Concise History of Mathematics by
INTRODUCTION
I. THE BEGINNINGS
II. THE ANCIENT ORIENT
III. GREECE
IV. THE ORIENT AFTER THE DECLINE OF GREEK SOCIETY
V. THE BEGINNINGS IN WESTERN EUROPE
VI. THE SEVENTEENTH CENTURY
VII. THE EIGHTEENTH CENTURY
VIII. THE NINETEENTH CENTURY
IX. THE FIRST HALF OF THE TWENTIETH CENTURY
Critical Appraisal of Physical Science As a Human Enterprise by
Introduction
Quantitative imperative vs the imperative of presuppositions
Understanding scientific progress: From Duhem to Lakatos
Kinetic theory: Maxwell’s Presuppositions
Periodic table of the chemical elements: From Mendeleev to Moseley
Foundations of modern atomic theory: Thomson, Rutherford, and Bohr
Determination of the elementary electrical charge: Millikan and Ehrenhaft
Paradox of the photoelectric effect: Einstein and Millikan
Bending of light in the 1919 eclipse experiments: Einstein and Eddington
Lewis’s covalent bond: From transfer of electrons to sharing of electrons
Quantum mechanics: From Bohr to Bohm
Wave-particle duality: De Broglie, Einstein and Schrödinger
Searching for quarks: Perl’s philosophy of speculative experiments
Conclusion: Inductive method as a chimera
Great Physicists: the life and times of leading physicists from Galileo to Hawking by
I. Mechanics
Historical Synopsis
How the Heavens Go Galileo Galilei
A Man Obsessed Isaac Newton
II Thermodynamics
Historical Synopsis
A Tale of Two Revolutions Sadi Carnot
On the Dark Side Robert Mayer
A Holy Undertaking James Joule
Unities and a Unifier Hermann Helmholtz
The Scientist as Virtuoso William Thomson
The Road to Entropy Rudolf Clausius
The Greatest Simplicity Willard Gibbs
The Last Law Walther Nernst
III. Electromagnetism
Historical Synopsis
A Force of Nature Michael Faraday
The Scientist as Magician James ClerkMaxwell
IV. Statistical Mechanics
Historical Synopsis
Molecules and Entropy Ludwig Boltzmann
V. Relativity
Historical Synopsis
Adventure in Thought Albert Einstein
VI. Quantum Mechanics
Historical Synopsis
Reluctant Revolutionary Max Planck
Science by Conversation Niels Bohr
The Scientist as Critic Wolfgang Pauli
Matrix Mechanics Werner Heisenberg
Wave Mechanics Erwin Schrodinger and Louis de Broglie
VII. Nuclear Physics
Historical Synopsis
Opening Doors Marie Curie
On the Crest of a Wave Ernest Rutherford
Physics and Friendships Lise Meitner
Complete Physicist Enrico Fermi
VIII. Particle Physics
Historical Synopsis
What Do You Care? Richard Feynman
Telling the Tale of the Quarks Murray Gell-Mann
IX. Astronomy, Astrophysics, and Cosmology
Historical Synopsis
Beyond the Galaxy Edwin Hubble
Ideal Scholar Subrahmanyan Chandrasekhar
Affliction, Fame, and Fortune Stephen Hawking
Chronology of the Main Events
A History of Mathematics by
Origins.
Egypt.
Mesopotamia.
Ionia and the Pythagoreans.
The Heroic Age.
The Age of Plato and Aristotle.
Euclid of Alexandria.
Archimedes of Syracuse.
Apollonius of Perga.
Greek Trigonometry and Mensuration.
Revival and Decline of Greek Mathematics.
China and India.
The Arabic Hegemony.
Europe in the Middle Ages.
The Renaissance.
Prelude to Modern Mathematics.
The Time of Fermat and Descartes.
A Transitional Period.
Newton and Leibniz.
The Bernoulli Era.
The Age of Euler.
Mathematicians of the French Revolution.
The Time of Gauss and Cauchy.
Geometry.
Analysis.
Algebra.
Poincare and Hilbert.
Aspects of the Twentieth Century.
References.
General Bibliography.
Appendix.
Index.
A History of Mathematics by
Table of Contents
I. MATHEMATICS BEFORE THE SIXTH CENTURY.
Ancient Mathematics.
The Beginnings of Mathematics in Greece.
Archimedes and Apollonius.
Mathematical Methods in Hellenistic Times.
The Final Chapters of Greek Mathematics.
II. MEDIEVAL MATHEMATICS: 500-1400.
Medieval China and India.
The Mathematics of Islam.
Mathematics in Medieval Europe.
Mathematics Around the World.
III. EARLY MODERN MATHEMATICS: 1400-1700.
Algebra in the Renaissance.
Mathematical Methods in the Renaissance.
Geometry, Algebra, and Probability in the Seventeenth Century.
The Beginnings of Calculus.
IV. MODERN MATHEMATICS: 1700-2000.
Analysis in the Eighteenth Century.
Probability, Algebra, and Geometry in the Eighteenth Century.
Algebra in the Nineteenth Century.
Analysis in the Nineteenth Century.
Geometry in the Nineteenth Century.
Aspects of the Twentieth Century.
Answers to Selected Problems.
General References in the History of Mathematics.
Index and Pronunciation Guide.
Mathematics and the Historian's Craft by
Introduction: The Birth and Growth of a Community
History or Heritage? An Important Distinction in Mathematics and for Mathematics Education
Ptolemy’s Mathematical Models and their Meaning
Mathematics, Instruments and Navigation, 1600-1800
Was Newton’s Calculus a Dead End? The Continental Influence of Maclaurin’s Treatise of Fluxions
The Mathematics and Science of Leonhard Euler (1707-1783)
Mathematics in Canada before 1945: A Preliminary Survey
The Emergence of the American Mathematical Research Community
19th Century Logic Between Philosophy and Mathematics
The Battle for Cantorian Set Theory
Hilbert and his Twenty-Four Problems
Turing and the Origins of AI,
Mathematics and Gender: Some Cross-Cultural Observations
Quirky Sides of Scientists by
Tenacity and Stubbornness: Einstein on Theory and Experiment
Convergence or Coincidence: Ancient Measurements of the Sun and Moon—How Far?
The Rationality of Simplicity: Copernicus on Planetary Motion
The Silence of Scientists: Venus’s Brightness, Earth’s Precession, and the Nebula in Orion
Progress Through Error: Stars and Quasars—How Big, How Far?
The Data Fit the Model but the Model is Wrong: Kepler and the Structure of the Cosmos
Art Illustrates Science: Galileo, a Blemished Moon, and a Parabola of Blood
Ensnared in Circles: Galileo and the Law of Projectile Motion
Aesthetics and Holism: Newton on Light, Color, and Music
Missing One’s Own Discovery Newton and the First Idea of an Artificial Satellite
A Change of Mind: Newton and the Comet(s?) of 1680 and 1681
A Well-Nigh Discovery: Einstein and the Expanding Universe.
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