Book:James R. Newman/The World of Mathematics
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James R. Newman: The World of Mathematics
Published $\text {1956}$, George Allen and Unwin Ltd
Subject Matter
- History of mathematics
A small library of the literature of mathematics from A'h-mosé the Scribe to Albert Einstein, presented with commentaries and notes by JAMES R. NEWMAN
Contents
- Introduction
- Part I: General Survey
- Philip E. B. Jourdain: Commentary
- 1. The Nature of Mathematics by Philip E. B. Jourdain
- Part II: Historical and Biographical
- Commentary
- 1. The Great Mathematicians by Herbert Westren Turnbull
- Commentary
- 2. The Rhind Papyrus by James R. Newman
- Commentary
- 4. Greek Mathematics by Ivor Thomas
- Robert Recorde: Commentary
- 5. The Declaration of the Profit of Arithmeticke by Robert Recorde
- Kepler and Lodge: Commentary
- 6. Johann Kepler by Sir Oliver Lodge
- Descartes and Analytical Geometry: Commentary
- 7. The Geometry by René Descartes
- Commentary
- 8. Isaac Newton by E. N. da C. Andrade
- 9. Newton, the Man by John Maynard Keynes
- Bishop Berkeley and Infinitesimals: Commentary
- 10. The Analyst by Bishop Berkeley
- Gauss: Commentary
- 11. Gauss, the Prince of Mathematicians by Eric Temple Bell
- Cayley and Sylvester: Commentary
- 12. Invariant Twins, Cayley and Sylvester by Eric Temple Bell
- Commentary
- 13. Srinivasa Ramanujan by James R. Newman
- Bertrand Russell: Commentary
- 14. My Mental Development by Bertrand Russell
- Alfred North Whitehead: Commentary
- 15. Mathematics as an Element in the History of Thought by Alfred North Whitehead
- Part III: Arithmetic, Numbers and the Art of Counting
- Poppy Seeds and Large Numbers: Commentary
- 1. The Sand Reckoner by Archimedes
- The Art of Counting: Commentary
- 2. Counting by Levi Leonard Conant
- 3. From Numbers to Numerals and From Numerals to Computation by David Eugene Smith and Jekuthiel Ginsburg
- Idiot Savants: Commentary
- 4. Calculating Prodigies by W. W. Rouse Ball
- Gifted Birds: Commentary
- 5. The Ability of Birds to "Count" by O. Koehler
- The Mysteries of Arithmetic: Commentary
- 6. The Queen of Mathematics by Eric Temple Bell
- $\left({P + P Q}\right)^{m / n}$: Commentary
- 7. On the Binomial Theorem for Fractional and Negative Exponents by Isaac Newton
- The Number Concept: Commentary
- 8. Irrational Numbers by Richard Dedekind
- 9. Definition of Number by Bertrand Russell
- Part IV: Mathematics of Space and Motion
- William Kingdon Clifford: Commentary
- 1. The Exactness of Mathematical Laws by William Kingdon Clifford
- 2. The Postulates of the Science of Space by William Kingdon Clifford
- 3. On the Space Theory of Matter by William Kingdon Clifford
- A Famous Problem: Commentary
- 4. The Seven Bridges of Königsberg by Leonhard Euler
- 5. Topology by Richard Courant and Herbert Robbins
- Dürer and the Mathematics of Painting: Commentary
- 6. Dürer as a Mathematician by Erwin Panofsky
- 7. Projective Geometry by Morris Kline
- Hermann von Helmholz: Commentary
- 8. On the Origin and Significance of Geometrical Axioms by Hermann von Helmholz
- Commentary
- 9. Symmetry by Hermann Weyl
- Part V: Mathematics and the Physical World
- Galileo Galilei: Commentary
- 1. Mathematics of Motion by Galileo Galilei
- The Bernoullis: Commentary
- 2. Kinetic Theory of Gases by Daniel Bernoulli
- A Great Prize, a Long-Suffering Inventor and the First Accurate Clock: Commentary
- 3. The Longitude by Lloyd A. Brown
- John Couch Adams: Commentary
- 4. John Couch Adams and the Discovery of Neptune by Harold Spencer Jones
- H. G. J. Moseley: Commentary
- 5. Atomic Numbers by H. G. J. Moseley
- The Small Furniture of Earth: Commentary
- 6. The Röntgen Rays by Sir William Bragg
- 7; Crystals and the Future of Physics by Philippe Le Corbeiller
- Queen Dido, Soap Bubbles, and a Blind Mathematician: Commentary
- 8. What Is Calculus of Variations and What Are Its Applications? by Karl Menger
- 9. The Soap-bubble by C. Vernon Boys
- 10. Plateau's Problem by Richard Courant and Herbert Robbins
- The Periodic Law and Mendeléeff: Commentary
- 11. Periodic Law of the Chemical Elements by Dmitri Mendeléeff
- 12. Mendeléeff by Bernard Jaffe
- Gregor Mendel: Commentary
- 13. Mathematics of Heredity by Gregor Mendel
- J. B. S. Haldane: Commentary
- 14. On Being the Right Size by J. B. S. Haldane
- 15. Mathematics of Natural Selection by J. B. S. Haldane
- Erwin Schrödinger: Commentary
- 16. Heredity and the Quantum Theory by Erwin Schrödinger
- D'Arcy Wentworth Thompson: Commentary'
- 17. On Magnitude by D'Arcy Wentworth Thompson
- Uncertainty: Commentary
- 18. The Uncertainty Principle by Werner Heisenberg
- 19. Causality and Wave Mechanics by Erwin Schrödinger
- Sir Arthur Stanley Eddington: Commentary
- 20. The Constants of Nature by Sir Arthur Stanley Eddington
- 21. The New Law of Gravitation and the Old Law by Sir Arthur Stanley Eddington
- Commentary
- 22. The Theory of Relativity by Clement V. Durell
- Part VI: Mathematics and Social Science
- The Founder of Psychophysics: Commentary
- 1. Gustav Theodor Fechner by Edwin G. Boring
- Sir Francis Galton: Commentary
- 2. Classification of Men According to Their Natural Gifts by Sir Francis Galton
- Thomas Robert Malthus: Commentary
- 3. Mathematics of Population and Food by Thomas Robert Malthus
- Cournot, Jevons, and the Mathematics of Money: Commentary
- 4. Mathematics of Value and Demand by Augustin Cournot
- 5. Theory of Political Economy by William Stanley Jevons
- A Distinguished Quaker and War: Commentary
- 6. Mathematics of War and Foreigh Politics by Lewis Fry Richardson
- 7. Statistics of Deadly Quarrels by Lewis Fry Richardson
- The Social Application of Mathematics: Commentary
- 8. The Theory of Economic Behavior by Leonid Hurwicz
- 9. Theory of Games by S. Vajda
- 10. Sociology Learns the Language of Mathematics by Abraham Kaplan
- Part VII: The Laws of Chance
- Pierre Simon de Laplace: Commentary
- 1. Concerning Probability by Pierre Simon de Laplace
- 2. The Red and the Black by Charles Sanders Peirce
- 3. The Probability of Induction by Charles Sanders Peirce
- Lord Keynes: Commentary
- 4. The Application of Probability to Conduct by John Maynard Keynes
- An Absent-minded Genius and Laws of Chance: Commentary
- 5. Chance by Henri Poincaré
- Ernest Nagel and the Laws of Probability: Commentary
- 6. The Meaning of Probability by Ernest Nagel
- Part VIII: Statistics and the Design of Experiments
- An Ingenious Army Captain and a Generous and Many-sided Man: Commentary
- 1. Foundations of Vital Statistics by John Graunt
- 2. First Life Insurance Tables by Edmund Halley
- Commentary
- 3. The Law of Large Numbers by Jacob Bernoulli
- Statistics and the Lady with a Fine Palate: Commentary
- 4. Sampling and Standard Error by L. C. Tippett
- 5. On the Average and Scatter by M. J. Moroney
- 6. Mathematics of a Lady Tasting Tea by Sir Ronald A. Fisher
- The Scientific Aptitude of George Bernard Shaw: Commentary
- 7. The Vice of Gambling and the Virtue of Insurance by George Bernard Shaw
- Part IX: The Supreme Act of Abstraction: Group Theory
- Certain Important Abstractions: Commentary
- 1. The Group Concept by Cassius J. Keyser
- 2. The Theory of Groups by Sir Arthur Stanley Eddington
- Part X: Mathematics of Infinity
- 1. Mathematics and the Metaphysicians by Bertrand Russell
- Hans Hahn: Commentary
- 2. Infinity by Hans Hahn
- Part XI: Mathematical Truth and the Structure of Mathematics
- The Foundations of Mathematics: Commentary
- 1. On the Nature of Mathematical Truth by Carl G. Hempel
- 2. Geometry and Empirical Science by Carl G. Hempel
- 3. The Axiomatic Method by Raymond L. Wilder
- 4. Goedel's Proof by Ernest Nagel and James R. Newman
- 5. A Mathematical Science by Oswald Veblen and John Wesley Young
- 6. Mathematics and the World by Douglas Gasking
- 7. Mathematical Postulates and Human Understanding by Richard von Mises
- Part XII: The Mathematical Way of Thinking
- An Eristic Controversy: Commentary
- 1. The Study That Knows Nothing of Observation by James Joseph Sylvester
- Charles Sanders Peirce: Commentary
- 2. The Essence of Mathematics by Charles Sanders Peirce
- Ernst Mach: Commentary
- 3. The Economy of Science by Ernst Mach
- Norman Robert Campbell: Commentary
- 4. Measurement by Norman Campbell
- 5. Numerical Laws and the Use of Mathematics in Science by Norman Campbell
- Hermann Weyl: Commentary
- 6. The Mathematical Way of Thinking by Hermann Weyl
- Part XIII: Mathematics and Logic
- Symbolic Logic, George Boole and a Horrible Dream: Commentary
- 1. Mathematical Analysis of Logic by George Boole
- 2. History of Symbolic Logic by Clarence Irving Lewis and Cooper Harold Langford
- 3. Symbolic Notation, Haddocks' Eyes and the Dog-Walking Ordinance by Ernest Nagel
- 4. Symbolic Logic by Alfred Tarski
- Part XIV: The Unreasonableness of Mathematics
- The Importance of Being Absurd: Commentary
- 1. Paradox Lost and Paradox Regained by Edward Kasner and James R. Newman
- 2. The Crisis in Intuition by Hans Hahn
- Part XV: How to Solve It
- 1. How to Solve It by G. Polya
- Part XVI: The Vocabulary of Mathematics
- Double Infinite Rapport and Other Mathematical Jargon: Commentary
- 1. New Names for Old by Edward Kasner and James R. Newman
- Part XVII: Mathematics as an Art
- John William Navin Sullivan: Commentary
- 1. Mathematics as an Art by John William Navin Sullivan
- Part XVIII: The Mathematician
- G. H. Hardy: Commentary
- 1. A Mathematician's Apology by G. H. Hardy
- The Elusiveness of Invention: Commentary
- 2. Mathematical Creation by Henri Poincaré
- The Use of a Top Hat as a Water Bucket: Commentary
- 3. The Mathematician by John von Neumann
- Part XIX: Mathematical Machines: Can a Machine Think?
- Automatic Computers: Commentary
- 1. The General And Logical Theory of Automata by John von Neumann
- 2. Can a Machine Think? by A. M. Turing
- 3. A Chess-Playing Machine by Claude Shannon
- Part XX: Mathematics in Warfare
- Frederick William Lanchester: Commentary
- 1. Mathematics in Warfare by Frederick William Lanchester
- 2. How to Hunt a Submarine by Phillip M. Morse and George E. Kimball
- Part XXI: A Mathematical Theory of Art
- George David Birkhoff: Commentary
- 1. Mathematics of Aesthetics by George David Birkhoff
- Part XXII: Mathematics of the Good
- 1. A Mathematical Approach to Ethics by George David Birkhoff
- Part XXIII: Mathematics in Literature
- The Island of Laputa: Commentary
- 1. Cycloid Pudding by Jonathan Swift
- Aldous Huxley: Commentary
- 2. Young Archimedes by Aldous Huxley
- Mr. Fortune: Commentary
- 3. Geometry in the South Pacific by Sylvia Townsend Warner
- Statistics as a Literary Stimulus: Commentary
- 4. Inflexible Logic by Russell Maloney
- 5. The Law by Robert M. Coates
- Part XXIV: Mathematics and Music
- Sir James Jeans: Commentary
- 1. Mathematics of Music by Sir James Jeans
- Part XXV: Mathematics as a Culture Clue
- Oswald Spengler: Commentary
- 1. Meaning of Numbers by Oswald Spengler
- 2. The Locus of Mathematical Reality: An Anthropological Footnote by Leslie A. White
- Part XXVI: Amusements, Puzzles, Fancies
- Augustus De Morgan, an Estimable Man: Commentary
- 1. Assorted Paradoxes by Augustus De Morgan
- A Romance of Many Dimensions: Commentary
- 2. Flatland by Edwin A. Abbott
- Lewis Carroll: Commentary
- 3. What the Tortoise Said to Achilles and Other Riddles by Lewis Carroll
- Continuity: Commentary
- 4. The Lever of Mahomet by Richard Courant and Herbert Robbins
- Games and Puzzles: Commentary
- 5. Pastimes of Past and Present Times by Edward Kasner and James R. Newman
- 6. Arithmetical Restorations by W. W. Rouse Ball
- 7. The Seven Seven's by W. E. H. Berwick
- Thomas John I'Anson Bromwich: Commentary
- 8. Easy Mathematics and Lawn Tennis by T. J. I'A. Bromwich
- Stephen Butler Leacock: Commentary
- 9. Mathematics for Golfers by Stephen Leacock
- 10. Common Sense and the Universe by Stephen Leacock
- Index
Sources
- 1964: William K. Smith: Limits and Continuity ... (previous) ... (next): $\S 1$: Introduction