MAOR, Eli 1937-

PERSONAL:

Born October 4, 1937. Education: Israel Institute of Technology, Ph.D. (mathematics), 1969.

ADDRESSES:

E-mail—[email protected].

CAREER:

Has taught mathematics at Ben Gurion University, Israel, at the University of Wisconsin—Eau Claire, and at Oakland University in Michigan; Oakton Community College, Des Plaines, IL, adjunct professor, 1990—; Loyola University of Chicago, Chicago, IL, professor of mathematics, 1995—.

AWARDS, HONORS:

National Council of Teachers of Mathematics Award, 1980, for article "What Is There So Mathematical about Music?"

WRITINGS:

To Infinity and Beyond: A Cultural History of the Infinite, Birkhäuser (Boston, MA), 1987.

e: The Story of a Number, Princeton University Press (Princeton, NJ), 1994.

Trigonometric Delights, Princeton University Press (Princeton, NJ), 1998.

June 8, 2004: Venus in Transit, Princeton University Press (Princeton, NJ), 2000, expanded edition published as Venus in Transit, 2004.

The Facts on File Calculus Handbook, Facts on File (New York, NY), 2003.

Consulting editor and contributor, Encyclopedia Britannica. Contributor of articles to Orion and Sky & Telescope.

SIDELIGHTS:

A longtime mathematician, Eli Maor has taught college mathematics in Israel and the United States and has done much to bring the complexities of higher mathematics to a popular audience through his writings. By incorporating the history of mathematics into his lectures and books, Maor conveys the revolutionary impact of mathematical discoveries that otherwise might seem commonplace or dull to non-mathematicians. As Melissa Houck put it in the Mathematical Intelligencer, "Maor is one of a small handful of mathematical authors who create a satisfying blend of historical anecdote and mathematical information that appeals to amateur and expert alike."

In 1987 he published To Infinity and Beyond: A Cultural History of the Infinite, which traces this curious concept from the ancient Greeks up through present speculations. As an example of the way infinity upends normal mathematical concepts, Maor retells Zeno's paradox, which showed that since a rock falling to ground must always fall half the distance, and then half of half the distance, and then half of that distance, and so on, it would theoretically never reach the ground. As Michael Guillen explained in Sciences, Maor sees this paradox as "a reflection of the Greeks' 'horror infiniti, their deeply rooted suspicion of the infinite.' He then recounts Western man's long struggle to grasp the infinite, from the classical era through the Renaissance and up to selected mathematical breakthroughs of the past two centuries—breakthroughs that, according to Maor, 'finally demystified infinity and put it on a firm basis.'" While noting Maor's wide range in exploring infinity's impact on science, philosophy, and art, Guillen and some other reviewers faulted him for what they felt was a lack of coherence. New York Times reviewer B. G. Yovovich, for one, found that "the book provides little more than a series of standard presentations of mathematical ideas and fails to integrate those ideas into the cultural history promised in the subtitle."

Maor turned to another mathematical oddity in e: The Story of a Number. Long eclipsed by pi in the world of abstract numbers, e is a number that actually represents a vital part of calculus, and its importance crops up in such practical areas as compound interest, as Maor reveals. As usual, his goal is to move beyond the cloisters of higher mathematics. "In the number e, Maor has found a unifying theme for some of the most exciting history of calculus," commented Times reviewer Ulrike Tillmann. "Yet his book should be accessible to anyone with a basic knowledge of mathematics." As usual for Maor, there is a good deal of history and personality in the book, including the story of eccentric Scottish mathematician John Napier's near miss in discovering e, and the bitter priority dispute between Leibniz and Isaac Newton over who really invented calculus. A Kirkus Reviews contributor commented, "Adults with open minds and students just beginning to make their way through algebra and trigonometry will find much that is easily digestible and even palatable in this lively presentation."

Those trigonometry students could also benefit from Maor's next book, Trigonometric Delights. Again, Maor "brings the subjects to life in a compelling blend of mathematics, history, and biography," according to a Science News contributor. Starting with the building of the Egyptian Pyramids, Maor brings out the curious interplay of trigonometry with geometry, astronomy, architecture, and cartography. He also provides a number of biographical sketches, including one on early female mathematician Maria Agnessi. "Students of trigonometry and their teachers will enjoy finding the core syllabus so refreshingly opened up," wrote mathematician Jeremy Gray in a review for Nature magazine. "If they find the accounts, especially towards the end of the book, to be tantalizingly short, this is all the more reason to emulate the author and find out more for themselves, and Maor gives advice on how this can be done."

The history of mathematics is intimately associated with the history of astronomy, and in June 8, 2004: Venus in Transit, which was later revised as simply Venus in Transit, Maor brings these strands together while also providing a surprisingly dramatic adventure story. The orbital patterns of Earth and Venus are somewhat in synch, so that a curious pattern develops. As Johannes Kepler predicted, Venus passed exactly between the Earth and the Sun in 1631, but he did not realize that the same thing would happen eight years later, and then not again until 1761, to be repeated in 1769, and then not until 1874 in a recurring eight-year/122-year pattern. By the eighteenth century, astronomers not only understood the pattern, but they believed that by figuring out the exact moment when Venus entered and left the Sun's disk they could calculate the size of the solar system. As 1761 approached, astronomers were eagerly seeking out the best vantage points, but just as in the space race of the 1950s and 1960s, national rivalries came into play. One French astronomer was unable to reach an ideal spot in Pondicherry because of the English-French struggle over India. Eight years later, a sudden fog dashed his hopes. Englishmen Charles Mason and Jeremiah Dixon—of Mason-Dixon line fame—had to dodge French gunfire to get to their spot in the Cape of Good Hope. As Booklist reviewer Michael Spinella observed, "Maor brings science history vividly alive in a manner reminiscent of Eco, with tales of eccentric astronomers, political corruption, and conspiracy." Similarly, Astronomy contributor William Schomaker commented, "This book will please the history aficionado and the most ardent astronomer."

BIOGRAPHICAL AND CRITICAL SOURCES:

PERIODICALS

American Scientist, November-December, 1998, William Thompson, review of Trigonometric Delights, p. 584.

Astronomy, October, 2000, William Schomaker, review of June 8, 2004: Venus in Transit, p. 110.

Booklist, February 15, 1994, Bryce Christensen, "The Story of a Number," p. 1044; March 1, 2000, Michael Spinella, review of June 8, 2004, p. 1182.

Dr. Dobb's Journal, July, 1999, Michael Swaine, "Another Kind of E-Book."

Isis, September, 2001, James Evans, review of June 8, 2004, p. 585.

Journal of the History of Science, June, 1995, Erik Sageng, review of e: The Story of a Number, p. 308.

Kirkus Reviews, April 1, 1994, review of e, pp. 462-463; February 15, 2000, p. 230.

Library Journal, February 1, 1994, Harold D. Shane, review of e, p. 108; April 1, 1998, Harold D. Shane, review of Trigonometric Delights, p. 119.

Mathematical Intelligencer, winter, 2001, Melissa Houck, review of e, pp. 74-75.

National Forum, winter, 1995, William L. Deaton, review of e, p. 47.

Nature, July 23, 1998, Jeremy Gray, "The Joy of Secants," p. 333; August 10, 2000, Don Fernie, "Venusian Visitation," p. 562.

New York Times, September 27, 1987, B. G. Yovovich, review of To Infinity and Beyond, p. 36.

New York Times Book Review, September 27, 1987, "Science and Technology; In Short," p. 36.

Science, June, 1994, Peter Borwein, review of e, p. 1952.

Science News, April 13, 2002, review of Trigonometric Delights, p. 240.

Sciences, September-October, 1987, Michael Guillen, review of To Infinity and Beyond: A Cultural History of the Infinite, p. 55; May, 2000, Laurence A. Marschall, review of June 8, 2004, p. 45.

Times (London, England), January 2, 1995, Ulrike Tillmann, review of e, p. 1.

Times Literary Supplement, August 11, 2000, Owen Gingerich, "There She Blows."

Whole Earth, summer, 1998, Michael Stone, review of e, p. 111.*