THE 2001 MAA NORTH CENTRAL SECTION SUMMER SEMINAR

BOOKS ON THE HISTORY OF MATHEMATICS.

For this summer seminar, it would be very nice if we had a collection of books to consult. I really don't want to bring several boxes of books with me, so if you can find some of the things on the list below in your library, please bring it along. To avoid lots of copies of the same things, let's coordinate what you will bring by sending Ivy Knoshoag at  iknoshaug@bemidjistate.edu . Those items marked by a bold dot are available at Bemidji State University so there is no reason to bring along copies of them. You need not feel restricted to this list. Bring something interesting of a historical nature --- the more variety the merrier.

The following books deal with some aspect of the history of mathematics, with a heavy concentration on the history of the calculus. Only a few, Baron 1969a, Boyer 1959a, Edwards1979a, Grattan-Guinness 1980, and Toepliz 1963a deal with large portions of the history of calculus. The others concentrate on an individual, a period, or a concept.

This is a bibliography of secondary sources; original works have been excluded even though many collected works contain very valuable introductions. Textbooks and books not dealing mainly with the calculus have, in most instances, been excluded, but it would be nice to have some of them too. An attempt has been made to cover the whole history of the calculus and to deal with the major figures but no attempt has been made to be comprehensive.

• Aaboe, Asger
1985a Episodes from the early history of mathematics, 1963. A nice introduction to mesopotamian mathematics.
• Aiton, Eric J.
1985a Leibniz. A Biography, Bristol and Boston: Adam Hilger Ltd., ISBN 0-85274-470-6.

Anon.
1989a Historical topics for the mathematics classroom, Reston, Va.: National Council of Teachers of Mathematics.

• Baron, Margaret E.
1969a The Origins of the Infinitesimal
Calculus, Pergamon Press.  An extremely valuable history up to the time of Leibniz and Newton. Available through Dover.

Bottazzini, Umberto
1986  The higher calculus: a history of real and complex analysis from
Euler to Weierstrass, translated by Warren Van Egmond. New York : Springer-Verlag,

• Boyer, Carl B.
1939a The History of the Calculus and Its Conceptual
Development, 1959 Dover reprint.  The original title The Concepts of the Calculus, A Critical and Historical discussion of the Derivative and the Integral more aptly describes the contents. Read this book carefully, for the Whiggish view of history presented here is outdated. He praises anything hinting at the limit idea and disparages the use of infinitesimals.
• Boyer, Carl B.
1968a A history of mathematics, revised by Uta C. Merzbach
. Wiley, c1989. An excellent history. Useful as a textbook.

Bunt, Lucas N. H., Jones, Phillip S., and Bedient, Jack D.
1988a The historical roots of elementary mathematics, Dover Publications, 1988.

Cajori, Florian, 1859-1930.
1919a A History of the conceptions of Limits and Fluxions
in Great Britain from Newton to Woodhouse, Chicago and London: Open Court, viii + 299 pp.

• Cajori, Florian, 1859-1930.
1919a A history of mathematical notations,
Dover Publications, 1993 (originally 1928-29). If you have a question about notation, this is the place to look.

Calinger, Ronald
1976a Gottfried Wilhelm Leibniz, Edwin B. Allen
. Mathematics Memorial, Rensselaer Polytechnic Institute, Troy, NY., 102 pp.  The best short biography of Leibniz.

Child, James M.
1916a The Geometrical Lectures of Isaac Barrow, Chicago
and London: Open Court.

Child, James M.
1920a The Early Mathematical Manuscripts of Leibniz,
Chicago and London: Open Court.  Valuable for the translations of the manuscripts of Leibniz dating from 1675 when he was in the process of inventing the calculus. One should be very cautious of the commentary for Child is of the opinion that Leibniz stole some of his ideas from Barrow.

Cohen, I. Bernard
1971a Introduction to Newton's 'Principia,' Harvard
University Press. Reprinted in paperback, 1978.

• Coolidge, Julian Lowell, 1873-1954.
1949a The mathematics of great amateurs, second edition 1990 with an
introductory essay by Jeremy Gray.
• Dauben, Joseph W., and Lewis, Albert C., editors.
2000a The History of Mathematics from Antiquity to the Present:
A Selective Annotated Bibliography, Revised Edition on CD-ROM edited by Albert C. Lewis, in cooperation with the International Commission on the History of Mathematics. ISBN 0-8218-0844-3, List: $49, All AMS Members:$39. The CD-ROM version of this book is very useful for entry into the research literature on the history of mathematics. Each of the 4833 entries is arranged by topic and has a brief annotation.

Devlin, Keith J.
1999a  Mathematics: the new golden age, New York: Columbia University Press, c1999.
A high level expository work that contains a fair amount of history.

• Dunham, William
1979a Journey through genius: the great theorems of mathematics, Wiley, c1990.
• Dunham, William
1999a Euler: the master of us all, Mathematical Association of America.
• Edwards, Charles E., Jr.
1979a The Historical Development of the Calculus,
Springer.  A very good sketch. A book worth buying. This is perhaps the best book to read first.

Engelsman, Steven B.
1984a Families of Curves and the Origins of Partial
Differentiation, North-Holland Mathematical Studies, # 94.

• Eves, Howard Whitley, 1911-
1984a Great moments in mathematics,
Mathematical Association of America, c1980. Useful for historical topics that were presented as lectures. One volume deals with topics before 1650, the other with later topics.
• Fauvel, John and Gray, Jeremy
1987a The History of mathematics: a reader,
Open University, 1987. Available from the MAA. Excellent selection of original source materials with brief introductions.

Gillispie, Charles Coulston
1971a Lazare Carnot, Savant, Princeton University Press.

Goldstine, Herman H.
1977a A History of Numerical Analysis from the 16th
through the 19th Century, Springer. Reviewed by B.N.Parlett, BAMS, (n.s.) 1(1979), 388-390. Parlett's comment about a formula'' for $\sigma 1/n$ is wrong. Goldstein (p. 118) misquotes Hofmann who says Leibniz was never able to come to grips with $\sigma 1/{n^2}$.

Gowling, Ronald
1983a Roger Cotes--Natural Philosopher, Cambridge
University Press.

Grabiner, Judith V.
1981a The Origins of Cauchy's Rigorous Calculus, MIT
press.

Grattan-Guinness, Ivor
1970a The Development of the Foundations of analysis for
Euler to Riemann, MIT Press.

Grattan-Guinness, Ivor
1980a From the Calculus to Set Theory, 1630-1910. An
Introductory History, London: Duckworth.  The six chapters, by some of the best contemporary historians of mathematics, provide an excellent and detailed history of the discovery and development of the calculus. Reviews by M.Kline (Isis  72(1981), 661-662) and L.Feigenbaum (Centaurus  28(1985), 67-68) point out that this work is hardly suitable for undergraduates and concentrates on the foundations of the calculus. This has been reprinted by Princeton University Press.

• Grattan-Guinness, Ivor
1998a The Norton history of the mathematical sciences : the rainbow of
mathematics, W.W. Norton, 1998. A general history of mathematics that contains a good deal of information about applications.
• Hall, Rupert A.
1980a Philosophers at War. The Quarrel Between Newton
and Leibniz, Cambridge University Press.  Useful for the general scientific background, but the mathematics is not treated. Reviewers have pointed out a number of difficulties with the work. See H.Bernstein, Am. Sci., 69(1981), 110; J.L.Greenberg, Ann. Sci., 38(11981), 591-596; and J.R.Jacob, Isis, 72(1981), 683-684, but it is an excellent source on the Newton-Leibniz priority dispute.

Hankins, Thomas L.
1970a Jean d'Alembert. Science and the Enlightenment,
Oxford: Clarendon Press.

Hairer, E., and Wanner, G.
1996a  Analysis by Its History, Springer.

Hawkins, Thomas
1970a Lebesgue's Theory of Integration. Its Origins and
Development, University of Wisconsin Press. Reprinted by Chelsea.

• Hofmann, Joseph E.
1974a Leibniz in Paris, 1672-1676. His Growth to
Mathematical Maturity, Cambridge University Press. Revised English translation of the 1949 German original. Reviewed by A. Weil, BAMS,  81(1975), 676-688.
• Hollingdale, Stuart, 1910-
1974a Makers of mathematics, London : Penguin, 1989.
A nice collection of biographical sketches that include some mathematical detail.

Joseph, George Gheverghese
1991a The crest of the peacock: non-European roots of mathematics,
London; New York: I.B. Tauris, 1991.

• Katz, Victor J.
1993a A history of mathematics: an introduction,
HarperCollins College Publishers, c1993.

Kennedy, Hubert C.
1980a Peano. Life and Works of Giuseppe Peano, Dordrecht:
D. Reidel. Available in paperback.

• Kline, Morris
1972a Mathematical thought from ancient to modern times,
reprinted 1990. This is where I go when I want to learn the history of some topic where I don't already know the mathematics, for he does a good job of explaining it. However, I have learned to be cautious of his historical details. But he gives good references.
• Kline, Morris
1980a Mathematics, the loss of certainty. New York : Oxford University Press.

Loria, Gino
Spezielle algebraische und transscendente ebene Kurven.
Theorie und Geschichte, Leipzig: Teubner. Two volumes.

• Mahoney, Michael Sean
1973a The Mathematical Career of Pierre De Fermat (1601-1665), Princeton University Press.

Manuel, Frank E.
1979a A Portrait of Isaac Newton, New Republic Books,
Washington, D.C. Paperback, 1968, Harvard University Press.

Reiff, R.
1889a Geschichte der unendlichen Reihen, München.
Reprinted 1969, Wiesbaden: Dr. Martin Sändig oHG.

Resnikoff, H. L., and Wells, R. O., Jr.
1984a Mathematics in civilization, Dover Publications.

Rose, Paul Lawrence
1975a The Italian Renaissance of mathematics: studies on
humanists and mathematicians from Petrarch to Galileo, Genéve: Librairie Droz. A lovely book.

• Rowe, David E., and McCleary, John, editors.
1889a The history of modern mathematics:
proceedings of the Symposium on the History of Modern Mathematics, Vassar College, Poughkeepsie, New York, June 20-24, 1988.
• Simmons, George Finlay, 1925-
1992a Calculus gems: brief lives and memorable mathematics, McGraw-Hill, c1992.
A lovely book, most useful to the calculus teacher.

Smith, Sanderson M.
1996a Agnesi to Zeno: over 100 vignettes from the history of math,
Key Curriculum Press, 1996. Useful for topics in the pre-calculus curriculum, but always be cautious of books like this.

• Stillwell, John
1989a Mathematics and its history, Springer-Verlag.
A way to learn lots of mathematics in a historical setting.

Struik, Dirk J. (b. 1894)
1981a The Land of Stevin and Huygens. A Sketch of Science
and Technology in the Dutch Republic during the Golden Century, D. Reidel Publishing Company, Dordrecht and Boston. Translation of the Dutch original of 1958.

Swetz, Frank
1987a Capitalism and arithmetic: the new math of the 15th century,
including the full text of the Treviso arithmetic of 1478, translated by David Eugene Smith, Open Court, 1987.

Toeplitz, Otto
1963a The Calculus. A Genetic Approach, University of
Chicago Press.

Tweedie, Charles
1922a James Stirling. A Sketch of his Life and Works along
with his Scientific Correspondence, Oxford: Clarendon.

van Dalen, D and Monna, A. F.
1972a Sets and Integration. An Outline of the Development,
Wolters-Noordhoff Publishing, Groningen, The Netherlands.

Walker, Evelyn
1932a A Study of the Traité des Indivisibles of Gilles
Persone de Roberval, Teachers College, Columbia University.

Wallis, Joseph Frederick
1938a The Mathematical Work of John Wallis, D.D.,
F.R.S. (1616-1703), London. Reprinted 1981 by Chelsea.

Wallis, Joseph Frederick
1952a The Scientific Work of René Descartes (1596-1650), London: Taylor and Francis.

• Westfall, Richard S.
1980a Never at Rest. A Biography of Isaac Newton,
Cambridge University Press. Paperback edition 19??.

The above works were found by searching the following subjects in various library catalogues:

• Mathematics---History.
• Mathematics--Popular works.
• Mathematics-History--20th century.

When you find one book that interests you, click on one of the subject headings and you will find all books so classified. Also you will get a list of `nearby' subject headings.

Alas it will not be possible to have a display of rare mathematical works, so you will have to be satisfied with a virtual book display:

And if you simply must have your own rare book, here is one place to look: