“It would have been a very enjoyable ride altogether, that evening’s spin along the banks of the Rhine, if I had not been haunted at the time by the idea that I should have to write an account of it next day in my diary. As it was, I enjoyed it as a man enjoys dinner when he has got to make a speech after it, or as a critic enjoys a play.”

*Diary of a Pilgrimage,*1891

Jerome was a blogger. The diary he mentions in the passage above was not a private journal for his inmost thoughts; it was a travelogue, which would be published as soon as he got back to London. What’s more, his companions on that evening spin along the banks of the Rhine knew perfectly well that they would soon be reading their own words filtered through Jerome’s imagination, and if they said something particularly asinine, the whole world would know about it. This knowledge must have raised the anxiety level for both the author and his friends.

In the modern age of blogging, nothing has changed but the time scale. When I take a stroll with friends along the banks of the San Antonio River, they don’t have to wait until we all return home to read my account of the evening. They can have it with their breakfast the next morning. Fortunately for them and me, my friends *never* say anything asinine; our conversations are filled with scintillating wit.

I am here in San Antonio for the annual Joint Mathematics Meetings, an event I have attended for the past 10 or 12 years. Large academic gatherings are all alike, but each one is alike in its own way. This one is distinguished by its jointness: There are two main sponsoring organizations—the American Mathematical Society and the Mathematical Association of America. Roughly speaking, the AMS represents the interests of research mathematicians, whereas the MAA has a focus on the teaching of mathematics at the undergraduate level. There’s also the National Association of Mathematicians, the Association of Women in Mathematics, the Society for Industrial and Applied Mathematics, and the Association of Symbolic Logic, all of which are also sponsors of the Joint Meetings, plus the National Council of Teachers of Mathematics, which is not (officially) represented here. If we could start over, it seems possible that the world of mathematics could get along with somewhat fewer societies, associations, and councils—but it’s too late for that. We may as well celebrate the diversity and enjoy the jointness.

As a science writer attending these meetings, I feel I should try to sample a bit of everything, but I gravitate to the AMS sessions, the ones with new research results to report. This isn’t just elistism and showing off (although those reasons would be more than enough). Now that mathematics is such a pop phenomenon, with a spate of math movies and plays and even a TV show, I have to dig deeper to find a topic I can have to myself for a little while. This week, I’ve been hanging out in the AMS Special Section on Mahler Measure and Heights of Polynomials, and so far I have not noticed crowds of reporters in the back of the room. I hope to write a little something on the subject before *USA Today* ruins it for me. But I’m not quite ready yet.

In the meantime, I’d like to say something about that pop phenomenon. Several years ago, Bob Osserman of the Mathematical Sciences Research Institute in Berkeley pointed out to me that some sort of cultural shift seemed to be underway, as mathematics was going from unspeakable to inescapable in various areas of the arts and entertainment. At the time, Tom Stoppard’s play “Arcadia” and the film “Good Will Hunting” were both popular hits. I was relentlessly skeptical. It’s just an illusion, I said; there have always been such works, but we forget them. Or if it’s real, it won’t last. If it lasts, it will do more harm than good. A few years later, at another of these Joint Meetings, I was the designated naysayer in a panel discussion on mathematics and the movies, organized by Allyn Jackson and Keith Devlin. On this occasion the film version of “A Beautiful Mind” had just opened. I took the dour position that no one really cared about mathematics; they just wanted stories about oddball geniuses. Last year at the Joint Meetings, we saw previews of a new television series, “NUMB3RS.” I predicted that it wouldn’t last to the end of its first season. This year, the Joint Meetings included a special reception to celebrate the fabulous success of “NUMB3RS,” attended by **Judd Hirsch**, among other bold-face names. I didn’t go. It’s not that I’m bitter or a snob or a sore loser. It’s just that I couldn’t be pulled away from a fascinating session on probability and stochastic processes.

The mathematical community seems to have adapted gracefully to its newfound celebrity. Rather than growing conceited, it may even be taking itself a little less seriously than it once did. For the past few years, a highlight of the meetings has been a quiz show called “Who Wants to Be a Mathematician?,” in which local high school students compete for cash prizes. The TV show that inspired this idea did not fare as well as “NUMB3RS,” but the mathematical spinoff is still going strong, conducted with great showmanship by Mike Breen and Annette Emerson of the AMS and Bill Butterworth of DePaul University.

This year there was an even wilder event: The Great Pi/*e* Debate, where Colin Adams and Tom Garrity (both of Williams College) stood up as champions for those famous numbers. Like any good debate, it was full of bombast and devoid of content. Also, the humor was not excessively sophisticated. The crowd loved it, but I have to report that I was slightly disappointed. I had actually come to learn something, and in particular I had hoped to solve a small, recurrent, personal problem. I write for an audience of nonspecialists, and when I mention pi or *e*, I sometimes need to append a brief phrase explaining or introducing those symbols. That’s easy for pi; as Adams quickly pointed out, pi is the ratio of a circle’s circumference to its diameter. But what is *e*? The customary identifying phrase is “the base of the natural logarithms,” but that’s not terribly helpful; those who need a definition of *e* probably also need a little help with “natural logarithms.” Garrity, in his (winning) defense of *e*, took a different approach, emphasizing that the function *y = e ^{x}* is its own derivative. This is an interesting and important property of

*e*, but again it’s not the pithy slogan I was looking for. On the other hand, solving my little problem was hardly the aim of the debate. I’m looking forward to next year’s mud-wrestling/wet-teeshirt contest between phi and gamma.

Just as pi (between 3 and 4) is the number that controls all circular, repetitive, rythmical processes in the universe (heartbeat, planetary orbit, etc.), so

e(between 2 and 3) is the number that controls all processes of explosion and decay (population, bomb, dying away of sound), and phi (between 1 and 2) is the number that controls all processes of natural growth (trees, cities, chambered nautilus), and Feigenbaum’s Constant (between 4 and 5) controls all process of complexification.