Some Recollections About Sammy Eilenberg
A couple of weeks ago, while visiting the Metropolitan Museum of Art in New York City, I was surprised to discover a collection of India and Southeast Asia antiquities donated by Samuel Eilenberg. Samuel Eilenberg —or “Sammy,” as many people referred to him— was one of the great mathematicians of the twentieth century. He was (as far as I know) the first American member of the Bourbaki group and, together with Saunders Mac Lane, created category theory. His work profoundly shaped modern algebraic topology and the emerging field of homological algebra, including his influential book with Henri Cartan.
Seeing those artifacts reminded me of my own interactions with him, and I thought it might be worthwhile to write down a few recollections that could perhaps be of interest to some readers and his biographers, as they illustrate his personality.
My interactions with Sammy took place when he spent a sabbatical at the University of Florida visiting my thesis advisor, Rudy Kalman. Sammy stayed in Kalman's home during his visit, and we shared an office suite. During that time he became interested in some of the principles of linear control theory, and he eventually wrote an entire chapter on the subject in his book on automata and languages, which appeared in the mid-1970s. The chapter dealt with linear systems over commutative rings and related automata theory to the realization theory of linear systems. I had several discussions with him about that work, and he was kind enough to acknowledge me in the book for pointing out a number of minor errors and offering comments on the manuscript.
The memories I particularly wanted to share, however, concern some personal interactions with him that seem rather humorous in retrospect.
The first involves a paper I had written on noncommutative rings, of which I was extremely proud. Sammy was, if I remember correctly, the editor-in-chief of the Journal of Pure and Applied Algebra. I asked whether he might be willing to consider the paper for publication, and as a courtesy he agreed to take a look at it.
The very next day, after I had given him the manuscript, he called me and asked me to come to his office. I arrived full of anticipation, expecting to hear what a wonderful paper I had written. Instead, he informed me —in words that were probably different, though not by much— that the paper was absolute rubbish.
Needless to say, I was devastated and immediately started to leave. But then he stopped me and said that he would help me rewrite the paper and teach me how a mathematical paper ought to be written.
What followed was fascinating because his philosophy of writing was almost the exact opposite of what my advisor had taught me. Kalman believed that one should begin with intuition and motivation, gradually leading the reader toward the main results. Eilenberg's view was completely different. I believe I remember his words almost exactly:
«"I don't care about your psychology or your motivations. Just tell me what the theorem is."»
In the end, I rewrote the paper following his advice, and he accepted it for publication in the journal.
Another interaction was considerably more embarrassing for me.
During a seminar he was giving, I asked several questions. After one of them, he stopped, looked directly at me, and in front of an audience that included several senior faculty members, declared that I was asking questions only to show everyone how smart I was.
You can imagine that I was not especially pleased by this observation, although in retrospect he may have had a point!
A few months later, however, I got a measure of revenge.
This occurred at a conference in Udine, Italy, attended by Eilenberg, Saunders Mac Lane, and many others. The conference concerned systems and control theory. During one of Sammy's lectures, he made a tiny algebraic mistake on the blackboard. I raised my hand and pointed it out.
He looked at me and, in front of an audience of perhaps a hundred senior researchers —remember that I was still a graduate student— announced once again that I was merely trying to show how smart I was and that, naturally, I was wrong while he was right.
He then continued the lecture, moving to another blackboard. The entire front of the room was covered with blackboards, and he continued developing his argument several boards away. After a while, as the derivation progressed, he apparently realized that I had been correct. He quietly walked back, changed the offending symbol to the one I had suggested, and then returned to the board where he had been working and continued lecturing as though nothing whatsoever had happened.
Needless to say, the audience erupted in laughter.
By the way, this was also the conference at which Gianni Marchesini stood up and accused Kalman of appropriating his work on bilinear systems. That was a spectacle in its own right. My own view was that Marchesini (who was also the conference organizer) certainly had important ideas, but what Kalman was presenting was not exactly the same work. In any case, that is another story. By the way, Gianni was a fantastic human being and a great scientist and colleague. I only recently learned that he passed away about three years ago.
Finally, while I am on the subject of Eilenberg stories, there is one in which I was present but played no role. This took place at a conference on category theory and its applications to systems and control theory, organized by Ernie Manes and Michael Arbib, both of whom were then at the University of Massachusetts. The conference was held in San Francisco. Many still active researchers, like Bill Belton were there. (Interestingly, there has been a rediscovery recently of category theory applications to systems, and the work of the topic, documented in papers and at least one book, seems to have been forgotten!)
Anyway, back to the story. Arbib, if I recall correctly, presented a paper on category theory applied to control theory. Eilenberg evidently felt that the results were not worthy of publication. Arbib's reply, as I remember it, was that no one had published those results before, and therefore they deserved to be published.
To this Eilenberg, without missing a beat, replied that, as a journal editor, if someone submitted a paper entitled The First 1,000 Numbers, consisting simply of the list of integers from 1 to 1,000, the paper would certainly not be acceptable, even though it had never been published before.
For me, still a student at the time, this was a simple but enduring lesson on the difference between novelty, interest, and elegance.
PS: here is the Met’s catalog entry for a book describing his donated collection: