First, I would like to thank Lynne Butler and Clara Chan for suggesting that we have this conference and for planning and organizing it. I am delighted to have this opportunity to review with you the story of Alternating Sign Matrices, their remarkable and unexpected connections with other mathematical problems, and to join with you in honoring the mathematical work of David Robbins, my good friend and colleague.
David and I go back many years together. We were undergrads together at Harvard but did not really get to know one another until our graduate student days at MIT. There we shared many pleasant hours, scribbling on napkins at Walker Memorial, tooling about Cambridge in David’s red Porsche convertible, and always there was the excitement of mathematical ideas, discoveries, examples, proofs. Too much some time, like the day of my wedding when we were waiting for David who was driving up from New York. He drove right by Norwich on the Connecticut Turnpike and kept following the road and the lines of some mathematical proof all the way to Rhode Island.
I came to know and appreciate David’s incredible talent as a problem solver. He quickly focusses on the core issue. “What’s the problem?” he asks, impatient with extraneous detail. He has an uncanny ability to identify and ferret out unexpected underlying patterns. Even more wonderful is his ability to explain his insights with patience and clarity.
When I came to CCR, urged on both by my memories, and by Tom Tucker, a mutual friend and colleague, one of my first orders of business was to get in touch with David and to encourage him to join us for one of our summer programs.
Bringing David to CCR is surely one of my most satisfying accomplishments, both for its impact on CCR’s work, and for the pleasure and fulfillment it has given David. The marriage of David’s talents and the problems and opportunities provided by the CCR program is as they say in yiddish, Beshert. They are chosen for one another. David has flourished at CCR. By the time he arrived here he was past 35, the end according to popular myth, of mathematical life. But he was just beginning his most creative work. Prior to coming to CCR David had published one paper, a high school math textbook, and a monthly problem solution. That was it. You are all aware of his contributions to the mathematical literature over the years he has spent at CCR, in particular the work on ASMs and enumerative combinatorics which we are celebrating at this conference. But this is only the tip of the square iceberg.
In the next two decades at CCR, David has authored some 129 research papers, papers which provided solutions to critical and significant problems. In addition, the methods he developed and taught to others have been the cornerstone for many further successes both here and at our sponsor.
He is a perfect fit not only for the problems but for the spirit of fellowship and camaraderie that characterize the CCR research staff. He has had some 82 different coauthors on those papers. His most frequent collaborators were Marshall Buck and Alan Richter each of whom were his coauthor on some 30 papers, and Clara Chan with whom he wrote 10 papers. The rest of us are down there in the single digits, but we all benefit time and again from the opportunity to work with David and to learn from him. Not infrequently someone develops a new technique whose underlying principles and performance limitations leave us scratching our heads. We all heave a collective sigh of relief when David offers to give a talk or write a survey paper on the subject, knowing that at last we will begin to understand. One example of which you may well be aware is the notes he prepared with Len Charlap giving an elementary introduction to the theory of elliptic curves. This paper has been widely circulated and has become the standard primer for those interested in beginning to study elliptic curves with an eye to algorithmic implementation.
Lee Neuwirth suggested to me that in my talk at this conference I should attempt to identify and describe the characteristics of David’s writing and lecturing which make him such an effective teacher. You yourselves have just had the opportunity to see David speak and to see how clearly, simply and intriguingingly he presents a subject. He takes care to identify the key points he wants to make, to emphasize them, to link them together in a compelling direct story line and to suppress distracting detail and unnecessary complexity. In short he follows the rules offered to aspiring writers of fiction. By the way, knowing all this has not allowed me to escape from the category Jim Schatz referred to earlier as “the other writers on the CCR staff.”
While reflecting on this theme, I found myself reading the newly published collection “Good Poems” edited by Garrison Keillor (a very good book, by the way!). In the introduction he discusses what it is that characterizes good poetry and I was surprised to find how so much of what he had to say could be paraphrased by substituting “mathematics” for “poetry” and “theorems” for “poems.”
Keillor first discusses some general rules for creating compelling writing, but then goes on to say “what makes all good poems matter, is that they offer a truer account than what we’re used to getting. They surprise us with clear pictures of the familiar.”
He quotes the poet Bukowski saying: “There is nothing wrong with poetry that is entertaining and easy to understand. Genius could well be the ability to say a profound thing in a simple way.”
There is much to be learned here.
In the context of our gathering here today to celebrate David’s work and the explorations and adventures we all have shared together, I was struck even more strongly by Keillor’s further remarks which I paraphrase. The subtitle for this conference should be “a conspiracy of friendship.” For the meaning of our work and our lives comes not so much from blurbish praise– brilliant, luminous, powerful– but to hear from friends and colleagues…. ‘good theorem,’ it’s all the compliment we would ever need or want.
Speaking of good theorems, I would like now to introduce our next speaker, Greg Kuperberg from U.C. Davis. I have also known Gregory for a long time, though not nearly so long as David Robbins. Greg had not been born that early. I did meet Gregory first when he was about 15 and on his way to attend Harvard. We were invited to Coke Reed’s home for a dinner to meet this promising young man and his parents. Greg demo’d a computer game he had written for the IBM PC which has now achieved the status of a classic and which (to his parents relief, I am sure) helped defray a good part of the expense of Greg’s undergraduate education. I have had the pleasure of watching Greg mature as a mathematician and to appreciate not only his good theorems but also the good works he has carried out for the mathematical community. He has not only thought long and hard about the future of mathematical publishing and communication but has devoted significant time and energy to orchestrating and implementing the use of electronic media.
Today he will describe his role in unlocking the mysteries of ASMs and discuss the new mysteries revealed by the unexpected connections of ASMs with quantum physics.