Article by John Derbyshire

I am sorry.  Really, really sorry.  I apologize.

I apologize to readers who e-mailed me last week and got bounced because my e-mailbox was full.  I apologize to NRO for being disgracefully late with this column.  I apologize for not having participated in The Corner for several days.  Most of all, I apologize for having nothing pithy to say about the state of the world, no red-meat political incorrectness to offer on gun control, racial profiling, immigration, militant homosexuals or the ChiComs.  I am sorry for all these things;  but, of course, I have an excuse.  Readers, I have been in the zone.

To be precise, from Tuesday last to Saturday I was attending an academic conference at the Courant Institute of Mathematical Sciences in New York City.  The title of the thing was:  “Workshop on Zeta Functions and Associated Riemann Hypotheses”.  Readers who are new to this column (and who are still with me after that last sentence) will need to know a certain endearing peculiarity of the Derb personality.  I suffer from a weakness — an obsession, almost — that has no name.  American slang employs the slightly disgusting expression “jock-sniffer” to refer to the type of person who, while not at all athletic himself, gets his thrills by hanging out with athletes.  Richard Nixon was an instance of “jock-sniffing”.  Well, I am the mathematical equivalent — a pocket-protector-sniffer, perhaps.  I am not much good at math, but just love being around mathematicians. 

That was what I was doing for most of last week, and that is why I got no useful work done, and why I have nothing in my head right now to make a decent column out of.  You will have to make do with mathematicians (though I shall spare you actual math).  I know, I know:  you ask for bread and I give you a stone.  I am really sorry.

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Mathematicians talking.  The elevator at the Courant Institute serves 13 floors.  The buttons inside the elevator are set out in three columns.  The floor numbers are located alongside the buttons in such a way that it needs a few second’s attention to figure out which button sends you to which floor.  I got into the elevator with two other conference visitors.  The first one went through the necessary moment of perplexity before locating the right button.  “By no means a straightforward mapping,” he remarked when he had found it.  “Definitely nontrivial,” agreed his colleague.

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Everyone’s a critic.  Science writer Bruce Schechter was at the conference, covering it for The New York Times.  (Like any honest reactionary, I loathe the Times.  I must give them credit, though, for their coverage of math and science, which is way above that of any other newspaper I know, except the even more politically deplorable London Guardian, which leads the world in this field.  Why can’t conservative newspapers “do” science and math?)  Meeting Bruce, I had a sudden recollection that I had been unkind in reviewing a book of his a couple of years ago.  There didn’t seem to be any hard feelings, though.  The main thing Bruce wanted to grumble about was the difficulty of presenting these very abstruse topics to a general readership.  Derb: “You think you’ve got problems.  I’m trying to write a book about this stuff.”  Bruce is an exceptionally good-natured guy, and I feel terrible for having carped at some tiny error in his excellent book.  Please be gentle with my book, Bruce.

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Blood sport.  There is no intellectual discipline more rigorous, demanding and unforgiving than math.  One speaker, ten minutes into his lecture, seemed to have contradicted a result well-known to some specialists in the audience.  They stopped him at once, and the poor guy had to go back and justify every step in his argument.  He got flustered:  the hounds, smelling fear, closed in on him, snarling.  It turned out he’d been using a non-standard notation that had confused the issue.  Once this was clear, he was allowed to live, but he left the podium a nervous wreck.  If you step up before a room full of mathematicians, be well prepared, and expect no mercy. 

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Peer review.  Not that matters of judgment are entirely absent, even when the math is sound.  If you’ve ever spent time with serious opera fans, you know how startlingly different their judgments can be.  At the crush bar in the interval you hear aficionado X saying:  “Isn’t the diva in terrific form?  Superb — oh! that rubato!”  Then you walk across the room and hear aficionado Y saying: “What a disaster!  She should have retired five years ago!  Did you hear her wobble in the cavatina?  And is that what passes for rubato nowadays?”  So with math.  A key player in the developments I’m investigating is French mathematician Alain Connes.  Here are two opinions about Connes’ theories, both from tenured professors with major mathematical achievements to their credit.  Gushes Professor A:  “This stuff is so exciting, isn’t it?  Connes will not only prove the Hypothesis, he’ll give us a unified field theory, too!”  Sniffs Professor B:  “All Connes has done is take an intractable problem and replace it with a different problem, that is equally intractable.”  Take your pick.

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Don’t judge a book by its cover.  Jeff Lagarias from AT&T Labs gave a very nice talk about two-variable zeta functions over finite fields.  Unfortunately I couldn’t take any of it seriously, because Jeff is a dead ringer for Michael Palin of the old Monty Python show.  I kept expecting him to break into the Lumberjack Song.  Quite a lot of mathematicians look utterly un-academic.  Peter Sarnak, Professor of Mathematics at Princeton University, and one of the most brilliant men in America, looks as little like a mathematician as anyone possibly could.  If you met him in the street and were asked to guess how he makes his living, your guesses would start off something like:  carny barker, middleweight boxer, personal trainer, junior mafioso, cop,...  “Mathematician” would be around guess number 849.  It isn’t all pocket protectors and white socks.

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Communal defenses.  Mathematicians, like the members of any other common-interest community, put out a certain amount of squid ink to confuse and deter outsiders.  Talking with Peter Sarnak about my book, which is targeted at non-mathematicians, I mentioned that among the topics I was finding most difficult to put into ordinary language was the “big oh” notation, a way mathematicians have of describing how fast a function increases when its argument gets indefinitely large (“goes to infinity”).  Sarnak: “You’d better talk to my colleague Nick [i.e. Nicholas Katz].  He never uses big oh.  Hates it, won’t use it.”  I was surprised to hear this — big oh has been standard notation for 93 years — but I thought it would make an interesting snippet for my book.  Then, that evening, I was talking with Andrew Wiles, the English mathematician who attained immortality by proving Fermat’s Last Theorem.  Wiles is now at Princeton, with Sarnak and Katz.  I mentioned Katz’s antipathy to big oh.  Said Wiles:  “That’s all nonsense.  It’s just a story they put around to tease newcomers.  Of course he uses it.  How could he not use it?”  So I had been taken for a ride.  Sarnak really should be a carny barker.

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Taking it with you.  Here is a story about big oh.  The great Hungarian number theorist Paul Turan died from cancer in 1976.  His wife was at his bedside at the end.  She reported that his last murmured words were:  “Big oh of one...”  Mathematicians tell this story with awed admiration.  “Doing number theory to the last!  A real mathematician!”

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Doctor Derb and Mister Hyde.  Since math is, let’s face it, a difficult subject, it’s odd that it attracts so many cranks and amateurs.  A couple of these managed to gatecrash the Courant conference somehow.  One was a lugubrious Indian gentleman intent on cornering Andrew Wiles with an elementary proof of Fermat’s Last Theorem.  (“Uses only high school math!  No modular forms!”  Yeah, right.  Hilbert, or it might have been Landau, had cards printed up saying:  “Dear Sir, Thank you for your proof of Fermat’s Last Theorem.  The first error is on page _____.”  When a crank proof came in, he’d give it to an undergraduate with one of the cards, to have the page number filled in and be mailed back.) 

I had a crank of my very own at Courant.  It was a strange-looking gentleman from mainland China, with some bee in his bonnet about the Riemann Hypothesis.  I made the mistake of showing off my Chinese to him the first evening.  After that he followed me everywhere.  There were other Chinese people at the conference, but all of them were studying or working in the States, and they all had him figured out at a glance — none of them would speak to him.  His English was rudimentary; goodness only knows how he followed the lectures. 

It got so bad I put out an APB to the half-dozen scholars I was on friendly terms with to rescue me if they saw me cornered by this man.  They weren’t very diligent about it, though, and I couldn’t shake him off.  Body language didn’t work.  The man started to be a real nuisance.  I like to go in early to the first lecture so I can get an aisle seat, but I feared if I did that, the crank would come and sit next to me, so I started going in at the last minute.  This lunatic was wrecking the conference for me.  At last I was rude.  I am not a rude person, and it takes a lot to force me into bad manners, but this oaf did it.  I don’t feel the least bit bad about this.  Take a course in body language, buddy.

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Not as dumb as I look.  One of the densest presentations was given by Israeli mathematician Shai Haran from the Haifa Technion.  I did my best with it, and I think grasped the main point; but if you had asked me, an hour later, to give a précis of the lecture, I wouldn’t have been able to.  As Haran was leaving the podium, in fact, I turned to the eminent mathematician sitting next to me and said: “I don’t think I got more than 20 per cent of that.”  My neighbor replied: “If you got 20 per cent, you were doing pretty well.”  Hey. 

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Doing good by stealth.  This whole conference was organized by the American Intitute for Mathematics, a private foundation based in Palo Alto.  AIM was set up in 1994 by John Fry, founder and CEO of Fry’s Electronics (a chain of retail stores), Brian Conrey, a college classmate of John’s, and Professor Gerry Alexanderson of Santa Clara University.  John Fry has put a ton of money — his own money — into AIM, from sheer love of math and desire to advance the state of human knowledge.  This is capitalism at its best:  when you’ve made your pile, you put something back — something real in this case, not like Bill Gates’s PC guilt trips.  It’s very American.  In England, when you’ve made a pile, you retire to a house called “The Old Vicarage” in some sleepy village, and join the local hunt. 

John is a better mathematician than I ever was.  He had the choice of going to graduate school or going into business;  he chose business.  There’s no doubt about his love of math, though — his face lights up when he talks about it.  A reserved and private man, he prefers to do good by stealth.  When I first heard about AIM, I went looking for a picture of John on the Internet.  There aren’t any.  He would probably be irritated if he saw these words.  I had therefore better say no more, except:  if there is a Fry’s store in your town, go buy yourself a beeping gadget of some kind, and help push the great wheel of pure knowledge forward an inch or two.  (In fairness, I should add that the Courant conference also got some funding from the National Science Foundation too — the first time that AIM has received this kind of support, I think.)