CALCULUS Understanding Its Concepts and Methods
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Karl Menger (1902--1985) --- Historical Sketch
Karl Menger, born in Vienna in early 1902, was the son of a famous economist, Carl Menger. His mother Hermione was a novelist of some note. As a high-school student, the young Karl made some serious attempts to become a writer, and he worked on writing a drama about a fictitious Pope Joan, but with no success. Indeed, a professional dramatist was disdainful of Karl's literary attempt, but, knowing the boy as a friend of his son, noted his genius for mathematics and physics.
As for Menger's higher education, he attended the University of Vienna with the intention of becoming a physicist. While there, he took a course entitled, What's new concerning the concept of a curve, taught by Hans Hahn (1879-1934). This sparked his interest in the topic, and he right away started working on the subject with Hahn. He also started working on ideas of dimension theory. He was forced by reasons of health to spend over a year in a sanatorium. However, his health did not stop him from his work---he emerged from the sanatorium with research papers he had written while there, and he obtained his doctoral degree with Hahn in 1924.
Right away, he was invited by the famous Professor L. E. J. Brouwer to take a position at the University of Amsterdam, and he worked with Brouwer for two years. Since Brouwer himself worked on the theory of dimension, it is reasonable to assume that they worked together on that topic, possibly among others. But they had a falling out for some unknown reason.
In 1927, happily for Menger, he was offered a chair of geometry back at the University of Vienna, and so he returned there, remaining until 1938, at which time he was happy---because of the political situation in Austria---to accept a professorship at the University of Notre Dame. In 1948, he accepted a post at the Illinois Institute of Technology in Chicago and remained in Chicago for the remainder of his life.
You met Menger's idea of curvature for plane curves, and one of the things he did in his productive life was to generalize that idea to curvature in higher dimensions. Another thing he did was to write a calculus textbook with novel ideas and approaches, but it was, unhappily, of limited success in the marketplace.
Karl Menger died in the autumn of 1985.
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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.