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Scientists' Nightstand: David Mumford

Mathematician David Mumford is known for his work in algebraic geometry and vision and pattern theory. A winner of the Fields Medal in 1974, he is currently a professor in the Division of Applied Mathematics at Brown University. His books include Indra's Pearls: The Vision of Felix Klein (Cambridge University Press, 2002).

Could you tell us a bit about yourself? Click to Enlarge Image

I'm a mathematician who has worked in both pure and applied math. These are very different: In pure math, the only thing that counts is proving theorems, which is to say unraveling the abstract structures of algebra, geometry and analysis. This is building castles in the sky. On the other hand, in applied math, you seek models for things going on in the real world, models which simplify reality but nonetheless capture the essence of some real system. The pure and applied sides complement each other, and I've spent roughly half my career on each. In applications, I have worked especially on visual perception and the neurophysiology of vision.

What books are you currently reading (or have you just finished reading) for your work or for pleasure? Why did you choose them, and what do you think of them?

On the one hand, I have wanted for some time to understand Arab culture better. It started with discovering the beautiful scientific work of Ibn al-Haytham (a.k.a. Alhazen) on vision, whom I would place on a par with Galileo and Kepler. Then my historian son sent me Maria Rosa Menocal's The Ornament of the World (Little, Brown, 2002), a wonderful, loving account of the Muslim society in medieval Spain, its greatness and its downfall. And then a friend told me about Philip Khuri Hitti's book The Arabs (Princeton University Press, 1943), and another friend told me you must take seriously The Thousand and One Nights—but only the J. C. Mardrus/Powys Mathers translation (The Book of the Thousand Nights and One Night, 1923), which doesn't take out the sex. So I'm in the middle of this!

But I have to confess a lifelong interest in science fiction, perhaps the subgenre which Freeman Dyson calls "theo-fiction." Olaf Stapledon is, in my view, one of the most provocative authors I have read. Recently a friend gave me the wonderful book The Master and Margarita, by Mikhail Bulgakov, recently translated by Diana Burgin and Katherine O'Connor (Ardis, 1995): It's a wild story of the devil toying with the good citizens of Moscow of the '20s and '30s. Check it out!

When and where do you usually read (specific location, time of day, etc.)?

Before going to bed or on planes.

Who are your favorite writers (fiction, nonfiction or poetry)? Why?

In college, I loved Joseph Conrad: No one can ratchet up the tension like he does. At various times, I have read avidly Joyce Cary, V. S. Naipaul, Robertson Davies, John Irving. I am a sailor, and I love sailing books—Alan Villiers and Joshua Slocum, for instance. My first wife was a poet, and she showed me some poems that seem so absolutely right—Theodore Roethke's "The Waking" and Phillip Levine's "They Feed the Lion."

What are the three best books you've ever read? Explain.

Oh boy: That's hard. I notice that an earlier respondent mentioned Freud's The Interpretation of Dreams (1900). I have to say this book was hugely influential on me, too, and I find it bizarre that Freud is discounted nowadays to such a huge degree. I think everyone should be aware that many things are going on in their minds without coming into consciousness. A second book which I found very provocative is Freeman Dyson's Disturbing the Universe (Harper & Row, 1979). The depth and breadth of his thinking is inspiring. Each piece here is something to mull over at length. I think I should choose a math book for the third. Now, math books are not cover-to-cover reads (for me, at least). They are rich sources of ideas into which you dip multiple times and find new insights each time. My candidate for the best math book is G. H. Hardy and E. M. Wright's An Introduction to the Theory of Numbers (1938), which is full of so many different sides of the subject and is beautifully written (for a math book!).

What book has influenced you most? Explain how.

I think I should look at the books that had a professional impact on me. In pure math, there was no one book: It was really my professors' lectures that brought this subject alive, especially those of George Mackey and Oscar Zariski. To get started in math, there is nothing like the human voice, the proof that all this abstraction is alive for someone else. But in applied math, there was one book. It is David Marr's book Vision (W. H. Freeman, 1982). For me, this book defined clearly a whole area of science. It shows how math and computer science can be brought to bear on psychophysics and neurophysiology in ways which seem an order of magnitude deeper than anything before (for example, earlier ideas in artificial intelligence or ideas of neural nets). The actual content is now a bit dated, but the approach is not.

Name three books you want to read but haven't gotten to yet.

On Food and Cooking: The Science and Lore of the Kitchen (Scribner, 1984), by Harold McGee. I have always thought the way to learn chemistry was to understand cooking, and this book does exactly that. Perhaps it should be read in conjunction with my old friend Larry Gonick's latest comic-book-style college text: The Cartoon Guide to Chemistry (HarperResource, 2004). An admission of my lowbrow tastes: The Complete Idiot's Guide to the Bible (Alpha Books, 1999). I have never been able to read more than a page of the Bible, especially the Old Testament, which—for me—is a mishmash of Hebrew tribal lore, and frankly this version seems pretty good. Maybe I'll understand a bit more of my heritage one of these days.

What book recommendations do you have for young readers?

Arguably, the most important step in everyone's education should be getting outside the narrow view of the world in which our culture immerses them. Aside from traveling, they can either read novels or read history. The hard part is to find the book which makes a different point in the space-time continuum come alive for you, the reader. This is very personal. Let me just say that I found my horizons stretched by Jared Diamond's Guns, Germs, and Steel (W. W. Norton, 1997) and Alfred Crosby's The Measure of Reality (Cambridge University Press, 1997) (both given me by my historian son).

What science book recommendations do you have for nonscientists?

Let me interpret your question as math books, because that's my field. There are, in my view, too many pseudo-math books purporting to be about some math topic which never dare to ask the reader to learn some actual piece of math, and hence are nothing but math gossip. The problem with recommending any math to a nonscientist is that they are quite likely to have negative impressions of math from high school. So, to be honest, I have to give a basic-level book which is user-friendly. If the nonscientist really wants to read some math, the book that drew me into math was the classic Mathematics for the Million, by Lancelot Hogben (1936). It is never outdated. A bit lighter but still honest is the more recent book by Phil Davis and Reuben Hersh, The Mathematical Experience (Birkhäuser, 1981). It's a great read.

Taking science more widely, Thinking Physics by Lewis Epstein (Insight Press, 2002) is a wonderful book introducing physics through a sequence of highly nontrivial puzzles, each followed (after you turn the page) by the answer and discussion. I got quite a few wrong myself. It's my ambition to write something as good as this about math (for the bright high school student or anyone older).

Name one book in your discipline that you would recommend for scientists outside your field. Explain your choice.

I'm tempted to name my own book (with coauthors Dave Wright and Caroline Series) Indra's Pearls (Cambridge University Press, 2002). We tried to take a research topic that incorporates some very beautiful pictures and does not require a huge amount of background and explain it to general audiences. The trouble is that any math book with real content does require serious application, and we did get so carried away that I fear its level grows exponentially chapter by chapter! But the pictures show highly nontrivial scaling phenomena and are worth a look.

If there is one topic in my area which I feel will be very influential on science as a whole, it is statistical learning theory. All too many scientists are not aware that statistics does not stop at the t-test and that many deep and important statistical ideas have been found lately. There is a recent text—too systematic, maybe—but full of the good stuff: Trevor Hastie, Robert Tibshirani and Jerome Friedman, The Elements of Statistical Learning (Springer, 2001). Some of the buzzwords are bootstrap, support vectors, boosting. My recommendation is to try to pick this up.

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