## Mathematics and Multi-Media

**June 25, 2004**

Hendrik Lenstra and Vaughan Jones, the mathematical stars of the MSRI-produced video porridge, pulleys and Pi.

**Book Review Philip J. Davis**

**porridge, pulleys and Pi.** *A video produced and directed by G.P. Csicsery. Mathematical Sciences Research Institute, Berkeley, California, 2004, 28:30 minutes, $40 (in U.S.), $45 (outside U.S). *

**Fermat's Last Tango.**

*A video based on a stage production by the York Theatre Company; book by Joann Sydney Lessner, lyrics by Joann Sydney Lessner and Joshua Rosenblum, music by Joshua Rosenblum; followed by short clips of Andrew Wiles explaining his personal philosophy of mathematics. Clay Mathematics Institute, Cambridge, Massachusetts, 2001, 100 minutes, $30.00.*

I often tell people that I've had a number of different careers within mathematics, but never in my life did I think that I would wear the hat of a reviewer of Broadway musicals. It's pretty clear how I got here. The various scientific think tanks, institutes, and foundations have been tempted by the media as a way of publicizing mathematics; at the same time, the dramatists, lyricists, film makers, producers, jaded by boy-meets-girl themes, whether comic or tragic, existential or postmodern, have been tempted by the subject matter of science. If over the years I had been on the ball, I could have reviewed *Copenhagen*, Proof, *N Is a Number, Arcadia, Moving Bodies, A Beautiful Mind, QED*. At a 1998 conference at Scripps College in Claremont, California, I just missed meeting John Cleese (of Fawlty Towers fame; a Cambridge grad and a very smart cookie indeed), and if I had been alert to the trend, I would have talked to him about doing a series called *Hilbert's Hotel* for the BBC.

Mathematics, cinema verité, and the music makers? What kind of marriage is this? Well, why not? There's no constitutional amendment prohibiting it. The raw material of struggle, conflict, the competition of people and their basic assumptions, successes, elation, tragedy---the *agon* of classical Greek drama---is as much present in the interaction between mathematics and society as it is in politics or in the death of a salesman. But it is not, I would say, present in mathematics when mathematics is conceived of as a body of abstract, platonic ideas.

*porridge, pulleys and Pi* is beautifully and professionally produced. The mathematical stars are Vaughan Jones, knot theorist, and Hendrik Lenstra, number theorist. Jones connects his knots with DNA. Lenstra relates his numbers to cryptography, to Escher's self-referential art, and to a restoration in Holland of a memorial to Ludolf van Ceulen (1580-1610).

The filmographic technique is the familiar documentary pasting together of often very short snippets. The stars are shown talking, explaining. They're at the blackboard. They're swimming, windsurfing, golfing---activities that "anybody" might engage in. The filmmakers have clipped in pictures of Jones and Lenstra as children and mention the awakening of the mathematical urge in their stars. Relatives of Jones and Lenstra step in to provide a few impressions.

What is the message of the video? Along with what might be called a "foundationally correct" component---that mathematicians can come from any background at all, e.g., Vaughan Jones is from remote New Zealand---the video makes the point that pure mathematics not infrequently has applications to the "real world." A third component of the message is that the stereotype of the mathematician as mad genius must be modified. What was most striking to my wife and me as we watched the film was the intensity of the engagement of the two stars with their mathematical material.

I think that the filmmakers tried to convey what's inside the mathematical mind and to explore the notoriously difficult question of how mathematical ideas originate in that mind. As regards the hard-core mathematics, the film tells viewers that such and such is the case without explaining how it is the case. Fair enough: To show how would require a two-semester graduate course at the very least.

I come now to *Fermat's Last Tango*, which is something altogether other. Is it a musical review or an operetta? Is it a tour de force or a jeu d'esprit? Since its six-week off-Broadway run in 2001, Tango has received many reviews, from both the theatre-going and the mathematical communities. The verdict is politely mixed in the former case, weakly enthusiastic in the latter.

Before I convey some brief impressions, a word of warning to readers: I was raised on Ginger Rogers and Fred Astaire, plus the 1937 version of *Pins and Needles*. (Google that one!) The production of *Tango* is for the most part spirited and lively, with occasional tedious stretches. The acting is accomplished and enthusiastic. The lyrics are witty, often satiric; the well-prepped lyricist has scattered mathematical terms and names throughout, like raisins in an Irish cake. The music? Well, since I consider *Man of La Mancha* (1965) the last musical whose score had any memorable qualities, the less said there the better.

I suppose it is superfluous to recall that the plot of *Tango* is a pastiche on Andrew Wiles and his proof of FLT. The plot line is simply the old heartwarming one: Fellow meets girl, fellow loses girl, fellow gets girl back, but for "girl" substitute "theorem." The Wiles character comes across as slightly and stereotypically nerdish. The Ghost of Fermat, who is the second major character, is a great invention, right out of Molière and Cyril Ritchard in restoration comedy. (More work for Google!) The hero's "math widow" will not please feminists. Her great moment (for me) came with her double entendres of the words "curves," "surfaces," and "modular forms." All in all, there is considerable fun in *Tango*, but it doesn't get close---perhaps its creators made the correct decision in not venturing too close---to what it means to do research in mathematics.

What's the target audience of these two videos? The general public? The intelligent laity? Math buffs, students, and professionals? I get the feeling that despite what the producers may have said, their productions were simply sent out into the world "on spec," as it were, to catch whomever they could and to make whatever impressions they could on those whomevers.

I return to the question of how one can get into the mathematical mind and present it comprehensibly to a wide audience. Popularization has been done in all manners of media. There is straight history. There are autobiography and biography. There are diaries, and there is nachlass to be interpreted. There are romantic novels (*Hypatia*, Charles Kingsley, 1851). There are satiric novels (*Uncle Petros and the Goldbach Conjecture*, Apostolos Doxiadis, 1992). There are plays. There are taped interviews---published and webbized. There are documentaries (such as *porridge*). And as we have seen, there are even musicals.

Each of these modes has its strengths and its weaknesses. What wouldn't we now give to witness Euler lecturing or writing one of his thousands of papers? The off-the-cuff remarks of Jones and Lenstra in *porridge* and the carefully thought through answers of Wiles in the postscript to the *Tango* tape are welcome contributions to the oral/visual archives of our profession. Still, which mode is best for conveying the nature of mathematical intuition or the source of mathematical ideas?

I've confronted this question recently as one of the interviewers in a SIAM project designed to collect oral histories about the early years of numerical analysis. A question that arose in the planning stages of the project was whether the project should go for live video interviews or for audiotaped conversations. For all that video has many virtues, the project directors opted for the latter.

A major consideration is that video is much more expensive to produce and distribute. I was told by MSRI that *porridge, pulleys and Pi* clocked in at $65,000, and that was for a film with only two stars. I would estimate the cost of an audiotaped interview (including travel, transcripts, overhead, and so forth) at $4000 or less per interview. As for the cost of a musical math drama, it could range from as little as $500 for an off-off-off-Broadway production to millions (if Tom Stoppard happens to be the playwright).

The SIAM project is targeted to mathematicians and historians of science, and so I have been able to get responses at a very technical level. But I confess to experiencing great difficulty in eliciting and capturing the creative originality of my subjects at a deep level. A typical response might go like this:

"I've been interested in subject S since I first read X's paper on the subject. It then occurred to me that Y's paper was also relevant, and I saw a way of combining the two and advancing the subject S. I did thus and so. Thus and so took off by itself and gave rise to a whole new chapter of which S is now a small part."

Writers of mathematical histories can use such material to good advantage and will be able to record the historic flow of material. But can the mystery of the "aha!" moment ever be revealed? I have never found much enlightenment either in the words of the great Poincaré on this subject or in the words of contemporary cognitive scientists. An act of creative genius resists total dissection.

*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 **[email protected]**. *