Anecdotes About Anecdotes

December 8, 2002

Book Review
Philip J. Davis

Mathematical Apocrypha. By Steven G. Krantz, Mathematical Association of America, Washington, DC, 2002, 214 pages (with an outstanding collection of photos, including one of Sonya Kowa-levskaya dressed for a party in a cat costume), $32.95.

"I love anecdotes . . . [but] if a man is to wait till he weaves anecdotes into a system, we may be long in getting them, and get but few, in comparison of what we might get."
---Samuel Johnson, in Boswell's A Tour of the Hebrides

Dr. Johnson loved anecdotes. Steven Krantz, a professor of mathematics at Washington University in St. Louis, loves anecdotes. Everyone loves anecdotes. Anecdotes are multi-purpose. They can serve as an antidote for a dull rainy afternoon when theorematic inspiration seems remote, or for a dull stuffy evening when the TV is saturated with stupid reruns. Anecdotes can spice up a classroom lecture or a dreary sermon. They can be garnered at International Congresses or used there for purposes of name-dropping. They can be picked up in otherwise mind-numbing biographies of mathematicians. They can, in the words of Constance Reid, in her preface to the book under review,

"encapsulate a mathematician's character or personality with all the economy of a formula."

At the same time, they can serve to encapsulate character falsely; such was the case with George Washington and the cherry tree. They can reduce a character to dust and ashes. I suppose the three most famous anecdotes about mathematicians would include the story of how Pythagoras (c. 550 BC) sacrificed an ox after he discovered that the square root of 2 is irrational. A second would be Archimedes yelling "Eureka" in the public bath. And a third would be Newton and his apple.

Why the word "apocrypha" in Krantz's title instead of the word "anecdotes"? The Apocrypha is the collection of works that didn't make it into the Bible. The apocryphal books are uncanonical, a bit iffy. But they contain material that was just too good to lose.

Krantz's stories are certainly too good to lose; they are fun to read, and he implies that most of them are verifiable---not iffy at all:

"(They) have been checked (in the fashion of investigative reporters) with other witnesses."

I know from my own tendencies as a storyteller that one often embroiders on what has been checked out and verified. Leaving the gap between what is true and what is verified to philosophers and metaphysicians to straighten out, I offer you the following credentials for Newton's apple: W.W. Rouse Ball, in his Essay on Newton's Principia, wrote that the story was told by persons well acquainted with Newton, one of whom was the vice president of the Royal Society at the time that Newton himself was president. Q.E.D.

Then there are the phrases that over the years have been attributed to many people but in the end get stuck on one person. The phrase "standing on the shoulders of giants," for example, is generally attributed to Isaac Newton. But you can find its like in the works of Bernard of Chartres (c. 1115), if not earlier in the Latin poems of Lucan (c. 50).

Krantz has anecdotalized more than 350 people, most of them from the 20th century. If you look at the index, you can easily eyeball those who have become strange and powerful attractors for anecdotes; among them: Besicovitch, Einstein, Erdös, Hardy, Hilbert, Lefschetz, Littlewood, von Neumann, Russell, Wiener. Apparently, to make the long list of Krantz's in-text references, you have to be both a genius and a bit of an eccentric.

Has Krantz woven his anecdotes into a system? Well, sort of---he has arranged his stories under such intriguing taxonomic designations as "Great Foolishness," "Great Ideas," "Great Pranks."

Just as movie reviewers do not usually give away the critical part of the plot, I am reluctant to reproduce here more than one of Krantz's stories. I'd like readers to experience the pleasure for themselves. But as a come-on, here's one about Stefan Bergman, whom I knew very well and liked enormously:

"There is considerable evidence that Bergman thought about mathematics constantly. Once he phoned one of his graduate students at the student's home number at 2:30 A.M., and said 'Are you in the Library? I want you to look something up for me.'"

Philip Davis is ready to confirm at least one anecdote in the book under review ---about Stefan Bergman, shown here at MIT in about 1952.

"Si non e vero, e ben trovato," as one of Dante's reviewers said of the newly appeared Inferno: If it isn't true, it ought to be. But actually, I can act as a witness to the Bergman story---not, perhaps, to confirm 2:30 A.M., but certainly 11:30 P.M.

Krantz has included two pages of resources for further reading, including five Web sites. To this list I should like to add two of my own favorite anecdotal databases: John Aubrey's Brief Lives, a wonderful, chaotic accumulation of biographical material and stories, and Augustus de Morgan's A Budget of Paradoxes, in two volumes (1915 edition).

Not a mathematician himself, Aubrey (1626-1697) had a soft spot for mathematicians and took notice of seventy-five of them. He said of his collection that the items were "like flotsam from a wreck." Brief Lives deserves to be better known; there is an excellent recent Penguin abridgement by John Buchanan-Brown.

De Morgan was a mathematician, and many of his stories deal with his encounters with mathematical cranks, such as circle squarers. Though we now have our own cranks saturating our e-mail, it is interesting to see how the flavor of the nuts has changed over the decades.

But Krantz was wise in limiting his anthology essentially to 20th-century figures. If he had included anecdotes about mathematicians from all times, he would have produced a book heavy enough to act as a doorstop. Besides, readers generally like their gossip up-to-date and served red hot.

My favorite all-time mathematical anecdote is not about a mathematician, but about the philosopher Thomas Hobbes (1588-1679). As reported by Aubrey, Hobbes

"was forty yeares old before he looked on geometry, which happened accidentally, being in a Gentleman's Library in . . . . A Euclid's Elements lay open, and 'twas the 47th Element liber I. He read the proposition. 'By G-, sayd he (he would now and then sweare an Oathe, by way of emphasis), this is impossible.' So he reads the Demonstration of it, which referred him back to such a Proposition: which proposition he read: that referred him back to another which he also read, and sic deinceps [and so on], that at last he was demonstratively convinced of that trueth. This made him in love with Geometry."

This comes close to my own experience when I was a high school freshman.

Then there comes the day when you hear (over someone's shoulder) something said about yourself. The birth of an anecdote, perhaps? But it turns out you don't recognize yourself in the story, and you are too guilty to admit you were eavesdropping and too vain to block its spread.

Enjoy the book. And check the index to see whether your own character has been encapsulated anecdotally.

Philip J. Davis, professor emeritus of applied mathematics at Brown University, is an independent writer, scholar, and lecturer. He lives in Providence, Rhode Island, and can be reached at

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