Brief Memories of Karl Menger
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