Makers of Mathematics

Description

Fascinating and highly readable, this book recounts the history of mathematics as revealed in the lives and writings of the most distinguished practitioners of the art: Archimedes, Descartes, Fermat, Pascal, Newton, Leibniz, Euler, Gauss, Hamilton, Einstein, and many more. Author Stuart Hollingdale introduces and explains the roles of these gifted and often colorful figures in the development of mathematics as well as the ways in which their work relates to mathematics as a whole. Although the emphasis in this absorbing survey is primarily biographical, Hollingdale also discusses major historical themes and explains new ideas and techniques. No specialized mathematical knowledge on the part of the reader is assumed. Superbly informative, this volume offers an accessible, interesting guide to one of the pillars of modern science, and to a supremely important aspect of human culture through the ages.;Cover; Title Page; Copyright age; Contents; Preface; List Of Illustation; Chapter 1: The beginnings; 1. Prehistory; 2. Egypt; 3. Mesopotamia; Chapter 2: Early Greek mathematics; 1. Introduction; 2. The Greek contribution; 3. The textual sources; 4. Thales and Pythagoras; 5. The classification of numbers; 6. The discovery of incommensurability; 7. Hippocrates of Chios; 8. 'Ruler and compasses' constructions; 9. The three classical problems; 10. Hippias of Elis; 11. Eudoxus of Cnidus; 12. The Eudoxan theory of proportion; 13. The method of exhaustion; 14. Eudoxan astronomy. Cover Title Page Copyright age Contents Preface List Of Illustation Chapter 1: The beginnings 1. Prehistory 2. Egypt 3. Mesopotamia Chapter 2: Early Greek mathematics 1. Introduction 2. The Greek contribution 3. The textual sources 4. Thales and Pythagoras 5. The classification of numbers 6. The discovery of incommensurability 7. Hippocrates of Chios 8. 'Ruler and compasses' constructions 9. The three classical problems 10. Hippias of Elis 11. Eudoxus of Cnidus 12. The Eudoxan theory of proportion 13. The method of exhaustion 14. Eudoxan astronomy. Chapter 3: Euclid and Apollonius1. Introduction 2. Euclid: his life and works 3. The Elements of Euclid 4. The regular pentagon and the golden section 5. The Euclidean algorithm 6. Rational approximations 7. Apollonius: his life and works 8. The Conics of Apollonius Chapter 4: Archimedes and the later Hellenistic period 1. Archimedes of Syracuse 2. Archimedes' works 3. Quadrature of the Parabola 4. On the Sphere and Cylinder 5. On Conoids and Spheroids 6. The Archimedean spiral 7. The Method 8. Angle trisection by neusis 9. Construction of the regular heptagon. 10. Numerical studies11. The later Hellenistic age 12. Ptolemy of Alexandria 13. Diophantus of Alexandria 14. Pappus of Alexandria Chapter 5: The long interlude 1. Introduction 2. China 3. India 4. The Muslim world 5. Leonardo of Pisa 6. An architectural note Chapter 6: The Renaissance 1. Introduction 2. Nicolas Chuquet 3. Luca Pacioli and Michael Stifel 4. Girolamo Cardano 5. Tartaglia and the strange story of the cubic equation 6. Cardano's published treatment of the cubic equation Chapter 7: Descartes, Fermat and Pascal 1. Introduction 2. René Descartes. 3. Descartes's philosophical position4. La Géométrie 5. Pierre de Fermat 6. Fermat and coordinate geometry 7. Towards the calculus 8. The theory of numbers 9. Blaise Pascal 10. Pascal's theorem and projective geometry 11. The cycloid 12. The mathematical theory of probability Chapter 8: Newton 1. Introduction 2. His life 3. Newton the man 4. Newton the natural philosopher 5. Analysis by infinite series 6. The fluxional calculus 7. Optical experiments and speculations 8. Geometrical researches 9. Early thoughts on mechanics and gravitation. 10. Researches in numerical mathematics11. Later years: the priority dispute Chapter 9: Newton's Principia 1. The writing and publication of the Principia 4. Book 2: The motion of bodies in resisting media 5. Book 3: The System of the World 6. The General Scholium Chapter 10: Newton's circle 1. Introduction 2. JohnWallis 3. Wallis's algebraic investigations 4. Isaac Barrow 5. Barrow and Newton 6. Barrow's geometrical lectures 7. Edmond Halley 8. Halley's cometary studies 9. Roger Cotes 10. Editor of the Principia 11. Cotes's mathematical researches Chapter 11: Leibniz.