(This speech was given by me at Leopoldo Nachbin's Memorial Service, at the University of Rochester chapel on May 12, 1993. Copies were sent to Leonard Gillman, Meyer Jerison and Paul Halmos, at their request. Later, about 1995, I sent a copy to one of Nachbin’s friends in Brazil, for inclusion in a little book he was publishing, mostly in Portugese, of memorials of this sort plus a brief biography of Leopoldo -- Ralph A. Raimi, May 9, 2005)

Leopoldo Nachbin, 1922-1993

"Not many mathematicians can claim to be the best mathematician within a thousand miles, but for many years Nachbin has been just that." This was written in 1962 by Paul Halmos. Halmos was a professor in Chicago at that time, and Leopoldo in Rio, and the letter containing these words was being sent to Leonard Gillman in Rochester. Gillman, who was Chairman of our department here at that time, needed some ammunition for the Dean who would have to approve the appointment that he was contemplating, so he got a letter from André Weil, too. Weil, who was not famous for praising other people, opened his letter with the following words, "Well, lets just say that he is a brilliant mathematician..."

I will not attempt to improve on the Chicago opinions, or to re-emphasize Nachbin's contributions to mathematics in the thirty years since they were written; there must be hundreds more qualified than I am to go on in this vein. Furthermore, it was not only as a mathematician that I knew Leopoldo, though that was where it began: When I was writing my thesis, in 1952 or 1953, I studied his 1950 paper on a theorem of the Hahn-Banach type for linear transformations, but it was not until he came here to join us that I realized how young he had been when in 1950 he was already well-known, and not only in Chicago -- and I, two years younger, was still a student.

It was characteristic of Leopoldo's career that he should be the subject of letters from Chicago to Rochester concerning events in Rio. The letters represented something even more cosmopolitan than they appear: Halmos, the author of the first of these estimates, came originally from Hungary, and Weil was as French as can be imagined. And Nachbin himself was not actually in Rio when the letters were written; he was a visiting professor in Paris.

It is true that the mathematical community is world-wide, but even among scholars Nachbin was particularly international. He was constantly on the road somewhere, on his way to or from or between visiting professorships or invited lectures; and he would fire off his multiple-warhead missives from the most remote places. Everybody got mail from him, usually a postcard featuring pictures of girls on a beach somewhere (though the ones from his own beach in Rio were the best). His international conspiracies were legendary. He created Institutes and governed them. He edited a series of books in Brazil, but inveigled professors he knew from all over, including Rochester, to write monographs for it. When I made a small speech at a diploma ceremony here, about "What good is mathematics?" or some such thing, to parents of our graduating class, the first thing I knew I was revising it for a little journal in Brazil called "Ciência e Cultura," where in due course it was printed. Why? Because Nachbin asked; you couldn't resist him.

Leopoldo brought graduate students from South America -- and not only from Brazil -- to Rochester; he brought former graduate students here as visiting professors. He got financing somehow to bring some of our Rochester students to Rio for a while, for he did spend a semester of most years in Rio. One of his many doctoral students here was Soo Bong Chae, whom we called the Korean Cannonball for his general enthusiasm, including an enthusiastic use of an imperfect (though daily improving) English. Nachbin took him to Rio for a year, and we heard within a few months that he was giving seminars there in an equally enthusiastic brand of Portugese. (Soo Bong is now a professor in Florida.)

Leopoldo remembered everyone, and on each of his travels he must have sent dozens of cards of greeting, as if to gather the world together with these threads of communication. Threads of gossamer, perhaps, with nothing in the way of tensile strength; but unbreakable and unforgettable in their spiritual strength. They said very little, these cards, but they were gentle as Leopoldo himself was gentle, they were kind as he was kind, and they were part of the social fabric of our trade, the structure that contains all mathematicians and not just the handful of specialists that each of us is naturally linked to in our working life.

One time my wife Sonya and I were visiting Spain, just as tourists, and we went to Santiago de Compostella, that famous pilgrimage town in the most remote northwest corner of Spain, on the way to nowhere. On the afternoon that Sonya went looking at things of little interest to me I walked over to the local university; it wasn't far away. Nothing was far away in that town. I had never heard of the university either, at Santiago, but it has been my custom when traveling to look in on the local math department if there is one, and talk to whoever possessed a language we could both talk in. This time they conducted me to the Chairman of their mathematical institute, or perhaps institute of analysis, a man named Isidro. "Rochester?" he said, "Then you must know Nachbin." From there we went on to other matters, but it was the name Nachbin that was my passport. When I left, Isidro asked me with a smile if I thought I could get him an invitation to Rochester, so he could be a sort of graduate student for a year, to study with Nachbin. He was half serious.

Nachbin's cosmopolitanism was not only generated by the life of mathematics; it was part of his actual heritage. Not until I had known Leopoldo for ten or fifteen years did I find out about his father, and if I had not myself had a father named Jacob -- as Leopoldo did -- I might not have found this out until even more recently. It happened that my own father came to Rochester on a visit, and I took him to Strong Auditorium here to see a concert or play by a student group. I saw Leopoldo in the audience, alone, and we came to sit with him; and in speaking to my father Jacob, an immigrant from Poland, he told us of his father Jacob Nachbin, equally an immigrant from Poland (though to Brazil), also in the early years of this century. I -- and my father -- learned that Jacob Nachbin had founded and edited the first Yiddish language newspaper in Rio. I discovered later that Jacob Nachbin was a scholar too, and a writer, and a man who corresponded in many languages with people in many countries. It turns out that there is even a book about Jacob Nachbin, a biography written by a certain Professor Falbel in Sao Paolo, which Leopoldo just two years ago asked the author to send me. I couldn't read very much of it, for it was mainly in Portugese, but I did learn that Jacob Nachbin, as a journalist, went to Spain in 1936 to cover the civil war, and disappeared without a trace.

Leopoldo was of high school age at that time. I asked him how the family managed; he merely said it was very hard, his mother worked very hard. Yet Leopoldo managed to get to the university in Rio and become a mathematician, publishing research papers by the time he was 20, maybe younger.

But as I have said, it was only partly as a mathematician that I knew Leopoldo. Another part was as a sort of editor. In his early days Leopoldo wrote mainly in Portugese and French, but once he came to Rochester he wrote almost entirely in English. Anyone who knew him knows how charming his English was in daily conversation, but he himself worried about it and wanted his papers and books to sound properly idiomatic in English. Many times he brought me a manuscript, asking me to correct what was not correct.

Let me assure you that everything he wrote was in fact correct, and without possibility of misunderstanding; but that was not enough for him. He wanted it to sound like English, as if a native were writing it. So I corrected a few things here and there, and explained to him the arbitrary bits of diction that idiomatic writing would demand, but this was under protest. He sounded much better in his own English, which had a spirit that neither I nor any other person born to the language would ever think of. And sometimes I cheated, and deliberately let pass some curiosity of his own devising that I considered an improvement over the style to which he said he aspired.

He wrote better than he was willing to believe, and in my own memory I would count that the mark of the man, both as mathematician and as friend: modest, friendly, and forever looking to make something a little bit more clear, even when he himself had already rendered it as clear and as sweet as anyone in his audience could ask.

Ralph A. Raimi

10 May 1993