Book:James R. Newman/The World of Mathematics

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James R. Newman: The World of Mathematics

Published $1956$, George Allen and Unwin Ltd.


Subject Matter

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
3. Archimedes by Plutarch, Vitruvius, Tzetzes
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