and work -- Essays on the theory of numbers -- [pt. 14]. Georg Cantor (1845-1918) : His life and work -- Selections from Contributions to the founding of the theory of transfinite numbers -- Articles 1 and 2 --

[pt. 15]. Henri Lebesgue (1875-1941) : His life and work -- Selections from Integrale, Longueur, Aire (Integral, Length, Area) -- [pt. 16]. Kurt Gödel (1906-1978) : His life and work -- On formally undecidable propositions of principia mathematics and related systems -- [pt. 17]. Alan Mathison Turing (1912-1954) : His life and work -- On computable numbers with an application to the entscheidungsproblem, proceedings of the London Mathematical Society.

Euclid (c.325 BC-265 BC) -- Archimedes (287 BC-212 BC) -- Diophantus (third century AD) -- René Descartes (1596-1650) -- Isaac Newton (1642-1727) -- Pierre Simon de Laplace (1749-1827) -- Jean Baptiste Joseph Fourier (1768-1830) -- Carl Friedrich Gauss (1777-1855) -- Augustin-Louis Cauchy (1789-1857) -- George Boole (1815-1864) -- George Friedrich Bernhard Riemann (1826-1866) -- Karl Weierstrass (1815-1897) -- Richard Julius Wilhelm Dedekind (1831-1916) -- Georg Cantor (1845-1918) -- Henri Lebesgue (1875-1941) -- Kurt Gödel (1906-1978) -- Alan Mathison Turing (1912-1954).

Euclid -- Archimedes -- Diophantus -- René Descartes -- Isaac Newton -- Pierre Simon de Laplace -- Jean Baptiste Joseph Fourier -- Carl Friedrich Gauss -- August-Louis Cauchy -- George Boole -- Georg Friedrich Bernhard Riemann -- Karl Weierstrass -- Richard Julius Wilhelm Dedekind -- Georg Cantor -- Henri Lebesgue -- Kurt Gödel -- Alan Mathison Turing.

From the geometry of Euclid, through the calculus of Newton, the probabilities of Laplace to the thought of Boole, this extraordinary volume allows readers to peer into the mind of genius by providing them with excerpts from the original mathematical proofs and results. It also charts the progression of mathematical thought - granting the reader a solid understanding of the very foundations of some of out current technologies.