Almost all of the presentations at this conference are in the form of expository or survey papers, comprehensive reviews of those areas of post-modern mathematics which are needed for an understanding of Wiles proof of Fermat's Theorem. I use the term post-modern mathematics advisedly, as there were very few number theorists in 1984 who could, at that time, understood even the vocabulary in which most of these lectures are presented. Equivalently, one could define "modern mathematics" as that part of the subject of which most of the general public hasn't a clue, and "post modern mathematics " as that part of modern mathematics which puts most mathematicians in together with the general public!
These are not, in other words, survey lectures for mathematicians in general, and certainly not intended to include scientists from other fields. At the same time, since the number of advanced sub-branches of mathematics which are used in Wiles' proof is large, it turns out that even the graduate students who have come here aren't able to understand more than a certain portion of what they are being taught: the word "understanding" is flexible of course. One doesn't always have to understand how a certain result was obtained, provided one understands the result itself, and something about the methods used. Despite the difficulties of communication there is no doubt that the experience is a valuable one for most of the participants .
The real problems in communication appear to take place not during, but between and after the lectures. Almost all conversations consist of shop talk on a very advanced level. When misunderstandings arise , or a lack of common ground is discovered , the conversation degenerates quickly into banalities. I don't automatically object to this : the small talk is neither more nor less amusing than it usually is among erudite folk when there is little else to talk about. An enormous vacuum does exist with respect to any attempt to relate the ideas of post-modern algebra, algebraic geometry and number theory, to
I always find this very exasperating. I suppose it is inevitable that this should be the case in any conclave of specialists. However, a standard phenomena, which is either annoying or amusing with all other scientific disciplines, turns into a veritable pathology at conferences devoted to specialized topics in mathematics. Among other things it makes for a great deal of social awkwardness. One never knows whether
One of the consequences of this , or one may be speaking in fact of the cause of it all, is that graduate students are , by and large, monotonously predictable. They remind one of nothing so much as the all but identical outlets of the big concession chains, MacDonalds, Pizza Hut, CVS, and so on. Still, graduate students are people underneath , by and large with good intelligence, and people always manage to have something interesting about them . It is usually easier to get them to talk when you inform them that you really know hardly anything at all about the subject of the conference, ( but that you are a mathematician). This removes the obligatory obsession with shop talk , as well as the need to otherwise restrict oneself to banalities.
A lounge has been opened every evening from 7 to 11 in Rich Hall , the B. U. dormitory in which the conference is being housed. It provides free soda, beer, potato chips, pretzels and popcorn and a ping-pong table . Graduate students and professors stand about or sit in groups, and it is easy for me just to go from one group to another, state that I am a reporter covering the conference for an Internet newspaper, and get them to open up.
Some of the more interesting participants are from Roumania. Corneliu Hoffman is currently a graduate student in Number Theory at the University of Southern California in Los Angeles. He doesn't really like living in the United States very much and is anxious to get back to Roumania, but the political situation is so terrible there that he doesn't think he can go back for quite some time. His position at USC is secure for another 3 years. We observed that American newspapers carry just about nothing about Roumania, and even less about Bulgaria, Albania, and not much more about any other Eastern European country for that matter. He said that he only knew about the situation over there by staying in touch with his family over the telephone. It was very hard to get newspapers here, and most of the Roumanian ones were quite unreliable anyway, pushing this or that propaganda or political platform.
As with most Roumanian intellectuals that I have met, he is much more interested in French cultural activity than in anything going on in the Anglophone world. We talked about Ionesco, Cioran, Brancusi, Eliade. He wanted to know more about Alexandre Grothendieck. Evoking my passing acquaintance with the colorful French mathematician has proven to be an easy subject for conversation with grad students looking for a way out of the shop-talk/trivia bind.
I discussed this with another graduate student, Jeffrey Hooper from Hamilton, Ontario. He feels that it explains the exaggerated interest in the persons who profess to have quick elementary proof of Fermat's Theorem, of whom there are a few at the conference All of Sunday has been set aside for 20 minute expositions of original research by all and sundry. The persons proposing "Fermat proofs" that are obviously crank, have been shunted into in the same room, to appear consecutively in a 2 hour morning session: a kind of 3-ring circus , or gong show of jesters and fools.
Jeffrey has a theory about why the conference organizers have done this. After a week of self-enforced attendance at lectures which are either very difficult or just about impossible to understand ( the distribution of "difficulty" and "impossibility" varying from person to person, depending on their specializations ) , the grad students will seize at the chance to blow off steam with a 2 hour comedy act . Some have even suggested that they might bring along a 6-pack, if it isn't forbidden by university regulations ( which it probably is) . The rationale behind this closely resembles that of the managers of Bedlam who charged admission for the English public to laugh at the lunatics. In this case, however, given the high incidence of mental illness present in the mathematics community, it may well turn into a spectacle of one part of the asylum turning out to laugh at the other.
I am perhaps being unkind, but there is definitely a certain kind of shallowness of emotive affect which is endemic to the world of mathematics, ( as well as that of all modern science, ( as well as the whole rest of the dehumanized race.)) The real victims of course will not be the rather sad individuals, ( at least one of whom I know personally, an intelligent man who suffers from acute manic depression ), who will bravely expose their specious 'proofs' to the experts, but the very hard working graduate students , ( and I will not rob them of this glory: graduate students in the sciences do work very hard, solving problems which, often enough, get sent to the journals over the name of their thesis advisor .) , who have painstakingly put together a 20 minute exposition of their own research in preparation for the Great Fermat Conference , only to discover that their audience has abandoned them for the pleasures of the Roman circus! I count 6 of these students on the official schedule for Sunday morning . They will be lecturing in two other rooms on the 5th floor of the College of General Studies on Sunday morning.
The looming question is : should I, as roving reporter, attend the crank sessions , just to expose this performer/spectator interface to the world ? Or should I go to the talks of the other , serious young mathematicians as a gesture of solidarity? Alas! For we know how this moral quandry will be resolved. I'm doing a job for the media , and the media wants blood and guts. I will keep you posted.
One of the reasons that I attend conferences is that I am sure to meet old acquaintances. I have in fact met a few of these at this one, but compared to others it has turned out to be something of a disappointment. The reasons are easily sought. For although I have been coasting American universities for all my life, and with particular intensity these last 15 years, I have only rarely encountered persons working in Number Theory. The demographics of those engaged in "applied algebraic geometry" , are bleaker still. Everywhere I have gone, I almost never meet anyone who has specialized in Number Theory. It does happen, but it is rare. Suddenly I find myself at a conference at which everyone is a number theorist. I am thrilled; but the consequence of this is that I've never met most of the people with whom I'm destined to spend the better part of a week.
I do find at least one old friend. I frequently encountered him in the late 70's and early 80's because he happened at that time to be gyrating in the same circles . After the first lecture on the first morning, ( A survey talk by Glenn Stevens of Boston University that sketched the history of the Fermat problem and solution since 1984; I will be referring to this in my Aug 16-17th report) , I observed a short individual with a Rasputin-like beard and scowl staring at me from across the auditorium. I later ran into him alone at the bottom of a staircase and realized that what I had taken for a scowl was actually a smile mixed with perplexity - the difficulty being that of identifying the facial expression under the beard.
He turned out to be David Feldman, an avant-garde pianist and composer turned mathematician. Back in 1979 I had been introduced to him by someone who at that time was my student in mathematics, but who has since gone on to be very famous in his own field: the composer/ computer scientist Jaron Lanier.
David hadn't heard from Jaron since he became a celebrity, whereas I has lost contact with him from about 1984. David seems to have put the pianist behind him. He now teaches at the University of New Hampshire, and I have never encountered him at any time since 1980 when he wasn't going to a math conference or engaged in something to do with mathematics.
Apart from David I've met one other friend at the conference, ( though I have encountered a number of those hostile Berkeley math department types who continue to regard me with that " What's that's creep doing here? Is he still alive, or am I dreaming?" look they reserve for me and people like me. To understand why this is so you must ask anyone who knows, what I was doing around Berkeley from 1983 to 1987.
One of these is Ken Ribet, a very famous number theorist and one of the people responsible for the proof of a theorem ( known as the 'epsilon conjecture' ) that was crucial to Wiles' research. Ribet used to see me around Berkeley, though I suspect he doesn't exactly remembered where he first laid eyes on me. He was staring at me with a kind of benign contempt when I approached him and asked him if I might interview him about the epsilon conjecture. Condescension turned to annoyance as he waved his hands and walked away, saying " If you don't mind, I'm burned out on the media. I'm not going to bother answering your questions."
I am not totally out of sympathy with him.
Most reporters are not professional mathematicians
and I'm sure his interviews were distorted in ridiculous ways.
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