Wapner, Leonard M. 1948-

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Wapner, Leonard M. 1948-

PERSONAL:

Born May 30, 1948, in Los Angeles, CA; married; wife's name Mona; children: Kirsty. Education: University of California, Los Angeles, B.A., 1970, M.A.T., 1971.

ADDRESSES:

Home—Seal Beach, CA. Office—El Camino College, 16007 Crenshaw Blvd., Torrance, CA 90506. E-mail—[email protected].

CAREER:

Mathematician. El Camino College, Torrance, CA, professor of mathematics, 1974—.

WRITINGS:

The Pea and the Sun: A Mathematical Paradox, A.K. Peters (Wellesley, MA), 2005.

Contributor to AMATYC Review and Mathematics Teacher.

SIDELIGHTS:

Leonard M. Wapner is an American mathematician. Educated in mathematics at the University of California, Los Angeles, Wapner entered academia as a professor of mathematics shortly after graduating. In 2005 he published his first book, The Pea and the Sun: A Mathematical Paradox. The book explains the Banach-Tarski Theorem, or Banach-Tarski Paradox, combining both technical elements of its proof as well as casual explanations for nonexperts and nonmathematicians. The paradox, in short, is that any spherical object can be disassembled into immeasurably small pieces and then reassembled to form another sphere immeasurably larger than its original form.

Writing in the New Criterion, Martin Gardner commented that "Wapner reminds us that both relativity and quantum mechanics bristle with paradoxes that are extreme violations of common sense but which are known to be true" in his first book. Gardner also noted that "chapters proving the paradox are tough going for mathematically uninformed readers, but don't let that put you off if you are such a person. Wapner has surrounded his central theme with a wealth of easily understood topics, much of it recreational, related in some way to the BT paradox." Helen Joyce, writing in Plus Magazine, found the topic "strange and counter-intuitive," but conceded that Wapner "gives a fascinating account, in a journalistic style, of the history of the Banach-Tarski Theorem." Joyce concluded that "what is presented in this book is maths for its own sake: beautiful, elegant, artistic, astonishing. I doubt whether it would appeal particularly to those who think of maths as a ‘useful tool’—although it might open their minds!" David M. Bressoud lamented on the Mathematical Association of America Web site that mathematics is largely considered an unpopular topic of study for the youth of today and wondered how to improve its attractiveness. While reviewing The Pea and the Sun, Bressoud noted that "distributing copies of this book would be one good way to accomplish this. An undergraduate with basic mathematical training, even a precocious high school student, should find this book engaging, surprising, and enlightening."

Citing advanced technical elements, Péter Komjáth, writing on the American Mathematical Society Web site, found difficulty in teaching the topic to younger mathematics students, noting that the theorem "is not a very hard proof, yet it is not easy to teach, say, to undergraduates." Komjáth did agree, however, that Wapner's subject is "an interesting choice" for publication. Komjáth took issue again with the editing job, citing that he "found a few typos" in the text and formulas. Overall, Komjáth stated: "The decision to write a popular book on the BTP allows several possibilities. One could write an entertaining book stating the theorem, describing its history, with easy, witty remarks. Or one could write a book that contains an elementary introduction to the corresponding mathematical notions. Or, finally, one could write a book with the full proof in an available form. Wapner admirably carried out his task by creating a book that has all three features." A contributor to the Midwest Book Review remarked that Wapner wrote the book in a "fresh, captivating, friendly style." The same contributor added that the book would be an interesting read for "any reader with a discerning, inquisitive mind into the nature of the so-called impossible."