André Haefliger, the contagious passion for math

I was invited for the first time to present my work at an international conference in July 1981. I was nervous, facing impressive specialists. After my conference, an old man came to see me (I know now that he was 52 years old). He congratulated me warmly for my presentation, but an important point in my demonstration had escaped him and he asked me for explanations. Panic: did he want to point out with delicacy an error of reasoning? I answered that I was using a result that I had read in André Haefliger’s thesis.

He then introduced himself, and I understood that I was facing André Haefliger, one of the founding fathers of the theory of layering that I cherished at the time. He had not forgotten his own thesis, but he tried to convince me (unsuccessfully) that I had gone further than him in the interpretation of his result. It is always impressive for a young scientist to come face to face with one of his heroes.

André Haefliger died on March 7, at the age of 95, near Geneva, where he was a professor from 1962 until his retirement in 1995. Since our first meeting, he has been a source of inspiration and a model of mathematician, both as a researcher, as a leader of the scientific community, as a teacher and as a friend. His thesis, defended in Strasbourg in 1958, had an esoteric title, to say the least: “Laminated structures and value cohomology in a bundle of groupoids”, enough to scare off more than one interlocutor, so much so that it was expressed in an abstract language, so common at the time.

In the Swiss mountains

A puff pastry structure is actually very similar to puff pastry. The idea is to fill the space with sheets, like the pages of a book. This theory was born a few years earlier and was motivated by the understanding of the structure of dynamic systems. In 1969 he invented the “Haefliger classifier”, a concept that excited the young community working on these questions. Older geometers now fondly recall their memories of the presentation of his discovery, at the top of Mount Aigoual in the Cévennes, huddled in a weather station that housed a small conference center. It was reportedly very cold, but the atmosphere was warm.

When he arrived as a professor at the University of Geneva, there was no research department in mathematics. André always said that he did not have an office and that he had to go to a public phone booth. He contributed greatly to the foundation of the remarkable mathematics section in Geneva, which today houses two Fields Medalists. The greatest mathematicians came from all over the world to visit him, to share their discoveries with him and receive his advice. He knew how to listen to young people and encourage them to work together, which is not so common in this field.

I was not present at Mont Aigoual, but I no longer count the weeks spent in the Swiss mountains, in groups of about twenty young researchers, working on the understanding of this or that mathematical novelty. All this in a simple, relaxed and friendly atmosphere where the very idea of competition was excluded.
His influence at the international level is considerable: one does not count any more his students, the students of his students, etc. Vaughan Jones, one of his former students, was awarded the Fields Medal in 1990. It can be said of André, as was said of Monge, that “he was not satisfied with making discoveries, he also made students, which is sometimes better”.