Contents: Topics in the history of mathematics and their philosophical background. Genesis and evolution of ideas in analysis, algebra, geometry, mechanics, foundations. Historical and philosophical aspects of concepts of infinity, mathematical rigor, probability, etc. The emergence of mathematical schools.
Particulars: Prerequisites: Math 112, 112Z, 112S or permission of the instructor. This year's offering focuses on the emergence of the Calculus in the XVII and XVIII centuries. The beginnings of Probability Theory will also be considered.
Textbook:
There will be many readings from different sources, including original ones. A good general overview is I. Grattan-Guinness, The Rainbow of Mathematics , W. W. Norton and Co., New York and London, 1997.
1. Galileo Galilei (1564-1642)
From The Assayer (1623), Translated with an Introduction and Notes by Stillman Drake, Random House, New York, NY, 1957; pages 237-238 and 267-269. Click here.
From Dialogues Concerning Two New Sciences (1638), Translated by Henry Crew and Alfonso de Salvio, with an Introduction by Antonio Favaro, Dover Publications, Inc., New York, 1954; pages 1-63. Click here.
2. Rene` Descartes (1596-1650)
From Rules for Guiding One's Intelligence in Searching for the Truth (1628). In Discourse on Method and Related Writings , Translated with an Introduction by Desmond M. Clarke, Penguin Classics, London, 1999; pages 115-130. Click here.
From Geometry (1637). Translated by David E. Smith and Marcia L. Latham, Thirtieth printing, Encyclopaedia Britannica, Inc., Chicago, IL, 1988; pages 295-308. Click here.
3. Pierre de Fermat (1601-1655)
From On a Method for the Evaluation of Maxima and Minima (1637). Translated by Dirk J. Struik, in Classics of Mathematics, Edited by Ronald Calinger, Moore Publishing Company, Inc., Oak Park, IL, 1982; pages 339-342. Click here.
4. Blaise Pascal (1623-1662)
From The Spirit of Geometry (1662), in The Logic of Port Royal, by Antoine Arnauld and Pierre Nicole, available at Eightheenth Century Collection Online; pages 385-387. Click here.
The Wager, no.~233 from the Pensees (ca.~1657). Click here.
5. Thomas Hobbes (1588-1679)
From Leviathan (1655). Revised student edition. Edited by Richard Tuck, Cambridge University Press, Cambridge, 1996; pages 24-31. Click here.
6. Baruch Spinoza (1632-1677)
From The Letters (ca. 1660-1670). Translated by Samuel Shirley, Introduction and Notes by Steven Barbone, Lee Rice, and Jacob Adler, Hackett Publishing Co., Inc. Indianapolis/Cambridge, 1995.
From letter no. 9, pages 91-92. Click here.
From letter no. 56, pages 278-279. Click here.
7. John Locke (1632-1704)
Of Probability, Chapter XXV from An Essay Concerning Human Understanding (1690). Edited with a Foreword by Peter H. Nidditch, Oxford University Press, 1987; pages 654-657. Click here.
8. Gottfried Wilhelm Leibniz (1646-1716)
Of Probability, Chapter XV from New Essays on Human Understanding (1704). Translated and edited by Peter Remnant and Jonathan Bennett, Cambridge University Press, 1981; pages 457-459. Click here.
See no. 11 below for additional texts by Leibniz.
9. John Wallis (1616-1703)
Proposition 191 ("Wallis' formula") from The Arithmetic of Infinitesimals (original title: Arithmetica Infinitorum) (1656). Translated from Latin to English with an introduction by Jacqueline A. Stedall, Springer-Verlag, New Yoor, 2005; pages 164-167. Click here.
10. Isaac Newton (1642-1727)
From Letter to Henry Oldenburg on the Binomial Series and from Letter to Henry Oldenburg on General Method for Finding Quadratures (1676). Translated by H. W. Turnbull, in Classics of Mathematics, Edited by Ronald Calinger, Moore Publishing Company, Inc., Oak Park, IL, 1982; pages 361-367. Click here.
From Mathematical Principles of Natural Philosophy (1687): Lemmata and scholium on "prime and ultimate ratios" (Book I, Section I) and on "moments" (Book II). Translation by Andrew Motte, revised by Florian Cajori, in Classics of Mathematics, Edited by Ronald Calinger, Moore Publishing Company, Inc., Oak Park, IL, 1982; pages 368-375. Click here.
From Introduction to the "Tractatus de Quadratura Curvarum" (1704). Translation by J. Stewart in Classics of Mathematics, Edited by Ronald Calinger, Moore Publishing Company, Inc., Oak Park, IL, 1982; pages 376-380. Click here.
From Mathematical Principles of Natural Philosophy (1687):
Author's Preface; pp. 1-2. Click here.
Scholium on Absolute Time and Absolute Space; pp. 1-13. Click here.
Axioms, or Laws of motion, with Corollaries; pp. 14-19. Click here.
Book I: The Motion of Bodies. Section 11: Scholium on Attraction; pp. 130-131. Click here.
Book III: System of the World (In Mathematical Treatment). Rules of Reasoning in Philosophy; pp. 269-271. Click here.
Book III: General Scholium; pp. 369-372. Click here.
From Optics (2nd Ed., 1717):
Queries 28, 30, 31; pp. 535-544. Click here.
11. Gottfried Wilhelm Leibniz (1646-1716)
From A New Method for Maxima and Minima as Well as Tangents, Which is Impeded Neither by Fractional nor by Irrational Quantities, and a Remarkable Type of Calculus for This (1684), and from the Supplementum Geometriae Dimensoriae... (1693). Translated by Dirk J. Struik, in Classics of Mathematics, Edited by Ronald Calinger, Moore Publishing Company, Inc., Oak Park, IL, 1982; pages 348-356. Click here.
From Discourse on Metaphysics (1686), parts 17-22. Edited and translated by Daniel Garber and Roger Ariew, Hackett, Indianapolis, IN, 1991; pages 69-75. Click here.
12. Johann Bernoulli (1667-1748)
From The Curvature of a Ray in Nonuniform Media (1697), with a biographical note by R. Calinger. Translated by Dirk J. Struik, in Classics of Mathematics, Edited by Ronald Calinger, Moore Publishing Company, Inc., Oak Park, IL, 1982; pages 389-392. Click here.
13. Pierre Moreau de Maupertuis (1698-1759)
14. Leonhard Euler (1707-1783)
15. Jean Le Rond D'Alembert (1717-1783)
From "Differential" (Encyclopedie, Vol.4) (1754), with a biographical note by R. Calinger. Translated by Dirk J. Struik, in Classics of Mathematics, Edited by Ronald Calinger, Moore Publishing Company, Inc., Oak Park, IL, 1982; pages 433-438. Click here.