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It was impossible to have contact with Karl Menger without being
influenced by him. He exuded the fine old European liberal values and
the continuing Enlightenment. Without your immediately knowing it, his
values became partly your own; also his mannerisms and his ways of
teaching were subconsciously absorbed.
I cannot recall ever having a conference with him which dealt with
course material, except in a few instances where I thought a hypothesis
needed tweaking or otherwise wanted to quibble, and I don't think he
would have welcomed the kind of tutoring that is widely expected of
faculty today. But his door was always open to the the discussion of
ideas, and if you were fortunate enough to have an idea that was a
little original, then he could embarrass you with his enthusiasm. "You
must write it up!" he would insist, in his strong accent with its
greatly distorted r-sound..
He was very kind and would often invite his students to his home or to
his favorite Swedish restaurant close by his house. Sometimes the social
aspect was for purposes of education a bit apart from mathematics, and
art, music or philosophy were discussed. Occasionally we made an outing
to see a painting or a piece of stained glass.
He loved the English language and he thought too that he loved American
democracy, without ever adapting to either of these completely. As with
many immigrants from wartime Europe, he was until his death neither fish
nor fowl; for it also would have also been impossible for him
successfully to return to Vienna. The play "Heldenplatz" by the great
Austrian writer Thomas Bernhard describes an academic, not so different
from Menger, who made the attempt, with disastrous consequences.
It is impossible for me to think of Karl Menger without at the same time
thinking of Berthold Schweizer. For beginning in the mid-1950's, at IIT,
Schweizer became Menger's extension and completion, his
"Lieblingsstudent", who would go on to build on the work Menger and on
that of Menger's earlier Lieblingsstudent Abraham Wald, in very
important ways, especially in the area of probabilistic geometry. And it
is impossible to think of Schweizer without at the same time remembering
Abe Sklar. The three of them formed a constellation of pairs that
persisted until Menger's death. Both Schweizer and Sklar also exerted
a strong influence on students that complemented that of Menger.
Finally, it is splendid that Menger's collaborator Franz Alt plans to be
present at the memorial conference. Alt and Menger, together with Otto
Schreiber, described new foundations for projective and affine
geometry. This work was then subsumed by its generalization, lattice
theory, and attracted the subsequent contributions of Garrett Birkhoff
and John von Neumann.
March 10, 2007
Villars-sur-Ollon, Switzerland
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