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## Casti's Tale

John Casti, a mathematician at the Santa Fe Institute and the author of a number of bestselling popular science books, includingParadigms Lost, recounts the following recent event."I was talking with a colleague at Santa Fe Institute, Brian Arthur, a well-known economist. We were interrupted by a knock on his office door, and when he opened it there was a journalist from Basle here to interview Brian for a Swiss economics magazine. When Brian introduced me, this gentlemen said, 'Finally I meet someone here that I've actually heard about besides Brian. ' Well, with people like Murray Gellmann, Stu Kauffman, Brian, Chris Langton, John Holland, and others around here all the time, you can imagine it was quite a shock to hear that this fellow knew more about me from my pop-science books than about any of these guys and their pathbreaking work. Such are the vagaries of information transfer in today's world, I guess."

"Such recognition, along with a steady stream of invitations to give public lectures, talks to student bodies, and after dinner speeches to non-mathematicians are among the rewards of venturing into the world of science popularization," Casti declares. Another benefit is that the process itself is rewarding:

"The choice to turn to popularizations has enabled me to learn a lot about a lot of different fields and problem areas, has brought me into contact with numerous people that I would never have met otherwise, people whose academic specialties range from anthropology to zoology. Furthermore, the research I did for these various books forced me to think about how all the areas of intellectual life relate one to the other. In addition, I have received literally thousands of letters from readers, some of which have developed into ongoing correspondence that has materially expanded my view of the topics I wrote about."

But there are perils too that await the successful popularizer. Casti continues his story this way.

"Lest you think my experiences have been uniformly positive, let me note the one downside of this kind of notoriety, one that I'm sure all of us [popularizers] share. It is simply the fact that the visibility from these books tends to outshine anything else we may do along more traditional academic lines. This, in turn, forces people to stamp us with the label of 'popularizer, ' which occasionally works to our dis- advantage. For example, when I first came here to SFI three years ago, a meeting of the powers-that-be decided that I should not be a member of the SFI External Faculty since I was really more of a writer than an academic researcher. It took some time and effort on my part to convince a few skeptics that I actually had some ideas besides how to tell a story."

## Devlin's Tale

Used to living in a world of precisely defined categories, mathematicians may be more prone than others to regard 'popularizer' and 'researcher' as disjoint sets, a partition that has a tendency to turn the word 'popularizer' into a term of derision in certain circles within the mathematics community. Certainly my own experience bears this out. The general disapproval of my early attempts at popularization on the part of some (not all) of my colleagues at the University of Lancaster, in England, took a more serious turn in 1985. In that year, faced with a government imposed budget cut that could only be met by cutting a third of the faculty within two years, the university brought in a new vice chancellor (president) to steer the institution through the decidedly troubled waters it suddenly found itself in. A former dean at MIT, with a reputation as a pretty tough cookie, he declared that the necessary savings would be achieved by "cutting out the dead wood." What this phrase meant, he explained, were those faculty who were not active in research. An increased emphasis on research was to be the key to our salvation, particularly research that attracted external funding.

With an active research program that had resulted in both a steady string of publications and external funding, I naturally felt that the chill winds of this new agenda would not blow in my direction. So I was completely taken aback a few months later to find myself one of the first mathematics faculty advised to leave. It was some time before I was able to piece together what had led to my name appearing on the cost savings list. One of the problems was, a senior administrator informed me, that I was no longer sufficiently active in research; rather, my interests had turned to, in a phrase I remember to this day, "less academically respectable activities." What those activities amounted to was that, since 1983, I had written a twice-monthly mathematics column in the national newspaper

The Guardian, I had worked with the BBC on the production of a documentary about mathematics,A Mathematical Mystery Tour, and I had started to work on a popular book on mathematics,Mathematics: The New Golden Age, which Penguin published in 1987. The fact that my research program had continued to flourish, and had indeed received external funding with an industrial partner, was simply discounted. Having been successful in my attempts at popularization, I had become a 'popularizer,' and therefore could not be, so the logic went, a 'researcher.' of course, I had tenure, so I did not have to leave. But the writing was on the wall, and so I left for the United States * to take up a position at a research institute at Stanford, as irony would have it.Not a typical experience, of course, and in many ways a reflection more on the difficulties the entire British university system was facing at the time than on the details of my own particular case. But my experience does highlight the tendency for many in the academic community to regard popularization as exclusive of all other academic activities.

## Stewart's Tale

A two-hour drive from Lancaster, at the far more financially secure University of Warwick, my colleague and fellow British mathematics popularizer Ian Stewart (author of The Problems of Mathematics and many other mathematics bestsellers) had a much easier time of it.

"I'm lucky, I think: Warwick genuinely approves of activities that take science to the public . You won't get promotion for it, but it won't count against you and it earns some kind of brownie points provided you aren't neglecting your main work (lectures, papers, administration, grants). Our annual report even asks for 'public output' to be listed by each member of faculty. [And] my colleagues here generally seem to approve of popularization, under similar conditions !"

Having found, in the United States, an academic institution not only receptive to my popularization work but actively supportive, I am maybe now in an even better environment than Stewart. (I still have a highly active research program as well.) I can certainly agree with his observations on the negatives of popularization even when there is no open hostility: as a regular columnist in

Scientific Americanand a fellow contributor toThe Guardian, Stewart says,"The main pitfall that I have found is not so much negative comments from colleagues, but a serious failure by some mathematicians to appreciate the difference between journalism and writing a math paper for a journal. There are complaints about due credit not being given (they often think that newspaper articles have lists of references at the end). They have no appreciation that newspapers and magazines have space limitations and house styles. They don't understand that editors and subeditors will hash your work about but leave your name on it . They don't appreciate that with a forty-eight-hour deadline you can't do a total literature search to discover that some obscure Armenian published something vaguely similar in 1922 in

The Korean Journal of Newt-Watching. They get upset if you tell readers that a manifold is a multidimensional surface but forget to add 'paracompact Hausdorff.' They get very upset if you happen to mention that some area - other than their own - might be important. They make sweeping criticisms without doing their homework, as with Marilyn vos Savant and the goats in Pa- rade, or people who attack chaos theory on the grounds that it has no applications, when the literature contains little else. And many still do not appreciate that unless somebody tells the public what mathematicians are doing, support for the subject (and I mean appreciation rather than money) will dry up."My final moan is about complaints of 'premature publicity.' The story has to go to the public while it's still hot, not after the Annals has printed it. If it later turns out that the work fell to bits, that's another story, not a cancellation of the first one. In any case such complaints are leveled in very uneven ways: compare Rego-Rourke on the Poincare Conjecture, Hsiang on Kepler's sphere packing problem, and Wiles on Fermat.

"This may all sound negative. Not so, at least, not for me. My feeling is that in broad terms the mathematical profession is much more supportive of popularization than it used to be, and appreciates it more. The really top people nearly all do it. It is the next tier down, the brilliant second-raters, who think they know what mathematics 'really is' (and want to make sure every-body else does it their way), who tend to be the most narrow-minded and ill-informed."

## Paulos's Tale

John Allen Paulos of Temple University has probably been the most successful in the pop-math business in recent years. His 1989 book

Innumeracywas on theNew York Timesbestsellers list for eighteen weeks, his 1992 sequelBeyond Numerarywas another great success, and hisA Mathematician Reads the Newspaperhas just hit the bookstores. Paulos characterizes the view of his colleagues toward his success with these words:"I suspect that the dominant attitude toward academics who write for a popular audience is not snideness, jealousy, or hostility, but rather indifference. This attitude is certainly defensible, but although not a task for everybody, disseminating and vivifying mathematical ideas for a large audience is, I think, quite important. Moreover, it does seem to be undervalued by the profession."

In Paulos's case, the runaway success of

Innumeracyalso led to a somewhat acrimonious exchange with a reviewer in the October 1993 issue of theAmerican Mathematical Monthly. The reviewer took Paulos to task for a number of numerical inaccuracies in a book that was, after all, about innumeracy. In his response, Paulos emphasized his goal as follows:"The aim of

Innumeracywas to make vivid some of the consequences of mathematical illiteracy - muddled personal decisions, emotional risk assessment, misinformed governmental policies, and, yes, a generalized susceptibility to nonsense . Eschewing calculations for the most part, it attempted to do this via stories, anecdotes, vignettes, and some informal exposition."Now, as it happens, there were some points in

Innumeracywhere I too thought that a little more accuracy and precision were required, so on that score I can at least see the reviewer's point. But I know from experience that in writing for the popular market, you have to be prepared to be loose with the truth - sometimes very loose. (on television or the radio, the problem is even more acute, as Paulos, who has appeared on programs as diverse asThe David Letterman Showand theMacNeil/Lehrer News Hour, can attest.) You have to paint a big picture using a very broad brush, and to hell with the details and the precision. This requires that you make judgment calls as to just how far you can go. The decision you make depends on the audience you are trying to reach. "Why do you keep using the term 'infinitely long polynomial'?" one of my Lancaster colleagues used to complain regularly. "You could just as easily use the correct term 'infinite series' . . . and maybe add a remark about convergence." My standard answer was accurate, but the message never seemed to get across. I did not use the technically correct terminology because, if I did, my Guardian editor would not print my article. He had four-hundred-thousand readers for whom the term 'infinite series' would most likely mean Coronation Street or Eastenders. Enough of those readers could remember polynomials from high school to allow me to use that term, and the ones that did not remember, or never knew, were in any case not likely to be reading the Devlin column. So 'infinitely long polynomial it always was. (And they did not 'converge' or 'diverge'; they either gave an answer or they did not.)

## Dunham's Tale

William Dunham also achieved significant sales with his book Journey Through Genius , published in l99O, and his more recent The Mathematical Universe ( 1994) . He is a professor at Muhlenberg College, a small college in Pennsylvania. As I found when I took a position at a small college in the United States (is 23OO undergraduates small?), such institutions can be very supportive of popularization. Dunham puts it this way:"Over the years since publication of

Journey Through GeniusandThe Mathematical Universe, I have worked at a small liberal arts college and (as a visitor) at a large research university. I can report that mathematical colleagues at both institutions have been generous in their comments. I take this as a recognition across the discipline that mathematicians must do a better job reaching out to the wider public. In a number of ways, from the prosaic matter of government funding to the more noble one of cultivating future mathematicians, the health of our discipline depends on it."At the small college, writing for the scientifically literate reader actually counts. It is regarded as a legitimate professorial enterprise, one that not only serves the institution but also helps the author obtain employment, promotion, and/or tenure. This should not be surprising, for the liberal arts college is a place that devotes a great deal of time to examining, critiquing, and interpreting our intellectual heritage for the non-specialist. Efforts such as mine seem to fit into this mold. But my writing would never be regarded as 'serious' at the research institution. There, a single article on, say, non-cyclic complex k-modules over quasi-affine hypersemigroupoids - even if it boasts a world-wide readership of half of half a dozen - carries infinitely more status than fifty books for the popular audience. The research paper, the previously unproved theorem, the lemma with your name on it, these are the legitimate goals of the mathematician within that environment. All else is a sidebar.

"In some ways, it is difficult to argue with this attitude. Indeed, I suspect that all of us who have been through mathematics graduate school have internalized such a view to a greater or lesser extent. The research institution stands as the arbiter of professional standards, even for those of us far from its gates. Perhaps this is as it should be. Yet higher education has multiple objectives. Not everyone, after all, will be a concert violinist, yet nearly everyone can enjoy and appreciate music. I hope that, for some educated readers, I can be a guide to the greater enjoyment and appreciation of mathematics . And that, it seems to me, is an achievement not without merit."

Dunham also has some advice for anyone tempted to start out along the path of popular mathematics writing:

"While writing

Journey Through Genius, I was continually made aware of the inverse relationship between a book's mathematical content and its sales potential. My editors at John Wiley were extremely supportive of my mathematical objective: to examine as faithfully as possible the paths by which great mathematicians proved their great theorems. Yet the editors reminded me time and again that a book resembling a graduate analysis text is unlikely to challenge Stephen King or Danielle Steele at the cash register. In this light, writing for the popular audience is a delicate balancing act, one whose difficulties are fully apparent only to those who have given it a try."One clear difference between my kind of writing and the authorship of a highly technical paper on those non-cyclic complex k-modules is that I tend to get a lot of mail from readers. Some of my correspondents, I am pleased to say, fall under the heading of 'fans.' others, I am less pleased to say, fall under the heading of 'cranks.' Underwood Dudley, of course, knows far more about this professional peril than I do, but if anyone wants to see one-paragraph proofs of Fermat's Last Theorem having the Riemann hypothesis as a trivial corollary, drop me a line. I think I have a stack of them in my desk.

"Still, fans tend to be remembered longer than cranks. In my case, a few of these fans have been mathematicians themselves, so a fringe benefit of authoring popular mathematics books has been a string of speaking invitations from across the country. This has been an extremely enjoyable, if totally unexpected development."

## Why Do We Do It?

Schooled as we are in a discipline that places an incredibly high demand on accuracy and precision, most mathematicians find they simply cannot - and I mean cannot - give up on enough of that precision to write for the pop market. You can see that by taking a stroll around your local, non-academic bookstore. You can number on the fingers of two hands (some-times even one) the mathematics popularizers whose books appear on the shelves. There are many more Fields Medalists around than there are mathematicians who have written successful mathematics books for the general reader.

Given that all of us in the pop-math-by-the-professional-mathematician business have met some kind of disapproval from our colleagues, why do we continue to do it? Certainly not because of the money. Even if you 'hit the big time' and find yourself with a regular spot in a newspaper or magazine, or a book on the science bestseller list, you are unlikely to find yourself a millionaire overnight. With very few exceptions (Paulos is probably one of them), there simply is not that kind of money to be made from mathematics books and magazine articles.

I can think of two answers. The first is a personal one, which Ian Stewart sums up with the words, "I write about mathematics because I am a mathematician with a journalistic streak who has a way with words." Amen to that.

The second answer is at the level of the profession. As the sales of popular mathematics books show, there is a market out there for accessible expositions of mathematics. People want to know. Some of them are influential and can affect the financial support the mathematics profession receives from government and private sources; most are not. However, in a field as misunderstood as ours, do we really want to turn our backs on the relative few who show any interest? So I say three cheers for the math popular-izers and more power to their elbows (actually, keyboards these days). But then, I would say that, wouldn't I?

Keith Devlin is the editor of FOCUS. His most recent pop-math books, both of which appeared in 1994, are Mathematics: The Science of Patterns, published by WSH. Freeman in their Scientific American Library series, and All the Math That's Fit to Print: Articles from The Manchester Guardian, published by the MAA in the Spectrum series.

This article was taken from FOCUS. Vol. 15, Num. 3, June '95, pgs. 4-7.

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