Describe your latest project.
My latest book, to be published in Spring 2008 by HarperCollins, is entitled How Math Explains the World. The twentieth century witnessed three eye-opening results in delineating the limitations of what can be accomplished in the physical, mathematical, and social Universe. Heisenberg's Uncertainty Principle, of which most people have heard, shows that we cannot know everything about the physical Universe — if we know where electrons are, we don't know where they're going, and if we know where they're going, we don't know where they are. Godel's Incompleteness Theorem says that in axiom systems of sufficient complexity, there exist statements which can neither be proved nor disproved. Arrow's Theorem shows that there are limits to how well a democracy can function in terms of translating the preferences of individual voters into the preferences of a society.

These results place limits on what we can know, or do, or achieve — but instead of proving to be roadblocks, they have actually opened new and surprising avenues. Heisenberg's Uncertainty Principle and the quantum mechanics of which it is a part has led to most of today's electronic marvels. The difficulty of solving certain mathematical problems ensures the safety of any account that you have protected with passwords. Instant Runoff Voting is being adopted in many communities as a better and cheaper way to hold elections.

Learning the limits of what we can know, or do, or achieve is especially important in a world in which our resources themselves are limited — for we cannot afford to chase dreams that simply cannot be realized.

What inspires you to sit down and write?
I consider myself extremely lucky that I fell into teaching mathematics as a profession. Math explains a lot about the world, and it's not nearly as complex or abstruse as many people think — the actual calculations may be rather involved, but the gist of what it says can be easily understood. I'm inspired to write about this the same way that you are motivated to tell a friend about a good Chinese restaurant you've just discovered.

Describe your favorite childhood teacher and how that teacher influenced you.
My favorite childhood teacher was Robert E. Wilson, who taught English-Social Studies in tenth grade. Mr. Wilson took the world's dullest subject, related it to the world today and to our own lives, and made it fascinating. Plus, he was colorful as hell.

Chess or video games?
I loved chess when I was younger — but it requires powers of visualization that I simply do not possess. I was very good at bridge and backgammon, where you don't need to visualize as much and can rely on deduction, inference, and probability.

For the life of me, I cannot see what others see in video games. It's almost as grim as practicing tennis by hitting against the wall, except that doing so improves your game.

What do you do for relaxation?
Tennis, piano, and ice skating. My wife and I like to dance. Well, she likes to dance and I like to make her happy.

Douglas Adams or Scott Adams?
Stephan Pastis. The best humorist since Tom Lehrer.

What was your favorite book as a kid?
Slan (A. E. van Vogt). I fell in love with the heroine.

What new technology do you think may actually have the potential for making people's lives better?
Genetic engineering — although by now it's no longer new.

If you could be reincarnated for one day to live the life of any scientist or writer, who would you choose and why?
Isaac Newton. The greatest genius of all time, although don't give me one of the days where he went to watch counterfeiters being executed.

What was your best subject in high school? Your worst?
Best — math. Worst — shop. We had to build a lamp in the shape of a pump to get out of junior high, and after three dismal attempts the shop teacher took pity on me and let me out.

Describe the best museum of science and/or industry you've ever visited and what made it great.
Chicago. It had absolutely everything you could want — a captured German U-boat, a working farm, part of a coal mine, and more hands-on science and technology than I've ever seen in my life. It was on the south side of Chicago near the University of Chicago, but well worth the trip from the suburbs. Since I live in Los Angeles, I haven't been back there for some time, so I hope it's kept up.

By the end of your life, where do you think humankind will be in terms of new science and technological advancement?
I wish I could see into the future to envision this; I'd sure know what stocks to buy (still kicking myself for not investing in Microsoft or Genentech). However, I do know what I'd like to see: a way for medical science to put the years that it's adding on to life somewhere in the middle rather than at the end.

Which country do you believe currently leads the world in science and technology? In ten years?
Now and for the foreseeable future — the good ol' USA. In order to be the leader, one must have a top-notch educational system for training scientists and engineers, and an entrepreneurial system which enables people to profit from progress.

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James D. Stein is a professor of mathematics at California State University, Long Beach. A graduate of Yale University and the University of California, Berkeley, he lives in Redondo Beach, California.