More Than Just a Grade: The HOM SIGMAA Student Contest Fosters Writing Excellence at UMKC - Appendix 2 (Researching the History of Mathematics)

Richard Delaware (University of Missouri – Kansas City)

This Appendix includes information on researching the History of Mathematics which I share with  students in my course.

Print Sources

Sources of Original Mathematical Documents in Translation

  • A Source Book in Mathematics, David Eugene Smith, Dover, 1959.
  • A Source Book in Mathematics, 1200-1800, ed. Dirk J. Struik, Harvard University Press, 1969.
  • Classics of Mathematics, ed. Ronald Calinger, Prentice Hall, 1995.
  • The History of Mathematics: A Reader, ed. John Fauvel & Jeremy Gray, Open University, MacMillan Press, 1987.
  • Pi: A Source Book, J. L. Berggren, Jonathan Borwein, & Peter Borwein, Springer Verlag, 1997.
  • A Source Book in Medieval Science, ed. Edward Grant, Harvard University Press, 1974.
  • From Kant to Hilbert: A Source Book in the Foundations of Mathematics, Vols 1 & 2, William B. Ewald, Oxford University Press, 1996.
  • A Source Book in Classical Analysis, Garrett Birkhoff, Harvard University Press, 1973.
  • Euclid, the Thirteen Books of the Elements, vols 1,2,3, trans. by Thomas L. Heath, Dover, 1956.
  • Contributions to the Founding of the Theory of Transfinite Numbers, Georg Cantor (1915), Dover, 1955.
  • The Early Theory of Equations: On Their Nature and Constitution, Golden Hind Press, 1986, contains translations of (pp.1–104) On the Recognition of Equations, by François Viète, 1615; (pp. 105–148) A New Discovery in Algebra, by Albert Girard, 1629; (pp. 149–218) On the Nature and Constitution of Equations, by Florimond de Beaume, 1657.
  • The Mathematics of Egypt, Mesopotamia, China, India, and Islam, A Sourcebook, ed. Victor J. Katz et al., Princeton University Press, 2007.
  • Sources in the Development of Mathematics – Series and Products from the 15th to the 21st century, Ranjan Roy, Cambridge University Press, 2011.
  • Mathematics Emerging: A Sourcebook 1540-1900, Jacqueline Stedall, Oxford, 2008.
  • Sourcebook in the Mathematics of Medieval Europe and North Africa, ed. Victor J. Katz et al., Princeton, 2016.

General Histories of Mathematics and References

  • A History of Greek Mathematics, vols 1,2, Thomas L. Heath, Dover, 1981 (1921).
  • Mathematical Thought from Ancient to Modern Times, Morris Kline, vols 1,2,3, Oxford Univ. Press, 1972.
  • Great Moments in Mathematics (Before 1650), Howard Eves, Dolciani Mathematical Expositions, Mathematical Association of America (MAA), 1983.
  • Great Moments in Mathematics (After 1650), Howard Eves, Dolciani Mathematical Expositions, MAA, 1983.
  • Math through the Ages: A Gentle History for Teachers and Others, William P. Berlinghoff and Fernando Q. Gouvêa, expanded second edition, MAA 2015.
  • Non-Euclidean Geometry, Roberto Bonola, Dover, 1955. [Includes translations of Bolyai and Lobachevsky papers.]
  • A History of Numerical Analysis from the 16th through the 19th Century, Herman H. Goldstine, Springer, 1977.
  • The Mathematics of the Heavens and the Earth: The Early History of Trigonometry, Glen Van Brummelen, Princeton, 2009.
  • A History of Algorithms, From the Pebble to the Microchip, Jean-Luc Chabert et al., Springer, 1999.

Specific Problems or Theorems

  • The Trisection Problem, Robert C. Yates, National Council of Teachers of Mathematics (NCTM) Classics in Mathematics Education, 1971.
  • The Pythagorean Proposition, Elisha Scott Loomis, NCTM Classics in Mathematics Education, 1972.
  • 100 Great Problems of Elementary Mathematics, Their History and Solution, Heinrich Dorrie, trans. by David Antin, Dover, 1965.
  • A Mathematical History of the Golden Number, Roger Herz-Fischler, Dover, 1987.

Individual Mathematicians

  • Archimedes, E. J. Dijksterhuis, Princeton Univ. Press, 1987.
  • Archimedes: What Did He Do Besides Cry Eureka?, Sherman Stein, Mathematical Association of America, 1999.
  • The Works of Archimedes, with the Method … , Thomas L. Heath, Dover, 1897.
  • Archimedes in the Middle Ages, 10 vol., Marshall Clagett, University of Wisconsin, 1964.
  • Aristarchus of Samos, The Ancient Copernicus, Thomas L. Heath (1913), Dover, 1981.
  • Diophantus of Alexandria, A Study in the History of Greek Algebra, Thomas L. Heath, Dover, 1885.
  • Leonardo Pisano (Fibonacci): Liber Abaci (Book of Calculation, 1202), trans. L.E. Sigler, Springer Verlag, 2002.
  • Leonardo Pisano (Fibonacci): Liber Quadratorum (Book of Squares, 1225), trans. L.E. Sigler, Springer Verlag, 1987.
  • Nicolas Chuquet, Renaissance Mathematician, ed. Graham Flegg et al., Springer, 1985, translation of parts of Triparty, 1494.
  • Cardano, the Gambling Scholar, Oystein Ore (1953), Dover, 1965.
  • Galileo Galilei: Two New Sciences, etc., trans. Stillman Drake, Univ. of Wisconsin Press, 1974.
  • The Analytic Art, Francois Viete, trans. by T. Richard Witmer, Kent State University Press, 1983.
  • Nicole Oresme and the Medieval Geometry of Qualities, ed. Marshall Clagett, Wisconsin, 1968.
  • John Wallis, The Arithmetic of Infinitesimals, 1656, trans. by Jacqueline Stedall, Springer, 2004.
  • Euler, The Master of Us All, William Dunham, Dolciani Mathematical Expositions, MAA, 1999.
  • The Mathematical Career of Pierre de Fermat 1601-1665, Michael Sean Mahoney, Princeton Univ. Press, 1973 (2nd Edition, 1994).
  • Kepler's Physical Astronomy, Bruce Stephenson, Springer-Verlag, 1987.
  • The Mathematical Works of Bernard Bolzano, Steve Russ, Oxford, 2005.
  • Cauchy’s Cours D’Analyse, annotated translation by Rob Bradley and Ed Sandifer, Springer, 2009.
  • Georg Cantor: His Mathematics and Philosophy of the Infinite, Joseph Dauben, Harvard University Press, 1990.

Chinese and Japanese Mathematics History

  • Chinese Mathematics in the Thirteenth Century, Ulrich Libbrecht, Dover, 1973.
  • Fleeting Footsteps: Tracing the Conception of Arithmetic and Algebra in Ancient China, Lam Lay Yong and Ang Tian Se, World Scientific, 1992.
  • A History of Japanese Mathematics, David Eugene Smith and Yoshio Mikami, Dover, 1914.

Islamic Mathematics

  • Episodes in the Mathematics of Medieval Islam, J. L. Berggren, Springer Verlag, 1986.

Probability, Statistics, Graph Theory, Number Theory

  • Games, God, and Gambling: The Origins and History of Probability and Statistical Ideas from the Earliest Times to the Newtonian Era, F. N. David, Hafner Publishing,1962.
  • A History of Probability and Statistics and Their Applications Before 1750, Anders Hald, Wiley, 1990.
  • The Doctrine of Chances, 3rd edition, A. De Moivre, 1756. Available through the American Mathematical Society (AMS).
  • The Logic of Chance, John Venn, 3rd edition, 1888, Dover, 2006.
  • The History of Statistics, The Measurement of Uncertainty before 1900, Stephen M. Stigler, Belknap Press, 1986.
  • Graph Theory 1736–1936, Norman L. Biggs, E. Keith Lloyd, and Robin J. Wilson, Oxford, 1976.
  • History of the Theory of Numbers, vols. 1-3, L. E. Dickson, Chelsea, 1919, Dover, 2005.
  • Number Theory and Its History, Orestein Ore, McGraw-Hill, 1948.
  • Combinatorics, Ancient and Modern, eds. Robin Wilson and John Watkins, Oxford, 2015.

High Quality Internet Resources

Many of these resources have links to other sites of interest. Be critical of the information you find!