# Opening Address by Prof. Dr. Friedrich Hirzebruch, Founding Director of the MPI for Mathematics

Dear Mayor,

Magnifizenz,

Spektabilis,

Ladies and gentlemen,

Three months ago our Cluster of Excellence, the Hausdorff Center for Mathematics was funded. Much has happened since then. The Center’s Board of Directors have accomplished much already. Six directors represent the six participating institutes (5 university institutes and the Max Planck Institute for Mathematics), in addition we have the Director of the Graduate School and the Director of the Hausdorff Research Institute for Mathematics, the hub of the Center. This new institute will run semester workshops comparable to the workshops at the Mathematical Sciences Research Institute in Berkeley and the Newton Institute for the Mathematical Sciences in Cambridge, UK. The working methods of the Max Planck Institute are comparable to those at the School of Mathematics of the Institute for Advanced Study in Princeton. In the USA you have to cross a whole continent to get from Princeton to Berkeley - the Atlantic Ocean even to get to the Newton Institute. In Bonn soon you just have to walk from Münsterplatz to Poppelsdorfer Allee.

Of the directors I’m mentioning by name only the Director of the Hausdorff Institute because he comes from out of town. It is Professor Matthias Kreck from Heidelberg, who for many years has been the Director of the Mathematical Research Institute Oberwolfach. He accepted the offer of a chair. He will be 60 years old this year and negotiations were not easy. However, Bonn University has handled everything with incredible speed. Thanks are due the Rektor and the Kanzler. I am especially pleased as Matthias Kreck was a doctoral candidate of mine. During the student revolt days 35 years ago he was my assistant.

The directors and the members of the Center deserve praise:

Much has been planned in detail, especially at the Hausdorff Institute, with programmes from this semester until the summer semester 2009. Already 53 positions were advertised for various lengths of time - 8 Bonn Junior Fellow positions, 30 Ph. D. scholarships and 15 post doc positions.

The directors of the Hausdorff Center for Mathematics have asked me to hold a small speech specifying their request as follows: "We would welcome if you could describe the period stretching from Plücker to Hausdorff to the golden fifties, the MPI and the Cluster of Excellence - from your personal point of view". Julius Plücker was professor at Bonn University from 1835 to 1868. This means that the requested period covers 172 years. I must hurry up.

The Rheinische Friedrich-Wilhelms-University Bonn was founded by the Prussian King Friedrich Wilhelm III in 1818. From the very beginning there were two chairs for mathematics whereby the second also included physics and astronomy. Plücker was the second holder of both chairs, at times he held both chairs simultaneously, from 1856 though only the second, the physics orientated chair.

Plücker is known to today’s physicists as the cofounder of spectral analysis, to the mathematicians through his works on the singularity of algebraic curves and his geometry of lines.

Two volumes "New Geometry of Space based on the Observation of the Straight Line as an Element of Space" were published 1868/69. Let me explain: a straight line turns into a point in the space of all straight lines, which has dimension 4. In 1866, at the age of 17, Felix Klein, the future great Göttingen mathematician, became Plücker’s assistant. He assisted in the completion of the two volumes on the geometry of lines and received his doctorate December 1868 in Bonn at the age of 19. The theme of his doctoral thesis belonged to geometry of lines. His Ph.D. supervisor Plücker died May 1868 and Felix Klein dedicated his dissertation to Plücker with the words: " In grateful memory of his unforgettable teacher Julius Plücker. The author". Rudolph Lipschitz, who was Plücker’s second successor on the first mathematics chair, was Felix Klein’s examiner. Lipschitz researched successfully in many fields of mathematics - from number theory to potential theory and elasticity theory. Plücker, Lipschitz and Klein worked together in Bonn from 1866 to 1868. Fortunately we already have lectures series named Plücker lectures, Lipschitz lectures and Klein lectures which will be integrated into the graduate school of the Hausdorff Center.

In addition to the two chairs, which had been in existence since 1818 and finally covered mathematics only, an additional associate professor position (Extraordinariat) was created in 1892 as a result of Lipschitz’ efforts. The first holder of this position was Hermann Minkowski who later created the mathematical foundation for Albert Einstein’s special relativity theory. This structure of chairs was unchanged when I came to Bonn in 1956. I was appointed to the Extraordinariat in June 1956 and a few weeks later I was full professor (Ordinarius). We are closing in on the golden fifties, to which we come later.

Now we will make a big leap: Plücker’s fourth successor on the first chair was Otto Toeplitz, Plücker’s fourth successor on the second chair was Felix Hausdorff, both outstanding and internationally highly esteemed mathematicians and both Jewish. Toeplitz was appointed professor in 1928, Hausdorff in 1921 already. Both were forced to retire in 1935. Shortly before the outbreak of the Second World War, Toeplitz and his family emigrated to Jerusalem where he died in 1940. Hausdorff, his wife and her sister committed suicide in 1942 shortly before their deportation to a concentration camp. On the initiative of Professor Brieskorn and Professor Hildebrandt two memorial plaques commemorating Hausdorff and Toeplitz have been placed in the entrance of this building.

As we are celebrating the opening of the Hausdorff Center today I will limit my report to Hausdorff.

Felix Hausdorff’s mathematical works are still of current interest. His main work "Basic Principles of Set Theory" was published in 1914. In 1927 Hausdorff published a second revised edition, which is a very different book. Hans Hahn (Vienna University), Hausdorff’s predecessor on his chair in Bonn and also Jewish, reviewed the book. He writes:"In every respect an exemplary presentation of a complex and thorny field, the kind of work which has spread the reputation of German science all over the world and of which the writer and all German mathematicians can be proud". A nine volume edition of all Hausdorff’s works is in preparation. The driving force is Egbert Brieskorn and Walter Purkert. Four volumes have already been published. The titles of the volumes show the scope of Hausdorff’s works. For example:

- Volume IV: Analysis, Algebra and Number Theory
- Volume V: Astronomy, Optics and Probability Theory
- Volume VI: Geometry, Space and Time

You see how justified we are in naming our Center of Excellence after Hausdorff. Volumes VII and VIII contain Hausdorff’s philosophical and literary works which he published under the pseudonym Paul Mongré, see Walter Purkert’s posters. During the era of the German Emperor Wilhelm II his one-act play "The Doctor of his Honour" in which Hausdorff criticises the dreadful habit of duelling was staged about 300 times in many towns in Germany. At the German Mathematical Society (Deutsche Mathematiker-Vereinigung - DMV) conference in Bonn last year the protestant student community’s theatre group played "The Doctor of his Honour" with great success.

And now as requested I will describe the golden fifties from my personal point of view:

In 1950 I received my doctorate in Münster from Heinrich Behnke, who was instrumental in the post-war rebuilding of mathematics in destroyed Münster. At this point I can explain my connection to Plücker: my Ph.D. supervisor was Behnke, Hecke was Behnke’s supervisor, Hilbert was Hecke’s, Lindemann was Hilbert’s, Klein was Lindemann’s and Plücker was Klein’s.

In 1952, after two years as scientific assistent in Erlangen where I held lectures much like a junior professor today, I was invited as a member (Visiting Research Fellow) to the Institute for Advanced Study in Princeton, New Jersey, USA. At the School of Mathematics of the Institute for Advanced Study were between 40 and 50 junior and senior visiting research fellows from all over the world who for one or two years could devote themselves completely to research unhindered by other commitments. They could choose in what direction they wanted to do research but nobody was isolated. The regular discussions during teatime or parties in the evenings were conducive to work.

In the inspiring atmosphere of the institute work progressed quickly. In December 1953 the results were completed which were later published in my book "New Topological Methods in Algebraic Geometry". These results led to my being offered a position in Bonn (1955). From June 1956 on I was professor in Bonn - as mentioned earlier. The two chairs existing since 1818 were held by Wolfgang Krull and Ernst Peschl (both since about 1938), who had both been instrumental in the rebuilding after 1945. This beautiful building, Wegelerstraße 10, was built after the war. With great pleasure I held my first course on calculus in this auditorium to about 150 mathematics and physics students in the summer term 1957. I also taught these students the following semesters. We celebrated Mafüfafafei (Mathematisch-Physikalische Fachschafts-Faschings-Feier = mathematics and physics student body carnival party) in this building and danced through the night. Once I held a carnival lecture in this auditorium. The student body awarded me the degree of a doctor carnevalensis honoris causa including official document and doctoral cap. My students from 1957 are almost 70 years old now. As you can see I was very happy in Bonn. I wish the Cluster of Excellence as much good fortune as I have had in Bonn- also in its teaching, and in spite of bachelor, master, curricula, modules, evaluating, accrediting, agencies.

When I started in Bonn, there was only the Mathematical Institute in mathematics. Ernst Peschl was committed to developing the field of applied mathematics and fought successfully for the creation of chairs for applied mathematics. The first new chair was filled with Heinz Unger in 1958 (functional analysis and numerical mathematics), the second in 1964 with Walter Vogel (probability theory and mathematical statistics), and the third in 1965 with Rolf Leis (mathematical methods in physics). Rolf Leis’ successor is Felix Otto, the Managing Director of the Hausdorff Center. This is how the Institute for Applied Mathematics started. By now it has a young daughter: the Institute for Numerical Simulation which was established at the request of Michael Griebel, when he was offered the directorship of the Fraunhofer Institute for Technical and Industrial Mathematics. The Mathematical Institute also expanded with new chairs: 1964 with Jacques Tits, 1966 with Wilhelm Klingenberg and 1970 with Stefan Hildebrandt.

In 1972 Berhard Korte was appointed to a professorship at Bonn University. Thus began the success story of the Research Institute for Discrete Mathematics which was founded in 1981 and 1997 moved into a beautiful new home housing also the Arithmeum. Werner Hildenbrand and Reinhard Selten came to Bonn in 1969 and 1984 respectively which strengthened the mathematical methods in economic science enormously. Ten professors from this field are members of the Center.

By now I have mentioned five of the six participating institutes. The Max Planck Institute for Mathematics is the sixth and now I return to the golden fifties.

I was so enthusiastic about Princeton that right from the beginning of my work in Bonn the idea of establishing an institute comparable to the School of Mathematics of the Institute for Advanced Studies was on my mind. I started by inviting visiting professors. During the summer semester 1957 the first Arbeitstagung took place, which from then on was held once a year and became known world wide under that name. There was no set programme but programme discussions and a selection of speakers during the week of the Arbeitstagung. Only the first speaker was determined in advance, and often it was Michael Atiyah. We are hopeful that now Sir Michael will attend the Arbeitstagung celebrating the fiftieth anniversary in June 2007. Bonn University, the Ministry in Düsseldorf and the German Research Foundation (DFG) were very supportive of my efforts to that respect. At negotiations in the golden fifties the ministry’s standard response to my requests was:" But of course, Herr Professor".

The successful workshops and the increasing number of stays by visiting professors and researchers lead to the successful proposal for a Collaborative Research Center "Theoretical Mathematics" (Sonderforschungsbereich - SFB 40) which was submitted to the German Research Foundation (Deutsche Forschungsgemeinschaft - DFG). The whole thing was a bit more complicated than that. When the new DFG-programme became known about 1965, all parts of mathematics in Bonn were excited (the Mathematical Institute and the Institute for Applied Mathematics) and invested a lot of work in the new proposal. After all, a new future programme for the next 10 to 15 years was at stake (Collaborative Research Centers are limited in time). There was a sense of excitement about the future, much like today. The application for one Collaborative Research Center in pure and applied mathematics was handed in. I was chosen to represent it to the German Research Foundation. I was sitting waiting outside the door of the responsible committee, when the mathematician Karl Heinrich Weise (Kiel University) came out and said: "We cannot approve the application, the SFB would be much too big, but we have decided to approve two Collaborative Research Centers for mathematics in Bonn if you agree". Thus the Collaborative Research Center SFB 40 (theoretical mathematics) and Collaborative Research Center SFB 72 (approximation and mathematical optimization in application-oriented mathematics) were created. During the following faculty meeting critical remarks were made: "Herr Hirzebruch, you were asked to return with the approval for one Collaborative Research Center not two!" or "If things continue like this, Bonn mathematics will soon have conditions like at Harvard!" to which I answered:" That would not be so bad!" The faculty laughed. Our Cluster of Excellence now has all chances that the fears of a faculty member come true.

The Collaborative Research Centers were a success. The Max Planck Institute for Mathematics grew out of the Collaborative Research Center SFB 40 and celebrated its 25th anniversary last year. Collaborative Research Center SFB 72 had successors, first Collaborative Research Center SFB 256 (nonlinear partial differential equations) and then the current Collaborative Research Center SFB 611 (singular phenomena and scaling in mathematical models).

All six institutes were such a success - also in filling numerous professorships that had become vacant due to retirement - that it was sheer impossible not to decide to fund our Cluster of Excellence. The members have difficult decisions laying ahead of them for example the filling of 5 new professorships. The Hausdorff Center will radiate in the international mathematics community so that many mathematicians, junior and senior, from all over the world, especially from Germany, can work successfully at the Hausdorff Center in all fields of mathematics.

Congratulations to the Cluster of Excellence in Mathematics: Foundations, Models, Applications!

Magnifizenz,

Spektabilis,

Ladies and gentlemen,