# Book:James R. Newman/The World of Mathematics

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## James R. Newman:

## 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

- 1. Mathematics and the Metaphysicians

*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

- 1. How to Solve It

- 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

- 1. A Mathematical Approach to Ethics

- 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