Accustomed as I am to making carefully prepared spontaneous remarks, I'd like to provide some personal reminiscences of Menger of IIT.
In 1949, Paul Schilpp, a philosopher at Northwestern University, published a volume "Albert Einstein: Philosopher & Scientist" on the occasion of Einstein's 70th birthday. It contains 25 essays commenting on various aspects of Einstein's work. As a physics graduate student at the University of Chicago, reading this volume in the 50's, I of course recognized names such as Sommerfeld, de Broglie, Pauli, and Bohr among the contributors. But I'd never heard of Karl Menger who wrote an article "The Theory of Relativity and Geometry". No matter. This was a strikingly clear, concise, elegant, instructive, and interesting paper containing many original ideas. Two of Menger's proposals really had a 'thumping' impact as he said "I venture the conjecture that, for the geometrization of physics, especially the physics of the microcosm, idealizations very different from those of Euclid might prove more adequate than his. One such alternative is a geometry where points are not primary entities. What is here contemplated is a geometry of lumps that is, a theory in which lumps are undefined concepts, whereas points appear as the result of limiting or intersectional processes applied to these lumps another possibility is here indicated, namely, the introduction of probability space in which a distribution function rather than a definite number is associated with every pair of elements." Einstein, in his rejoinder, mentions Menger's ideas (doubts about the nature of the continuum), but cautions "as long as one has no new concepts which appear to have sufficient constructive power, mere doubt remains. Adhering to the continuum originates with me not in a prejudice, but arises out of the fact that I have been unable to think up anything organic to take its place."
Sixty years on, it's clear that Menger and Einstein had a prophetic insight: Probablistic metric spaces have evolved from a 'possibility' to a flourishing branch of mathematics at the hands of Wald, Schweizer, Sklar and others. And, of course, we all recognize that the string and loop theories of physics are merely avatars of Menger's lumps. Disregard of Einstein's warning that generalizations lacking the guidance of disciplined constraints have no constructive power is the fundamental defect of current string formalisms. At the end of Menger's article, in small typed, there is an address "Illinois Institute of Technology, Chicago". I'd never heard of that either. But soon I found my way from 57th and Ellis to 33rd and State (in GPS terms to 3308 South Federal) where on the third floor of a 'Hunersteige' (old Viennese slang for a very unprepossessing building) I found a small fabulously untidy office fired up by Menger's energy. We got along instantaneously. That night I called my old college friend Bert Schweizer long distance in Washington DC and urged him to forget drudging at the Naval Research Laboratory, and come to Chicago to become Menger's graduate student. That's exactly what Bert did. None of us had any doubts that that was the right thing to do & it was the beginning of a very happy and productive time. Eventually, of course I also came to IIT and joined the Menger circle but that's another story for another time!