If you are looking for the grand master of Swiss mathematics, the name Beno Eckmann springs to mind. At 87, Eckmann is permanent visiting professor at the Eidgenössische Technische Hochshule (ETH). Despite the emeritus status given him some 20 years ago, he is as active as ever.

Eckmann grew up in the city of Berne, the capital of Switzerland. He was a happy lad who found school life easy enough but enjoyed himself especially during math lessons. As a young boy he showed no signs, however, of wanting to make mathematics his profession. In fact, his tutors advised against this path since, in their minds, everything that could be revealed in the field of mathematics had already been discovered. On top of that, young Eckmann was told, mathematics offered few career prospects.

These warnings notwithstanding, Eckmann decided in 1935 to follow his inclinations and enrolled in physics and mathematics at the ETH in Zurich. Suddenly a new world opened up for him. Here, at one of the most advanced scientific institutes in the world, some of the best-known scientists had taken up teaching positions. Among them were Wolfgang Pauli, the future Nobel Prize winner for physics, and the German mathematician Heinz Hopf. They saw it as their mission to look after the rather small group of mathematics students. Hopf, who had emigrated from Germany in 1931, was at the time the leading mathematician working in topology, then still a very young field that deals with structures of higher-dimensional spaces. Eckmann was aware of the opportunity that presented itself and seized on it with both hands. He asked the eminent mathematician to tutor and guide him in the

writing of his doctoral thesis. The thesis was judged to be quite outstanding even when measured against the high standards of the ETH, and Eckman was duly awarded a prize.

Eckmann’s reputation soon spread beyond the boundaries of Zurich, and in 1942 he was offered a chair as extraordinary professor at the University of Lausanne, in the French-speaking part of Switzerland. But it was a time of war and Switzerland was under threat. Being a patriot, the young lecturer did not hesitate when he was called up for active service but managed to skillfully combine his army service—as a spotter for the artillery—with his duties at the university. Two weeks of lectures alternated with two weeks of military service.

After the war, Eckmann was invited for a two-year visiting position at the Institute for Advanced Study (IAS) in Princeton, New Jersey. There he got acquainted with Hermann Weyl and other members of what was considered the golden guild of mathematicians and physicists—Albert Einstein, Kurt Gödel, and John von Neumann. Einstein, needless to say, was in huge demand. He was the superstar whom everybody wanted to get to know in person. Actually, the discoverer of relativity was fed up with his celebrity status and the constant stream of visitors. However, Eckmann seemed to be an exception in Einstein’s eyes, and the grand old man of physics invited him to his home for tea. Maybe Einstein still had a soft spot for Zurich and Berne in which he had spent some quite memorable years and from where Eckmann himself hailed. More probably the liking he took to the young man from Switzerland was due to his winning personality and his honest and talented approach to science.

The other superstar at the IAS, John von Neumann, was much more approachable, Eckmann recalls. A faint smile settles on his lips when he remembers the anecdotes with which von Neumann regaled his friends back in the Princeton days. (One such story has the mathematician, whose penchant for fast cars did not, unfortunately, match his driving skills, speeding along a country road. “Here I go at 60 miles an hour,” von Neumann told his

listeners quite seriously, “when, all of a sudden, a tree steps forward and … crash.”)

In 1948 Eckmann was offered a full professorship at the ETH in Zurich. The list of papers he published adds up to some 120 articles. This may not seem particularly long when compared to what is considered to be a standard “portfolio” for today’s mathematicians, but the papers are comprehensive and long. They covered fields that were in constant flux, pointed in new directions, and offered completely new insights.

It is not the list of publications alone, however, that accounts for Eckmann’s reputation. What impresses is the number of Ph.D. students he looked after and guided in their work. They number over 60. Doctoral students who chose him as their thesis adviser were particularly impressed by the cutting-edge work in which Eckmann was continuously engaged. They also were attracted by the humane and friendly way in which he communicated with each and every one of them. It is not surprising that having been fortunate to find in Eckmann a model professor, over half of his doctoral students became professors themselves and thus were able to offer proper supervision to their own students. A genealogical tree that hangs on the wall behind this still lean and trim octogenarian lists no less than five generations with over 600 doctoral offspring.

Eckmann was always fascinated with the connections between geometry, algebra, and set theory. He always sought pathways between problems that he had already solved to new mathematical problems. For a research mathematician, relevancy should never be a guiding principle, Eckmann cautions. Nevertheless, sometimes one hits unexpectedly on an application to practical issues. A case in point for Eckmann was a theoretical piece of research that he published in 1954. To his complete surprise, the result found an application to economics nearly half a century later.

Eckmann’s influence is also apparent in a project he initiated in 1964. Scientists at the time were at a loss as to how they should disseminate their research. This was before the era of the Internet, and the publication of new results in journals could take many months or even years.

Faster dissemination of new results was possible only occasionally at workshops or conferences. Eckmann was determined to find a solution to this unsatisfactory state of affairs. One day an idea sprang to his mind—how results of broad interest could be published and marketed with little expense. He promptly shared it with one of the heirs of Julius Springer, founder of the famous scientific publishing house of the same name in Heidelberg. The heir in question just happened to be studying biology in Zurich at the time.

The idea was simple enough: Just mimeograph the manuscripts with hardly any editing, bind them, and sell them at the lowest cost possible. Thus the series “Lecture Notes in Mathematics” was born in 1964. It became a most valuable service to the community of mathematicians worldwide and, thanks to the continued supervision and care given to it by Eckmann and one of his colleagues, the series now comprises some 1,800 volumes.

Eckmann never shied away from administrative responsibilities. He still believes that professors owe it to their institutions to devote themselves to administrative duties as well as research work. In this respect he always set a good example. Especially noteworthy is the research institute for mathematics at the ETH (Forschungsinstitut für Mathematik), founded in 1964, of which Eckmann was director for a good 20 years. Today many such institutes exist—for example, in Barcelona and in Columbus, Ohio. Eckmann is still associated with a number of such institutes in Israel that he also helped found, namely at the Technion in Haifa, the Hebrew University of Jerusalem, Bar Ilan University in Tel Aviv, and Ben Gurion University in Beersheva.

Reflecting on a mathematical career that has now spanned nearly 70 years, Eckmann cannot but comment on how much his subject has changed. This constant state of flux brings with it not only the necessity but also the opportunity for new approaches and innovative concepts.

Whenever he started exploring a new idea, it was as if he embarked on an adventure. Optimism alternated with disappointment until the moment when, hopefully, a break-

through was achieved. The feeling that befalls a scientist at such an occasion is impossible to describe, Eckmann says somewhat nostalgically. Only those who have been lucky enough to experience it for themselves really know what this means.

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