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Research Biography September 2007 by Elwyn Berlekamp In the first grade in Strasburg, Ohio, I learned to play a game called "Dots and Boxes". It was the beginning of a lifelong interest. Fifteen years later, I began to perceive some of the large amount of interesting mathematics which underlies this game. In high school in Ft. Thomas, Kentucky, I found myself less interested in athletics than many of my other classmates and the local community. When I first heard that there was a place called MIT that had no football team, I immediately aspired to go there. For me, that turned out to be a wonderful choice. As I freshman at MIT, I was very interested in chemistry. And physics. And mathematics. And computers. I soon also became interested in economics. Unable to decide between majoring in mathematics or in electrical engineering, I pursued both. And then I continued doing so for the next five decades, and still counting. The research highlights of my career are depicted in the sketches surrounding my picture on my home page. Most of these topics lie in the union of two broad categories: codes and games Games such as Dots & Boxes, Domineering, Amazons, or Go include many positions which a good player quickly recognizes as splitting into two or more weakly interacting components, corresponding to different regions of the board. In many such instances, the mathematical value of the position (a sophisticated concept) is precisely equal to the sum of the values of the components, and so a mathematical decomposition occurs even though the two regions are connected and the correctness of the decomposition is quite nontrivial. In other positions which superficially look similar, the decomposition yields incorrect results because the subtle interactions between the components turn out to be stronger. Similar issues occur in many branches of mathematics (e.g., when is a group the wreath product of two of its subgroups?). They also occur in all of the sciences and in medicine: how important are the side effects and the drug-drug interactions? Decomposition issues also lie at the heart of the design problem of computer systems, be they hardware or software or both. The crucial design decision is usually how to partition the overall system into tractable modules, and how much and what sorts of interactions to allow between the modules. I personally view combinatorial game theory as a very fruitful domain in which to explore the general issues of modularity. |
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