John Derbyshire is an interesting fellow. Most bloggers know him as a political commentator for National Review. The literary minded know him as the author of a critically acclaimed novel (Seeing Calvin Coolidge in a Dream). His most recent book – Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics – goes in a different direction: advanced math. Here is a teaser from the dust jacket:
Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, Riemannâ€™s hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof — and those who have been consumed by it.
Born and raised in England, Derbyshire it turns out is a mathematician and linguist by education. He has made his home here in the States for the last fifteen years (and was recently granted citizenship) often working as a systems analyst for Wall Street firms. In his “spare time” Derbyshire also writes for the New Criterion and the Washington Times among others.
Intrigued by this new book, I thought it would be interesting to ask Mr. Derbyshire a few questions and he graciously agreed to answer them. The interview below was conducted by email.
1) You write political commentary and book reviews for your day job and have written a critically acclaimed novel. Why write a book about a very complex math problem?
I am quite interested in politics, and have some strong opinions. It can be fun to write about. I like all kinds of reading and writing, too. Math, however, is a little oasis of pure intellection, serene and quiet, and I love to stop off there for a while now and again, as a rest from all the noise and dirt. Well, I stopped off a bit too long one day, a 10-page proposal for a book about the Riemann Hypothesis was the result, and a foolish publisher took me on.
2) There are a lot of unsolved math problems, what makes the RH such a compelling riddle for mathematicians?
It’s the big one, the great white whale. I don’t think there is any practical reason for wanting to crack it. Well, people will tell you there is; but that is like all those justification for the manned space program that NASA used to come out with–you know, non-stick frying pans and so on.
Everybody involved knew that the real justification was the challenge and excitement of it. Same with the RH. It has withstood everything mathematicians could throw at it, all through the 20th century. It’s a challenge.
3) The central character in the book is far from a household name outside the math community. What type of person was Bernard Riemann? What made him interesting to write about?
He was a sickly, unhappy and antisocial person, never really at ease away from the family hearth. He drove himself to prodigies of brilliant, creative work, partly I think to keep the demons at bay, partly out of a deep religious conviction that in this way, and only in this way, he could be useful to his Creator–fulfill the Creator’s purpose for him. He was very pious, and very filial–the son of a clergyman.
4) A number of the key players in this story have a connection to
Goettingen, Germany. What was it about Goettingen that made it such a center of math for so long?
Gauss started it. Then there was a succession of brilliant mathematicians: Dirichlet, Riemann, Klein. In a way, though, it’s a mysterious thing, how a rather sleepy provincial place like that built up such a reputation. I am certain that if Gauss hadn’t got the ball rolling, nobody would have heard of Goettingen. On the other hand, I can’t see any reason why the place might not have sunk back into obscurity after Gauss… or after Riemann, or after Klein… I guess I don’t really have a full answer.
5) Why are you pessimistic about RH being solved any time soon?
From hanging out with the researchers for several months. As I said, the mood you get is of troops in a war that, in 2002, was in a kind of lull after some sensational advances, and in which nobody really has a clear idea how to push things forward. A lot of really interesting ideas didn’t pan out in the way that had been hoped. We need some fresh ideas. They will come, I’m sure, but they will need digesting and promoting… We are years, probably decades from a solution… Unless we are not: see my note about Hilbert in Chapter 22.iii.
6) There is a rather serious amount of math in this book. What type of reader were you aiming for? What constraints did the math put on your writing?
Well, I took the point of view that there wasn’t much point writing a book about the RH unless you tell the reader WHAT IT IS. You can’t do that without a lot of math. I bit the bullet, and tried to figure out the absolute minimum of math I would have to use. I was encouraged, talking to people in the early stages, to find out how many people–non-mathematicians, I mean–know quite a lot of math. Lots of journalists know basic calculus, for example. Who woulda thunk it? “Who is this book for?” That’s the question publishers always ask. It’s for an intelligent reader who was good at high school math and is willing to take in a wee bit more, who wants to know what the RH is all about.
7) American students have often struggled in areas like math and science.
Those who excel in them are often thought of as â€œgeeksâ€ etc. Why do think that is?
Well, although our country has great universities, and a huge number of first-class minds in all areas of knowledge, we are not, fundamentally, an intellectual nation. Americans are the “can do” people, a practical people–inventors, business people, farmers, engineers, entertainers, accountants, lawyers. Math–at any rate, the areas of math I have written about–analysis, number theory–is pure thought, and that’s a bit rarefied for such a practical people. And in fact, it is historically rare for math to be sexy. It was sexy in first-millennium India; it was sexy in Hungary for a few decades from the 1880s on; it was sexy in ancient Athens for a while. I think that for most of human history, though, in most places, pure mathematicians have had trouble getting dates.
8) You say in the book that math is counter-intuitive in many ways. Is that what turns people off?
Yes, there is that. The mathematical way of thinking is unnatural in some sense. It actually repels a lot of people. My wife, for instance. When my subscription copy of the MAA monthly arrives in the mail, I sit there after dinner chuckling over the theorems, and my wife shakes her head and says: “How can you READ that stuff?” One day while I was writing the book, I had lunch with a friend of mine, a brilliant man who had had a successful career on Wall Street. He asked what the book is about. I said: “Prime numbers.” He asked me if 1 is a prime number. I said mathematicians did not include it as such. “Why? It fits the definition, doesn’t it?”
Yes, I said, it does, but as a matter of convention… “But if it fits the definition, isn’t it a prime?” I kept trying to explain, and he kept not getting it. Here was this very intelligent man, who was never going to get any way into understanding prime numbers, because he was stuck on this trivial–to a mathematician!–legalistic point. Just a different way of thinking.
9) Many of the ideas touched on in the book have had an impact outside of pure math but those involved were pursuing these ideas outside any search for practical benefit. What do you see as the point or meaning behind pure or abstract math?
I can’t see that there is any. It’s just pure intellectual pleasure.
The amazing thing is that later–years, decades, sometimes CENTURIES later–it turns out to be useful. It ALWAYS does. As Hadamard said, in that wonderful quote I include in Chapter 22: “The answer appears to us before the question…” But the driving energy behind mathematical inquiry, 99 percent of it, comes from sheer intellectual curiosity.
10) You have now written a novel with a traditional fiction publisher; have published a novel through an â€œon demandâ€ or instant publisher, and now a work via a academic press (of sorts). Do you think â€œon-demandâ€ or self-publishing will develop into more than just a vanity press?
Probably not. With the possibilities for promotion that the Internet provides, though, all forms of vanity publishing–including “on-demand” self-publishing–have a much better chance to be successful. Lots of people are making money–not fortunes, but a check for a couple of thousand dollars twice a year–with “on-demand” self-publishing. Sooner or later there will be a best-seller. The big old publishing houses will continue to dominate, though.
11) As a writer you seem very hard to pin down. Literary and well read but knowledgeable in math and computers; a novelist but uninterested in much philosophical introspection; a metrocon but sympathetic to paleocons, etc. Have you always been eclectic in your views and interests?
You have put it very kindly. The truth is that I am a butterfly, without any really deep understanding of anything much–a dilettante, really. Most of my knowledge is pretty superficial. I was a terrible studentâ€”never really got good study habits. And it is not true that I am well read. I find it very difficult to read things that don’t “catch” me. For example, I know next to nothing about American literature, most of which I find very dull. Conversely, I find it hard to stop reading stuff that DOES “catch” me. I read all 16 (as then was) of the Patrick O’Brien Aubrey-Maturin novels, one right after another. Same with Elmore Leonard: I just kept going back to the library for more. Then one day I was reading one, and I thought to myself: “Hey, I remember this Albanian character…” I had read my way all through Leonard’s crime fiction, then started again. Nor is it really the case that I am sympathetic to paleocons. I think they are living in a fantasy world–this sleepy, righteous, agrarian republic, virtuously minding its own business here in the middle of nowhere. It’s a fantasy: nobody’s going to let us mind our own business, the world’s too small. The reason I hang out with paleocons is that on a lot of topics they speak more honestly than “respectable” conservatives can, and I find that very refreshing. Don’t get me wrong: there are good reasons for the self-imposed restraints that “respectable” conservative journalists like me accept–mainly, that we would be crucified byt the liberal media establishment if we broached those limits, and have to give up opinionating and go find some boring office job somewhere. (This is probably going to happen to me sooner or later, actually. I am not very careful about what I say, having grown up in the era before Political Correctness, and never having internalized the necessary restraints. I am a homophobe, though a mild and tolerant one, and a racist, though an even more mild and tolerant one, and those things are going to be illegal pretty soon, the way we are going. Of course, people will still be that way in their hearts, but they will be afraid to admit it, and will be punished if they do admit it. It is already illegal in Britain to express public disapproval of homosexuality–there have been several prosecutions. It will be the same here in 5-10 years, and I shall be out of a job. Fortunately I have marketable skills.) It’s nice to know that there are people braver than we are, though. Kind of like watching the U.S. Marines in action.
UPDATE: Mr. Derbyshire provided some clarification on these contentious issues here.
12) What is the biggest difference between living in the States and living abroad?
Space. Everything’s so spread out here. The other places I know well–England, China–are terribly crowded by comparison. I read somewhere that the population density in the Chinese countryside, in the fertile areas of the east and south lowlands, is higher than in the average American suburb. I believe it. And there are so many trees here! You can drive 20 miles north of New York City and see nothing but trees, all the way to the horizon. Amazing! Did you know that there are more trees in New York state today than there were 100 years ago?
13) One last question: do you read blogs? If so any in particular?
Not systematically. Of course, if someone directs me to something interesting on a blog, I read it. Otherwise, if I’m at a loose end, there are a few blogs I will go to, to see what they are up to. I like Fred Reed, who I think is wise and funny, and check in there regularly. Noah Millman’s
“Gideon’s Blog” is great for original thinking about big public issues, especially anything to do with the Middle East. Larry Auster often says interesting things, though his site is a humor-free zone unfortunately. I have great trouble understanding how people get through life with no sense of humor, but a surprising number do. Randall Parker (ParaPundit.com) is good, and generally simpatico, though sometimes descending into tiresome wonkiness. VDARE is an excellent site for anything related to immigration and ethnicity. Not sure it counts as a blog; but it has really clever people saying interesting things–Steve Sailer, Sam Francis, Paul Craig Roberts. It’s also very well constructed, with masses of links.
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