1984 Lecturer: Mary Ellen Rudin
Paracompactness
Mary Ellen Rudin is a professor emeritus at the University of Wisconsin at Madison, where she held the Grace Chisholm Young and Hilidale Professorships. She was born in 1924 in Hillsboro, Texas. She completed both her undergraduate and graduate studies at the University of Texas, where she worked with R. L. Moore. She was also greatly influenced by F. B. Jones.
After receiving her PhD in 1949, Rudin taught at Duke University and then went with her husband, mathematician Walter Rudin, to the University of Rochester, and later to the University of Wisconsin. There she was a lecturer until 1971, when she became a full professor.
Rudin’s primary research area is set-theoretic topology, and she is particularly well known for her ability to construct counterexamples. Her Noether Lecture discussed several set-theoretic questions related to paracompactness. Metrizability in a topological space provides a great deal of structure: a metric space is, for example, paracompact. But if one does not require metrizability, and instead asks to what extent normality (assuming all spaces are Hausdorff) achieves the structure of paracompactness, one discovers a very complex world of counterexamples whose product with the closed unit interval is not normal. It is undecidable in Zermel-Frankel set theory whether there is a perfectly normal nonmetrizable manifold, and the question of whether every normal Moore space is metrizable has a more complex, unsatisfactory answer. Rudin’s Noether Lecture explored these and similar problems in nonmetrizable topological spaces.
Rudin enjoys teaching and has had a large number of PhD students. During most of her career, she had part-time, temporary positions, but she doesn’t consider this to have been an obstacle. “I always thought of myself as a mathematician,” she said in an interview in the March 1988 issue of the College Mathematics Journal, “I didn’t have to prove to anybody that I was a mathematician, and I didn’t have to do all the grungy things that you have to do in order to have a career as a mathematician. The pressure was entirely from within. I did lots of mathematics, but I did it because I wanted to do it and enjoyed doing it, not because it would further my career.” A mother of four and a grandmother of two, she has been able to combine her research and family life by simultaneously immersing herself in both. “I have never minded doing mathematics lying on the sofa in the middle of the living room with the children climbing all over me,” she told the interviewers. “I feel more comfortable and confident when I’m in the middle of things, and to do mathematics you have to feel comfortable and confident.”
