> The only way to learn mathematics is to do mathematics—Paul Halmos Paul Halmos taught for two years in the 1970s at the University of California, Santa Barba

> The only way to learn mathematics is to do mathematics—Paul Halmos Paul Halmos taught for two years in the 1970s at the University of California, Santa Barbara, where I was an undergraduate majoring in linguistics. I was also interested in math, and I ended up taking three courses from him: an introduction to mathematical logic, with about twenty students; a seminar on set theory and the foundations of arithmetic, with four or five students; and a one-on-one tutorial on point-set topology. For the latter two courses, he taught based on his “do mathematics” principle. He would provide us with definitions of basic concepts and then have us work through a series of not-so-difficult problems that led eventually to proofs of the major theorems. He let us do most of the work ourselves, though if we got stuck he would provide pointers to help us keep moving ahead. His method was inspired by that of Robert Lee Moore [1], though Halmos was not as hard-assed about it as Moore reportedly was [2]. In the seminar, he encouraged the students to work together. More than forty years later, I remember many details of the two problem-based courses, while the first course, in which he lectured on mathematical logic, has mostly slipped from my memory. [1] https://en.wikipedia.org/wiki/Moore_method https://en.wikipedia.org/wiki/Moore_method [2] https://mathshistory.st-andrews.ac.uk/Extras/Halmos_Moore_method/ https://mathshistory.st-andrews.ac.uk/Extras/Halmos_Moore_me...