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  \textbf{\large Henri Cartan 1904--2008}\\[3mm]
  Friedrich Hirzebruch\\[3mm]
  In: Notices Am. Math. Soc. 57, 8 (2010) 972-975.\\[10mm]
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I met Henri Cartan for the first time in Oberwolfach in 1951. We met
for the last time during the celebration of his 100th birthday in
Paris 2004. I gave a lecture with the title ``Henri Cartan: A great
friend, mathematician, and European''. I shall use the part of this
talk that does not overlap Remmert's report.

On the occasion of Behnke's eightieth birthday on October 8, 1978,
celebrated in Münster, Henri Cartan gave a beautiful dinner speech. We
were all sad that Heinrich Behnke unexpectedly could not attend the
dinner because of illness. He died one year later. Cartan's dinner
speech was printed by Springer-Verlag under the title ``Quelques 
souvenirs par Henri Cartan''. In his speech Cartan recalled his first
visit to Münster in 1931. Behnke, a young professor, then thirty-two
years old, had decided to make Münster an active and interesting
center for the young people around him. For this purpose he had
invited a young French mathematician of twenty-six years having
related interests who gave four lectures in German and one in French
during his one-week visit. Cartan met Peter Thullen, and this was the
beginning of a scientific cooperation and long-lasting
friendship. Cartan reported also about his second visit to Münster in
1938. In the meantime the famous \emph{Ergebnisse-Bericht} (Springer-Verlag)
by Behnke and Thullen had appeared in 1934. Thullen had left Germany.
The political atmosphere was depressing. There were not many
students. But still mathematics went on. Behnke's assistant was Karl
Stein, who had received his Ph.D. degree in 1936.

During the war, the friendship between Cartan and Behnke was not
interrupted; Behnke, for example, received a mathematical letter from
Oka in December 1940 and informed Cartan about it. In 1943 Cartan's
brother Louis was deported to Germany. About this tragedy, Cartan says
in ``Quelques souvenirs'' addressed to Behnke:

\begin{quote}
  ``Je ne puis pas non plus oublier toutes les démarches que vous avez
  faites durant les années 1943 et 1944 (en vain, hélas) pour tenter
  de retrouver la trace de mon frère Louis, déporté en Allemagne au
  mois de février 1943, et qui ne devait jamais revenir. (I cannot
  forget, too, all the efforts you made during the years 1943 and 1944
  (in vain, alas) to try to find any trace of my brother Louis, who
  was deported to Germany in the month of February 1943, and who never
  returned.)''
\end{quote}

Already in 1946 Cartan came to Oberwolfach, where he met Behnke again
after eight years. The Oberwolfach guest book records that Cartan
participated in a concert (Haydn, Bach, Beethoven) on November 1,
1946, and lectured on Galois theory for noncommutative fields on
November 4, 1946.  In this way Cartan began his efforts to reconcile
the mathematicians on both sides of the Rhine (cf.  Remmert's
contribution).

Cartan was always interested in the work of Behnke and his students,
in particular Stein, Grauert, Remmert, and myself.

For Stein's sixtieth birthday (1973) Cartan lectured at a conference
in Munich and wrote an article ``Sur les travaux de Karl Stein''. He
reported in particular about Stein's \emph{Habilitationsschrift} (1940),
which concerns Cousin's second problem. The title (translated into
English) is: ``Topological conditions for the existence of holomorphic
functions with a given zero divisor''. This is related to the famous
Theorem B of Cartan and Jean-Pierre Serre.

Cartan reported about my thesis (written under Behnke and Hopf) in the
Bourbaki seminar of December 1953. In the thesis I had introduced
complex spaces of dimension 2 and described the resolution of their
singularities.

In his \emph{Habilitationsschrift}, Hans Grauert proved that, for a Stein
manifold X and a complex Lie group L, the classification of
topological principal fiber bundles over X with structural group L
coincides with the classification of analytic principal fiber bundles
over X with structural group L. This includes the solution of Cousin I
and II (L = C or C*, respectively). Grauert published his work in
three parts in \emph{Mathematische Annalen} in 1957 and 1958 and thanked
Cartan for advice. Cartan lectured on Grauert's results in the
``Symposium Internacional de Topologia Algebraica, Mexico 1956''.

In his contribution Remmert shows that Henri Cartan was a real
European. I want to emphasize this by the following remarks:

The first European Congress of Mathematics took place in Paris from
July 6 to July 10, 1992. In his opening speech, Cartan calls the
congress an event of great importance showing that the mathematicians
know the solidarity of the countries of Europe, which are different in
so many ways but have a rich common heritage and a common
future. Cartan was especially glad that this first European Congress
reunited the mathematicians from the two parts of Europe that were
separated for such a long time. Cartan's eighty-eighth birthday was
celebrated during the first European Congress at the residence of
the German Ambassador in Palais Beauharnais.
                                                          
The Association Européenne des Enseignants (European Association of
Teachers) was founded in Paris in 1956. Cartan was president of the
French section. As such he took the initiative to invite participants
from eight European countries to a meeting in Paris in October
1960. Emil Artin, Heinrich Behnke, and I were the German members.  The
second meeting of this committee was in Düsseldorf in March 1962. As a
result, the \emph{Livret Européen de l'Etudiant (European Student's
  Record)} was published and distributed by the European Association
of Teachers. The booklet contained a description of minimal
requirements for basic courses. It was supposed to increase the
mobility of students from one country to another. The professor of one
university would mark in the booklet the contents of courses attended
by the student.  The professor at the next university would then be
able to advise the student in which courses to enroll. The booklet was
not used very much. For me it was often useful when reforms of the
contents of courses were discussed.

The efforts of Cartan to harmonize mathematical studies in Europe date
back more than fortyfive years. Now we are implementing the Bologna
process. In all European countries bachelor's and master's degrees are
to be introduced. Is this the harmonization we wanted?

Cartan, the European, was also active at the international level. He
was president of the International Mathematical Union for the four
years 1967 to 1970. He addressed the International Congress of
Mathematicians in Nice in 1970 during its opening ceremony and
announced the names of the Fields Medal winners. Sergei Novikov, one
of the four winners, was unable to attend, indicating the political
difficulties of the time.

The mathematicians of my generation, from Germany and everywhere else,
learned from Henri Cartan. His papers, books, and seminars were a
source of inspiration. He showed us the right way of developing
international cooperation. He and his wife were charming hosts for
many visitors to Paris. He has left us, but we will always remember
him with gratitude.


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