Review of the Literature
The “popular” literature on mathematics is booming. Every year excellent new books are added to the shelves. There are books that intend to teach a particular branch of mathematics. Textbooks of course are a whole industry unto themselves. There are books meant for the casual or “pleasure” reader, which deal with special topics beyond the standard high school or lower-division college level—lots of them on probability and statistics, and recently, good books about topology, about group theory, about graphs and networks, about non-Euclidean geometry.
Then there are books about the history of mathematics, sometimes in the form of collections of brief biographies arranged chronologically. There are books about the philosophy of mathematics. There are lots of books about teaching and education, even apart from those specifically meant for the professional training of teachers. In particular, books about geniuses and prodigies, and books about math anxiety and math avoidance and even “math for dummies.” And finally there are biographies and autobiographies of mathematicians. It is from this last group that much of the material in this book has been taken. Of course, in writing this book we have tried to look at all possible sources. So here we would like to offer you our overview and evaluation of the many, many books we have used.
First of all, violating modesty, let us mention The Mathematical Experience by Philip J. Davis, Reuben Hersh, and Elena Marchisotto. This book is now over 20 years old but is still useful. Its main intention was to remove the curtain or veil that hid the life and thinking of mathematicians from the reading public. In doing so, it accomplished something novel: presenting in reasonably accessible form some of the latest theories and results from pure mathematics, including logic, harmonic analysis, and group theory, to the general public. It was a breakthrough that encouraged many other authors to undertake similar rash enterprises.
We list below a few recent books in several different categories that we found interesting and readable. But the main purpose is to list the biographies and autobiographies, with special notice for the ones we consider outstanding. (Not all of them have actually been referred to in this book.)
BIOGRAPHY COLLECTIONS
The honors class: Hilbert’s problems and their solvers, Benjamin H. Yandell. Natick, Mass.: A.K. Peters, 2002.
This history of the research inspired by Hilbert’s famous
list of 23 problems is invaluable.
Men of mathematics, E.T. Bell. New York: Simon and Schuster, 1965.
A standard classic, not a totally reliable history text but intensely readable and extremely widely read by past, present, and future mathematicians.
Remarkable mathematicians: From Euler to von Neumann, Ioan James. Washington, D.C.: Mathematical Association of America, 2002.
Driven to innovate: A century of Jewish mathematicians and physicists, Ioan James. Witney, Oxfordshire: Peter Lang, 2009.
AUTOBIOGRAPHY
The apprenticeship of a mathematician, André Weil. Translated from the French by Jennifer Gage. Boston: Birkhäuser, 1992.
André Weil’s autobiography goes only as far as his midcareer and has hardly any mathematics, but its flavor of casual presumption of unquestioned supremacy does communicate the flavor of this unique personality.
Ex-prodigy: My childhood and youth, Norbert Wiener. New York: Simon and Schuster, 1953.
I am a mathematician: The later life of a prodigy. Garden City, N.Y.: Doubleday, 1956. An autobiographical account of the mature years and career of Norbert Wiener and a continuation of the account of his childhood in Ex-prodigy.
A mathematician’s apology, G. H. Hardy. With a foreword by C. P. Snow. New York: Cambridge University Press, 1992.
A mathematician grappling with his century, Laurent Schwartz. Translated from the French by Leila Schneps. Boston: Birkhäuser, 2001.
Enigmas of chance: An autobiography, Mark Kac. Berkeley, Calif.: University of California Press, 1987.
Adventures of a mathematician, S. M. Ulam. New York: Scribner, 1976.
The recollections of Eugene P. Wigner as told to Andrew Szanton. New York: Plenum Press, 1992.
The education of a mathematician, Philip J. Davis. Natick, Mass.: A. K. Peters, 2000.
I want to be a mathematician: An automathography, Paul R. Halmos. New York: Springer-Verlag, 1985.
Conveys well the unique flavor and personality of this famous American writer and teacher of mathematics.
Random curves, Neal Koblitz. New York: Springer, 2008.
Lively and controversial memoir of a leading algebraist, cryptographer, and activist educator.
MODERN BIOGRAPHY
Perfect rigor, Masha Gessen. Boston: Houghton Mifflin Harcourt, 2009.
The life of Grisha Perelman, who proved Poincaré’s conjecture.
Charles Sanders Peirce: A life, Joseph Brent. Bloomington, Ind.: Indiana University Press, 1993.
Courant in Göttingen and New York: The story of an improbable mathematician, Constance Reid. New York: Springer-Verlag, 1976.
Constance Reid’s books set a high standard for literary quality and careful research. We have used her biographies of Hilbert, Courant, and her sister Julia Robinson.
Hilbert, Constance Reid. With an appreciation of Hilbert’s mathematical work by Hermann Weyl. New York, Springer-Verlag, 1970.
Julia, a life in mathematics, Constance Reid. Washington, D.C.: Mathematical Association of America, 1996.
A convergence of lives: Sofia Kovalevskaya, scientist, writer, revolutionary, Ann Hibner Koblitz. Cambridge, Mass.: Birkhauser Boston, 1983
Alan Turing: The enigma, Andrew Hodges. Foreword by Douglas Hofstadter. New York: Walker, 2000.
Stephen Smale: The mathematician who broke the dimension barrier, Steve Batterson. Providence, R.I.: American Mathematical Society, 2000.
The man who knew infinity: A life of the genius Ramanujan, Robert Kanigel. New York: Scribner, 1991.
An outstanding literary achievement.
Ramanujan: Twelve lectures on subjects suggested by his life and work, G. H. Hardy. New York: Chelsea.
The wind and beyond: Theodore von Kármán, pioneer in aviation and pathfinder in space, Theodore von Kármán with Lee Edson. Boston: Little, Brown, 1967.
The man who loved only numbers: The story of Paul Erdős and the search for mathematical truth, Paul Hoffman. New York: Hyperion, 1998.
My brain is open: The mathematical journeys of Paul Erdős, Bruce Schechter. New York: Simon and Schuster, 1998.
Alfred Tarski: Life and logic, Anita B. Feferman and Solomon Feferman. New York: Cambridge University Press, 2004.
Politics, Logic, and Love: The life of Jean van Heijenoort, Anita Burdman Feferman. Wellesley, Mass.: A.K. Peters, 1993.
Van Heijenoort was murdered by an ex-wife, after a career as a historian of logic, following years of service as private secretary to Leon Trotsky.
Willard Gibbs, Muriel Rukeyser. New York: Dutton, 1964.
Logical Dilemmas: The life and work of Kurt Gödel, John Dawson. Wellesley, Mass.: A.K. Peters, 1997.
Incompleteness: The proof and paradox of Kurt Gödel, Rebecca Goldstein. New York: W.W. Norton, 2005.
Abraham Robinson: The creation of nonstandard analysis—A personal and mathematical odyssey, Joseph Warren Dauben. Princeton, N.J.: Princeton University Press, 1995.
Georg Cantor: His mathematics and philosophy of the infinite, Joseph Warren Dauben. Cambridge, Mass.: Harvard University Press, 1979.
The unreal life of Oscar Zariski, Carol Ann Parikh. Boston: Academic Press, 1991.
Readable and reliable.
King of infinite space: Donald Coxeter: The man who saved geometry, Siobhan Roberts. New York: Walker, 2006.
John von Neumann and Norbert Wiener: From mathematics to the technologies of life and death, Steve J. Heims. Cambridge, Mass.: MIT Press, 1980.
Henri Poincaré, critic of crisis: Reflections on his universe of discourse, Tobias Dantzig. New York, Scribner, 1954.
R. L. Moore: Mathematician and teacher, John Parker, Washington, D.C.: Mathematical Association of America, 2005.
Emmy Noether, 1882–1935, Auguste Dick. Translated by Heidi Blocher. Boston: Birkhäuser, 1981.
Count down: Six kids vie for glory at the world’s toughest math competition, Steve Olson. Boston: Houghton Mifflin, 2004.
Logic’s lost genius: The life of Gerhard Gentzen, Eckart Menzler-Trott. Providence, R.I.: American Mathematical Society, 2007.
Jean Cavaillès: A philosopher in time of war 1903–1944, Gabrielle Ferrieres. Studies in French Civilization, 16. Translated by T. N. F. Murtagh. Lewiston, N.Y.: Edwin Mellen Press, 2000.
Cavaillès was a logic professor at the Sorbonne who spent his afternoons organizing sabotage against the Nazi occupiers; fictionalized in the 1969 movie Army of Shadows.
Ernst Zermelo: An approach to his life and work, Heinz-Dieter Ebbinghaus and V. Peckhaus (contributor). New York: Springer, 2007.
Niels Henrik Abel and his times, Arild Stubhaug and Richard R. Daly. New York: Springer, 2000.
The Mathematician Sophus Lie, Arild Stubhaug and R. Daly. New York: Springer, 2002.
CLASSIC BIOGRAPHY
Isaac Newton, James Gleick. New York: Pantheon Books, 2003.
The life of Isaac Newton, Richard S. Westfall. New York: Cambridge University Press, 1993.
Never at rest: A biography of Isaac Newton, Richard S. Westfall. New York: Cambridge University Press, 1980.
The mathematical career of Pierre de Fermat (1601–1665), Michael S. Mahoney. Princeton, N.J.: Princeton University Press, 1973.
Blaise Pascal: Mathematician, physicist, and thinker about God, Donald Adamson. New York: St. Martin’s, 1995.
Joseph Fourier: The man and the physicist, John Herivel. Oxford: Clarendon Press, 1975.
Joseph Fourier, 1768–1830: A survey of his life and work,
I. Grattan-Guinness in collaboration with J. R. Ravetz. Based on a critical edition of his monograph on the propagation of heat, presented to the Institut de France in 1807. Cambridge, Mass.: MIT Press, 1972.
Life of Sir William Rowan Hamilton, Robert Perceval Graves. New York: Arno Press, 1975.
Sir William Rowan Hamilton, Thomas L. Hankins. Baltimore: Johns Hopkins University Press, 1980.
Carl Friedrich Gauss: Titan of science, G. Waldo Dunnington. With additional material by Jeremy Gray and Fritz-Egbert Dohse. Washington, D.C.: Mathematical Association of America, 2004.
Carl Friedrich Gauss: 1777–1977, Karin Reich. Translated by Patricia Crampton Bonn-Bad Godesberg: Inter Nationes, 1977.
Euler: The master of us all, William Dunham. Washington, D.C.: Mathematical Association of America, 1999.
Sophie Germain: An essay in the history of the theory of elasticity, Louis L. Bucciarelli and Nancy Dworsky. Boston: D. Reidel, 1980. Sold and distributed in the United States and Canada by Kluwer, Boston.
HISTORY
A history of mathematics: An introduction, Victor J. Katz. Boston: Addison-Wesley, 2009.
Mathematicians under the Nazis, Sanford L. Segal. Princeton, N.J.: Princeton University Press, 2003.
Golden years of Moscow mathematics, Smilka Zdravkovska and Peter L. Duren (Eds.). Providence, R.I.: American Mathematical Society, 1993.
An eyewitness account of an inspiring and tragic episode.
A century of mathematics in America, Peter Duren, (Ed.). With the assistance of Richard A. Askey, Uta C. Merzbach. Providence, R.I.: American Mathematical Society, 1988–1989.
Mathematics at Berkeley: A history, Calvin C. Moore. Wellesley, Mass.: A.K. Peters, 2007.
Mathematical thought from ancient to modern times, Morris Kline. New York: Oxford University Press, 1990, 1972.
ORIGIN OF CHAOS
Poincaré and the three body problem, June Barrow-Green. Providence, R.I.: American Mathematical Society, 1997.
The chaos avant-garde: Memories of the early days of chaos theory, Ralph Abraham and Yoshisuke Ueda (Eds.). River Edge, N.J.: World Scientific, 2000.
Chaos: Making a new science, James Gleick. New York: Viking, 1987.
The mathematical experience, Philip J. Davis and Reuben Hersh. With an introduction by Gian-Carlo Rota. Cambridge, Mass.: Birkhäuser, 1980.
How mathematicians think. William Byers. Princeton, N.J.: Princeton University Press, 2007.
Mathematics: Frontiers and perspectives, V. Arnold et al. (Eds.). Providence, R.I.: American Mathematical Society, 2000.
Mathematical people: Profiles and interviews, Donald J. Albers and G. L. Alexanderson (Eds.). Introduction by Philip J. Davis. Boston: Birkhäuser, 1985.
More mathematical people: Contemporary conversations, Donald J. Albers, Gerald L. Alexanderson, and Constance Reid, (Eds.). Boston: Harcourt Brace Jovanovich, 1990.
The two volumes, Mathematical People and More Mathematical People, have fascinating interviews with many living mathematicians.
The mathematician’s brain, David Ruelle. Princeton, N.J.: Princeton University Press, 2007.
Littlewood’s miscellany, Béla Bollobás (Ed.). New York: Cambridge University Press, 1986.
Radical equations: Math literacy and civil rights, Robert P. Moses and Charles E. Cobb, Jr. Boston: Beacon Press, 2001.
Bob Moses, with the assistance of Charles Cobb, tells his story and presents his theories and goals.
Women in mathematics: The addition of difference, Claudia Henrion. Bloomington, Ind.: Indiana University Press, 1997.
Math education at its best: The Potsdam model, D. K. Datta. Framingham, Mass.: Center for Teaching/Learning of Mathematics, 1993.
Complexities: Women in mathematics, Bettye Anne Case and Anne M. Leggett (Eds.). Princeton, N.J.: Princeton University Press, 2005.
Indiscrete thoughts, Gian-Carlo Rota. Boston: Birkhäuser, 1997.
Jackson, A. (1999). The IHEs at forty, Notices of the American Mathematical Society 46(3), 330.
Récoltes et semailles, Alexandre Grothendieck. First 100 pages translated by Roy Lisker (2007). Conditions for obtaining these pages can be read at the Grothendieck circle web site http://www.grothendieckcircle.org July 20, 2007.
A document unique in the history of science.
Lisker, R. (1990). Ferment vol. V(5), June 25. The quest for Alexandre Grothendieck; #6 October 1: Grothendieck 2; #7 October 25: Grothendieck 3; #8 November 27; Grothendieck, 4: #9 January 1: Grothendieck 5. These are contained in a book entitled, The Quest for Alexandre Grothendieck, available from the author. Middletown, Conn.
You failed your math test, Comrade Einstein, Shifman, M. (Ed.). Singapore: World Scientific, 2005.
Mathematics under the microscope, Alexandre Borovik. Wordpress. http://micromath.wordpress.com. Also Providence, R.I.: American Mathematical Society, 2010.
The Number Sense, S. Dehaene. New York: Oxford University Press, 1997.
An introduction to understanding how mathematics sits in the human brain.