MIT professor Kiran Kedlaya is a mathematician, a juggler, a singer, a bicyclist, and a photographer – but he is first and foremost a puzzler. He got hooked as a kid. A very rambunctious kid. “My parents, trying to figure out some way to keep me out of their hair, got me a subscription to Games magazine,” he says. Their scheme kept him from bouncing off the walls, and he’s been solving puzzles of one sort or another ever since.

He started competitive crossword puzzle-solving during graduate school and appears in a couple of scenes in the just-released documentary Wordplay about the New York Times puzzle editor Will Shortz and the American Crossword Puzzle Tournament, the oldest and largest crossword puzzle tournament in the nation. He finished fourth in the 2005 contest depicted in the movie, and in 2006, he won second place.

Is there a connection between math and crosswords? Dr. Kedlaya thinks that math, music and computer science – popular professions among “solvers” – tap into a similar part of the brain. Wordplay, says Dr. Kedlaya, suggests that the link is using language in unique way. In a crossword, figuring out the word from the clue is not sufficient; decoding how the letters cross is vital, too.

For Dr. Kedlaya, solving and creating puzzles go hand in hand. One of his crosswords was published in the legendary New York Times crossword page, and he attended the National Puzzlers’ League conference in San Antonio in July of this year. In the NPL, where his nom de puzzle is “Kray” (Kiran means “ray” in Sanskrit, and he added a K because he had some to spare), some of the best amateur, semi-pro, and professional puzzle constructors and solvers in the country swap puzzles. He has also been a key player in the MIT Mystery Hunt. The winners of each year’s hunt construct the following year’s collection of interrelated puzzles whose answers must be combined (and sometimes recombined) in some fashion to provide clues to the location of a single coin hidden somewhere on the MIT campus. Dr. Kedlaya’s team won in 1999, 2001, and 2004.

Dr. Kedlaya solves and creates the puzzles of his profession as well. Winner of two gold medals (1990 and 1992) and one silver medal (1991) at the International Mathematical Olympiad, he has provided questions for the USA Mathematical Olympiad nearly every year since winning the prestigious international competition. During his college years at Harvard, he was a three-time Putnam Fellow (one of the top five finishers in the Putnam Competition). After earning his bachelor’s degree in Math and Physics in 1996 and his doctorate in Mathematics from MIT in 2000, Dr. Kedlaya spent the next three years at UC Berkeley holding a National Science Foundation Postdoctoral Fellowship. He then joined the Mathematics department at MIT in 2003 as an assistant professor, and thrives in the intense, exciting environment. This year Dr. Kedlaya was awarded a prestigious three-year Alfred P. Sloan Research Fellowship, intended for the very best young faculty members in particular areas of math and science.

Dr. Kedlaya, a number theorist, describes his work as being near the boundary of algebraic geometry, which he thinks of as a descendant of Euclidian geometry. Instead of studying simple polynomial equations which describe circles, straight lines, and parabolas, he studies much more general polynomial equations that don’t describe geometric or algebraic objects. While his primary focus is pure mathematics, he occasionally dabbles in areas of computer science. “Cryptography, coding theory – there are certain areas of computer science that relate nicely to polynomial equations,” he says.

His non-math interests vary widely. He speaks Spanish and Russian and a smattering of other languages as well, sings in the MIT Chamber Chorus, plays Ultimate Frisbee, and is working on improving his juggling skills. His work allows him to travel to conferences and seminars all over the world and gives him lot of opportunities to practice another one of his hobbies, photography.

“It’s important to tell kids who are interested in math as a career that there are many venues to do it, not just in the academic area within math departments,” says Dr. Kedlaya. People working in computer science, economics, finance, and other fields, whether in academia or industry, all can do interesting math. “Look for math anywhere you can find it,” counsels Dr. Kedlaya. Puzzles, after all, come in many types.

Questions and Answers

Here are Dr. Kedlaya's answers to your questions.

What are your primary fields of study?

My principal fields are number theory and algebraic geometry. I'm also quite interested in how those two areas relate to theoretical computer science.

Can you say anything about the kinds of math questions you’re working on now?

I'm mostly interested in objects called zeta functions. The original such function, introduced by Riemann, can be used to analyze the distribution of prime numbers. One can use other zeta functions to study the ways a given polynomial factors when you consider its coefficients modulo different primes.

What do you think the compelling questions in mathematics will be in five years?

This is a tough thing to predict! Five years ago I might have suggested the Poincaré Conjecture, but that one is now settled. One cluster of compelling questions is the Langlands Program.

What kind of puzzle got you into solving?

When I was very young, I quite fancied arithmetic and logic puzzles, partly because they seemed much easier than word puzzles for which I didn't have the vocabulary yet. Somewhere along the way, I learned how to solve cryptic (British-style) crosswords, which was a good intermediate step: since every answer is clued both by a definition and by a bit of wordplay (i.e., as an anagram, or by putting two shorter words together, or adding one letter to another word), I could both solve for words I didn't know beforehand and along the way learn their meanings.

What is your favorite puzzle type, and do you do Sudoku puzzles?

Nowadays, I do mostly regular American crosswords and some cryptics; I find that they exercise a part of my brain that otherwise gets a bit restless. By contrast, at this point the math/logic puzzles like Sudoku feel a bit like work to me, without the benefit of a real discovery at the end!

How long does it take you to do the New York Times crossword?

The Times puzzles are graded by difficulty, Mondays being the easiest, Saturdays the hardest (and Sundays somewhere in between). I typically take about 3 minutes for the Monday puzzle, and anywhere between 5 and 15 minutes for the Saturday.

How long did it take you to create your New York Times-published puzzle?

I'd estimate a few hours, total, including coming up with the puzzle theme. Professional constructors tend to do it more efficiently.

How do you manage to balance work vs. play in your life?

I don't make any special effort to. My work feels enough like play (and occasionally vice versa) that the balance seems to take care of itself.

For more information

• Dr. Kedlaya's homepage
• Math Problems Directory, Dr. Kedlaya's project to catalog sources of information about mathematical problem-solving on the Web.