Reading List on History of Special Topics in Mathematics

Prepared by Victor Katz.

Ancient Mathematics

Otto Neugebauer, The Exact Sciences in Antiquity (Princeton: Princeton University Press, 1951)

B. L. van der Waerden, Science Awakening I (New York: Oxford University Press, 1961)

B. L. van der Waerden, Geometry and Algebra in Ancient Civilizations (New York: Springer, 1983)

Jens Høyrup, Lengths, Widths, Surfaces:  A Portrait of Old Babylonian Algebra and Its Kin (New York:  Springer, 2002)

Richard J. Gillings, Mathematics in the Time of the Pharaohs (Cambridge: MIT Press, 1972)

Li Yan and Du Shiran, Chinese Mathematics: A Concise History, translated by John N. Crossley and Anthony W. C. Lun (Oxford: Clarendon Press, 1987)

Jean-Claude Martzloff, A History of Chinese Mathematics, translated by Stephen S. Wilson (Berline:  Springer,  1997)

Shen Kangshen, John S. Crossley and Anthony W.-C. Lun, The Nine Chapters on the Mathematical Art:  Companion and Commentary (Oxford:  Oxford University Press, 1999)

B. Datta and A. N. Singh, History of Hindu Mathematics (Bombay: Asia Publishing House, 1961) (reprint of 1935-38 original)

Denise Schmandt-Besserat, Before Writing: From Counting to Cuneiform (Austin: University of Texas Press, 1992)

Greek Mathematics

Thomas Heath, A History of Greek Mathematics (New York: Dover, 1981) (reprint of 1921 original)

Wilbur Knorr, The Evolution of the Euclidean Elements (Dordrecht: Reidel, 1975)

Wilbur Knorr, The Ancient Tradition of Geometric Problems (New York: Dover, 1993) (reprint of 1986 original)

D. H. Fowler, The Mathematics of Plato's Academy: A New Reconstruction (Oxford: Clarendon Press, 1987, 1999)

J. Klein, Greek Mathematical Thought and the Origin of Algebra (Cambridge: MIT Press, 1968)

E. J. Dijksterhuis, Archimedes (Princeton: Princeton University Press, 1987)

S. Cuomo, Ancient Mathematics (London: Routledge, 2001)

Benno Artmann, Euclid: The Creation of Mathematics (New York:  Springer, 1999)

Michael N. Fried and Sabetai Unguru, Apollonius of Perga’s Conica: Text, Context, Subtext (Leiden, Brill, 2001)

Reviel Netz, The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History (Cambridge:  Cambridge University Press, 1999)

Medieval Mathematics

Ulrich Libbrecht, Chinese Mathematics in the Thirteenth Century: The Shu-shu chiu-chang of Ch'in Chiu-shao (Cambridge: MIT Press, 1973)

J. Lennart Berggren, Episodes in the Mathematics of Medieval Islam (New York: Springer, 1986)

George Gheverghese Joseph, The Crest of the Peacock: Non-European Roots of Mathematics (Princeton:  Princeton University Press, 2000)

Edward Grant and John E. Murdoch, eds., Mathematics and Its Applications to Science and Natural Philosophy in the Middle Ages: Essays in honor of Marshall Clagett (Cambridge: Cambridge University Press, 1987)

David E. Lindberg, ed., Science in the Middle Ages (Chicago: University of Chicago Press, 1978)

Roshdi Rashed, The Development of Arabic Mathematics:  Between Arithmetic and Algebra, translated by A. F. W. Armstrong  (Dordrecht:  Kluwer Academic Publishers, 1994)

Algebra and Number Theory

B. L. van der Waerden, A History of Algebra from al-Khwarizmi to Emmy Noether (New York: Springer, 1985)

Lubos Novy, Origins of Modern Algebra (Prague: Academia Publishing House, 1973)

Hans Wussing, The Genesis of the Abstract Group Concept (Cambridge: MIT Press, 1984)

André Weil, Number Theory: An Approach through History from Hammurapi to Legendre (Boston:  Birkhäuser, 1984)

Leo Corry, Modern Algebra and the Rise of Mathematical Structures (Boston: Birkhäuser, 1996)

Helena M. Pycior, Symbols, Impossible Numbers, and Geometric Entanglements:  British Algebra Through the Commentaries on Newton’s Universal Arithmetick (Cambridge:  Cambridge University Press, 1997)

Geometry

Carl Boyer, History of Analytic Geometry (New York: Scripta Mathematica, 1956)

Jeremy Gray, Ideas of Space: Euclidean, Non-Euclidean and Relativistic (Oxford: Clarendon Press, 1989)

Boris Rosenfeld, A History of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space, trans. by Abe Shenitzer (New York: Springer, 1988)

Michael J. Crowe, A History of Vector Analysis (New York: Dover, 1985)

Calculus and Analysis

Carl Boyer, The History of the Calculus and its Conceptual Development (New York: Dover, 1959)

Margaret E. Baron, The Origins of the Infinitesimal Calculus (Oxford: Pergamon Press, 1969)

C. H. Edwards, The Historical Development of the Calculus (New York: Springer, 1979)

Ivor Grattan-Guinness, ed. From the Calculus to Set Theory, 1630- 1910: An Introductory History (London: Duckworth, 1980)

Umberto Bottazzini, The Higher Calculus: A History of Real and Complex analysis from Euler to Weierstrass (New York: Springer, 1986)

Ivor Grattan-Guinness, The Development of the Foundations of Mathematical Analysis from Euler to Riemann (Cambridge: MIT Press, 1970)

Judith V. Grabiner, The Origins of Cauchy's Rigorous Calculus (Cambridge: MIT Press, 1981)

Niccolò Guicciardini, Reading the Principia: The Debate on Newton’s Mathematical Methods for Natural Philosophy from 1687 to 1736 (Cambridge:  Cambridge University Press, 1999)

Probability and Statistics

F. N. David, Games, Gods, and Gambling (New York: Hafner, 1962)

Ian Hacking, The Emergence of Probability (Cambridge: Cambridge University Press, 1975)

Ian Hacking, The Taming of Chance (Cambridge: Cambridge University Press, 1990)

Stephen M. Stigler, The History of Statistics (Cambridge: Harvard University Press, 1986)

Lorraine Daston, Classical Probability in the Enlightenment (Princeton: Princeton University Press, 1988)

Theodore M. Porter, The Rise of Statistical Thinking (Princeton: Princeton University Press, 1986)

Gerd Gigerenzer et al, The Empire of Chance: How Probability Changed Science and Everyday Life (Cambridge: Cambridge University Press, 1989)

Lorenz Krüger, Lorraine J. Daston, and Michael Heidelberger, eds., The Probabilistic Revolution (2 volumes) (Cambridge: MIT Press, 1987)

Anders Hald, A History of Probability and Statistics and Their Applications before 1750 (New York: Wiley, 1990)

Anders Hald,  A History of Mathematical Statistics from 1750 to 1930 (New York:  Wiley, 1998)

Foundations of Mathematics

Gregory H. Moore, Zermelo's Axiom of Choice: Its Origins, Development, and Influence (New York: Springer, 1982)

Alejandro R. Garciadiego, Bertrand Russell and the Origins of the Set-Theoretic "Paradoxes" (Basel: Birkhäuser, 1992)

I. Grattan-Guinness, The Search for Mathematical Roots, 1870-1940:  Logics, Set Theories and the Foundations of Mathematics from Cantor Through Russell to Gödel (Princeton:  Princeton University Press, 2000)

Ethnomathematics

Claudia Zaslavsky, Africa Counts: Number and Pattern in African Culture, 3rd edition (Chicago:  Lawrence Hill Books, 1999)

Marcia Ascher, Ethnomathematics: A Multicultural View of Mathematical Ideas (Pacific Grove, Ca.: Brooks/Cole, 1991)

Marcia Ascher, Mathematics Elsewhere: An Exploration of Ideas Across Cultures (Princeton:  Princeton University Press, 2002)

Helaine Selin, ed., Mathematics Across Cultures:  The History of Non-Western Mathematics (Dordrecht:  Kluwer, 2000)

 


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If you have comments, send email to V. Frederick Rickey at fred-rickey@usma.edu .
Revision posted 7 January 2003.