"Mathematics is a common undertaking of the entire mathematics' community," said 87 year-old Beno Eckmann, FIM's founder and emeritus ETH professor of mathematics on the occasion of the congress to celebrate the anniversary in July. He went on to say, "This is why our most important tool is the exchange that takes place between mathematicians in all specialist areas." And Marc Burger, current FIM director and himself a mathematics professor, explains, "Above all, mathematics needs bright minds. It's the people who are important, their interactions and a place where these can occur."

An institute for visitors

"FIM is just such a place. For 40 years mathematicians from all over the world have been able to meet here," continues Burger. "Almost all of the very well known mathematicians were here – including John Nash, the main character in the film adaptation of the book "A Beautiful Mind". At FIM, the only permanent fixtures are the director and an administrative staff of three. A stream of visitors, around 150 of them last year with a maximum of 30 at any one time, occupies the rest of the rooms in the institute. On average they stay for two or three weeks.

"This model is unique worldwide," explains Burger. Admittedly, research institutes for mathematics have been springing up everywhere over the past couple of decades, but they are run on quite a different concept. "Institutes like the Bernoulli Centre at EPF in Lausanne or the Mathematical Sciences Research Institute in Berkeley, invite lecturers who fit in with their current programmes. Others, such as the School of Mathematics at the Institute for Advanced Studies in Princeton, have several permanent members of the institute and a few, occasional, visitors." For the most part, however the latter live and work in "Splendid Isolation“ – without contact to the young mathematicians studying at the guest university.

Exchange of knowledge – not only with ETH

At FIM the situation is very different. Visiting lecturers make their own experience and insights accessible in the form of "mini-courses", workshops or postgraduate classes. When a particularly exhaustive subject crops up, a conference is organised around it. This is where young mathematicians can build up useful contacts for a future academic career. And naturally, FIM also serves the Department of Mathematics by catching the interest of good mathematicians. Once they become members of the faculty they can propose their own visitors.

During their visits many FIM visitors are also invited to other Swiss universities. The latter can check FIM's homepage (1)to find out who is staying in Switzerland and for how long. Burger says, "This means that other universities also benefit from our visitors, and this strengthens the networking capabilities of all concerned".

Billiard balls on triangular tables

Some of the visitors manage to implement – together with colleagues at FIM or from other Swiss universities – a specific research project. For example, Alex Eskin, professor at the University of Chicago was at FIM in July working on dynamic systems. To put it simply, he is trying to determine the number of possibilities that a billiard ball has, on a triangular table, after a given length of time, to land up at its point of departure. He discusses his deliberations with Dave Morris, a colleague from the University of Lethbridge in Canada.

Discussing the comportment of billiard balls on a triangular table: Alex Eskin (left) and Dave Morris, both visitors at FIM. large

Discussions like this are important because the road leading to mathematical insights is often long and winding. "Mathematicians are always on the lookout for the 'psychological trigger', something that will point them in the right direction," says Burger. Sometimes such a release trigger can come from a vague suspicion, a hunch or a daring speculation that surfaces in an exchange with a colleague and illuminates an idea. "But even a small gesture or a casual remark of the can lead to a sudden insight.

""Almost all of the very well known mathematicians were here – including John Nash, the main character in the film adaptation of the book "A Beautiful Mind", says FIM director, Marc Burger. large

Independent and well embedded

Professors and doctorate students from D-MATH can put forward names of visitors they would like to invite to FIM. According to Marcela Krämer, member of FIM staff, the requests are usually granted. The final decision lies with the director. "Visitors need to be not only top researchers but also able to communicate their knowledge," says Burger.

Despite close co-operation with the Mathematics Department, FIM, as Eckmann emphasises, is an independent entity. "FIM's function is to provide a framework to invite mathematicians whose specialist expertise is relevant to current research." Burger adds, "If a sought after mathematician suddenly becomes available and has time to come, we have to get her or him here straight away – without having long discussions and formalities."

The "Eckmann Hilton"

According to Eckmann, the founding of FIM was already gratifyingly simple. "Thanks to Hans Pallmann, the then President of ETH Zurich, we were able to begin even before the whole project had been officially agreed. On the 1st January 1964 a group of invited people sat around a round table in a room in the main building. Later the institute moved into a little house on Zehnderweg – which soon came to be known as the "Eckmann Hilton". Years later FIM moved back into the main building.

Sustainable programme

To a certain extent, each FIM director renounces part of his own research interests for the duration of his term. As a sweetener he can invite mathematicians with similar areas of interest to his own to the institute. "In this way," says Burger, "every director over the years has raised the profile of his own area of research."

Anniversary Congress 2004: Beno Eckmann, founder of FIM, and Catriona Byrne from Springerverlag large

The first director, Eckmann, took the lead with algebraic topology, which deals with three-dimensional structures and related questions of algebra. Dynamic systems arrived with Jürgen Moser, a discipline that describes time-dependent processes, such as weather or climate systems. Armand Borel's specialty was Lie groups – simply put, symmetrical observation theory. Burger's predecessor, Alain-Sol Sznitman, is interested in random movements in a non-ordered environment, the question, for example, of how steam moves through the ground coffee in an espresso machine?" Burger himself is concerned with rigidity phenomena in geometry and in dynamic systems. Theories developed here find application, amongst other things, in the analysis of the configuration of molecules. He sums up, "Today we have visitors here from all these areas – and more."

No duties, no distractions

"FIM organises accommodation for the visitors, covers their living costs and pays something towards their travel expenses," Burger goes on to say. "In addition they have a place of work at ETH and the necessary infrastructure." The institute is funded entirely by the Swiss National Science Foundation and ETH own funds. "Until now we haven't felt any effects from the government's budget cutting measures," he says.

And the visitors? They are, apparently, highly appreciative of the opportunity. "When people are here, they work like mad," says Enrico Bombieri, professor of mathematics at the Institute for Advanced Study in Princeton and regular FIM visitor. "No holidays or excursions – and that, here, in Switzerland! A sojourn at FIM gives one time and space to concentrate, no duties and no distractions."