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 notation*s, 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
Histor*y, 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:

- Some rare books in the library at West Point. More pictures will be added in August.
- Some items the department at West Point. More pictures will be added in August.
- Rare Math Books at the University of Michigan,
- Rare books at the Smithsonian.
- Rare books at American University.

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

Prepared by V. Frederick Rickey, July 2001. Send comments to fred-rickey@usma.edu .