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**R. L. Moore. Mathematician and teacher.**
*(English)*
Zbl 1069.01007

Washington, DC: Mathematical Association of America (MAA) (ISBN 0-88385-550-X/hbk). xiv, 387 p. (2005).

Parker describes the life and work of a Texan gentleman and professor of mathematics, Robert Lee Moore (1882–1974) and Parker does this very well. Moore was not only a brilliant mathematician and one of the main founders of the American school of point set topology, but a great teacher and an interesting and controversial man. The contributions of Moore to mathematics are important, but the Moore method that he used in his classes – characterized by Paul Halmos as the ’only right method to teach anything and everything’ – is also definitely still worth serious attention. It is the radical opposite of pouring results into students, whether they understand them or not. Moore taught his students to think. The students would do the work, give proofs with gaps, wrong proofs, refine definitions and finally come up with the results themselves. It is difficult to overestimate Moore’s influence. Several of his 50 PhD students became famous mathematicans and when the preface was written they claimed together 1678 doctoral descendants. Fascinating and moving is the extraordinary long letter Moore wrote to Mary Ellen Rudin in 1948. He had spotted her mathematical talent and he explained his method to her; he took her on in 1948. We also learn that Moore’s ‘Southern values did not extend to teaching African Americans’, but after reading the biography one is left with the impression that a meeting with a great black mathematical talent might have made Moore adjust his values on this point. Mathematics and spotting and nourishing mathematical talent was everything for him. The book is an important and well written contribution to the 20th century history of mathematics in the United States.

Reviewer: Teun Koetsier (Amsterdam)