R. L. Moore was a professor of mathematics at the University of Texas. His field was topology, and it is safe to say that most American topologists include Moore on their mathematical family tree. (He is my mathematical great-great-grandfather.) What was so special about his mode of teaching was that he didn't lecture, he didn't "profess." He sat in the back of the room, mostly quiet, occasionally asking a question, allowing his students to find the answers in their own ways.
In fact, the students pretty much determined the pace of the course and the direction it would take. They often came up with their own names for the new ideas they found they needed in order to proceed.
Was Moore an easy professor? Hardly. He did not accept lazy students into his classes. There was always stiff competition to "get" the latest theorem, or to find the most elegant proof. His students loved him, and many, such as R.H. Bing, R.D. Anderson, and M.E. Rudin, went on to become world class mathematicians themselves.
Moore's influence is still strong. Many current professors of mathematics use his teaching methods, not only in topology, but in algebra, analysis, calculus, game theory, geometry, and other courses. Many of these same professors, from all fields of pure and applied mathematics, fondly remember a Moore Method course as their favorite undergraduate class.
The MAA has made a video interview with R.L. Moore discussing his career and his teaching: search the MAA Store for videos. The well-known University of Texas Mathematics Department maintains the internet site The Legacy of R.L. Moore. Its mission is to promote effective methods of learning and teaching in all disciplines. Also interesting is the Mathematics Genealogy Project, where you can see the influence of Moore and two other Texas mathematicians through their students. Perhaps you can find your professor on this "family tree."
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