Byers, William 1943–

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Byers, William 1943–

(William Paul Byers)


Born September 19, 1943, in Montreal, Quebec, Canada; married; children: two. Education: McGill University, B.Sc., 1964, M.Sc., 1965; University of California, Berkeley, Ph.D., 1969.


Home—Montreal, Quebec, Canada. Office—Concordia University, 1455 de Maisonneuve Blvd. W., LB 921.07, Montreal, Quebec H3G 1M8, Canada. E-mail—[email protected].


Concordia University, Montreal, Quebec, Canada, professor of mathematics, 1972—. Lonergan University College, Montreal, acting principal, 1994-95, principal, 1995-2003.


How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics was named an outstanding academic title, Choice, and an outstanding publication in science and technology, Library Journal, both 2007.


How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics, Princeton University Press (Princeton, NJ), 2007.

Contributor to Chronicle of Higher Education and mathematics journals.


William Byers's first book, How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics, is a "compelling discussion of the intersection of mathematical thinking, psychology, and philosophy," wrote Elizabeth Brown in Library Journal. Arguing against the idea that math is only logical, Byers emphasizes the ambiguity and creativity involved in it. "To me, mathematics is one of the great areas of human creativity," Byers told Peggy Curran in an interview for the Montreal Gazette. As Gregory Chaitin said in New Scientist, "To create a new field of mathematics, you have to feel comfortable with paradox, with creative tension, with sloppy and dangerous new ideas, and you have to want to rock the boat, not conform slavishly." Concerned that an exclusive focus on rationality is harming mathematics, Byers explores the field's nonrational elements and delves into the philosophical implications of looking at mathematics in this way.

Byers's work has drawn both praise and some criticism. Chaitin deemed How Mathematicians Think "courageous," and J. Mayer called it a "truly exceptional work" in his Choice review. Reuben Hersh in the Notices of the American Mathematical Society said it was "profound, unpretentious, and courageous." On the other hand, writing in MAA Online, David J. Stucki expressed the concern that some of Byers's arguments are "weak and unconvincing," even though he acknowledged his sympathy with many of Byers's conclusions. Robert Dawson in CMS Notes was "impressed by what he accomplishes" but admitted that he felt the book did not deliver all it promised; he nonetheless concluded that, "read critically … this is an interesting book." Several writers highlighted Byers's interest in the teaching of mathematics. Donal O'Shea, writing in Nature, claimed that the author's teaching experience provided some of the book's "extraordinary salience and authority," and he described How Mathematicians Think as "lively and important." Peter Cameron, reviewing the book in the Times Higher Education Supplement, concluded that from it "you will learn some mathematics and, more important, you may begin to see how mathematicians think."



Brain, April, 2008, Michael Atiyah, "Thoughts of a Mathematician," pp. 1156-1160.

Choice, November, 2007, J. Mayer, review of How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics, p. 503.

Civil Engineering Journal, January, 2008, review of How Mathematicians Think, p. 91.

CMS Notes, December, 2007, Robert Dawson, "How Mathematicians Think?," pp. 4-5.

Concordia Journal, September 13, 2007, Barbara Black, "Embrace Ambiguity in Math and in Life."

Gazette (Montreal, Quebec, Canada), September 29, 2007, Peggy Curran, "Mathematician Puts People Back in the Equation."

Globe and Mail (Toronto, Ontario, Canada), August 4, 2007, Siobhan Roberts, review of How Mathematicians Think, p. D6.

Library Journal, July 1, 2007, Elizabeth Brown, review of How Mathematicians Think, p. 116.

Math Horizons, April 24, 2008, Lee Kennard, review of How Mathematicians Think.

Nature, October 25, 2007, Donal O'Shea, "What Do Mathematicians Do?," p. 982.

New Scientist, July 28, 2007, Gregory Chaitin, "Less Proof, More Truth: Gregory Chaitin Applauds a Call to Action for Mathematicians, and Wonders If It Might Be the Start of Something Big," p. 49.

Notices of the American Mathematical Society, December, 2007, Reuben Hersh, review of How Mathematicians Think.

Physics World, December, 2007, Andrew Robinson, "Creative Thinking."

Science News, September 8, 2007, review of How Mathematicians Think, p. 159.

Times Higher Education Supplement, September 14, 2007, Peter Cameron, "The Proofs Are in the Imagination."


MAA Online, (July 5, 2007), David J. Stucki, review of How Mathematicians Think.

William Byers Home Page, (June, 2008).