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Mary Ellen Rudin

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7 Dec 1924

Hillsboro, Texas, USA

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Mary Ellen Rudin's name before she married was Mary Ellen Estill. Her parents were Joe Jefferson Estill, who was a civil engineer, and Irene Shook, who was an English teacher in a High School before marrying Joe. Mary Ellen's family was a fairly typical middle-class Presbyterian one and for ten years she was an only child, until her younger brother was born. Her parents were both from Winchester, Tennessee and both of Mary Ellen's grandmothers had graduated from Mary Sharp College in Winchester. This tradition of education was strongly felt in the family and Mary Ellen's parents had high expectations for her.

Joe Estill was engaged on road building projects around Leakey, Texas and it was in that small isolated town that Mary Ellen was brought up. Certainly an engineer to improve the roads was vital. To reach Leakey in the 1920s was certainly not easy with the only route being a 50 mile dirt road through a canyon which forded the Frio River seven times. Uvalde is situated at the bottom of the canyon and the road travelled north from there up the Frio river, then beyond Leakey to the town of Junction which is as far north of Leakey as Uvalde is to the south. Mary Ellen spoke of her childhood in Leakey:

We had few toys. There was no movie house in town. We listened to the radio. But our games were very elaborate and purely in the imagination. I think actually that that is something that contributes to making a mathematician - having time to think and being in the habit of imagining all sorts of complicated things.

Mary Ellen attended a small High School in a class of five students. Given her remarkable achievements one would naturally expect that she would have shone in this environment but in fact this was not so, and she normally came in the middle of her class. When she entered the University of Texas in 1941 she did not have high expectations, nor did she have any set ideas as to the subjects she wanted to study. It was almost by accident that she came to study mathematics. She went to a large hall full of students on the day for registration:

... there were few people at the mathematics table so I was sent over there. The man who was sitting there was an old white-haired gentleman. He and I discussed all kinds of things for a long time. When I went to my math class the next day, I found the professor was R L Moore - the same man who talked to me at the registration table.

Mary Ellen had registered for R L Moore 's trigonometry class and she would take one of his classes every year until she graduated with her B.A. degree in 1944. R L Moore spotted Mary Ellen's mathematical talent right from the start and he was determined that she would become a mathematician:

I'm a child of Moore. I was always conscious of being manoeuvred by him. I hated being manoeuvred. But part of his technique of teaching was to build your ability to withstand pressure from outside. So he manoeuvred you in order to build your confidence. He built your confidence that you could do anything. I have that total confidence to this day.

As to R L Moore 's teaching methods she wrote:

His way of teaching was to present you with things that had not yet been proved, and with all kinds of things which might turn out to have a counterexample, and sometimes unsolved problems - that is, unsolved by anyone, not only unsolved by you. So you had some idea of what it meant to be a mathematician - more than the average undergraduate does today.

Although the Moore Method proved good for Mary Ellen Estill, she understood that it was not right for everyone:

I wouldn't for anything have let my children go to school with Moore! That is, I think that he was destructive to anyone who didn't fit exactly into his pattern, he did not succeed in giving the people that worked with him an education. It's a mistake to go to school under those circumstances in general.

R L Moore was not the only inspiring mathematics lecturer who taught Mary Ellen at the University of Texas. Another was F Burton Jones , who himself had been one of R L Moore 's students. When Mary Ellen Estill graduated with a B.A. in 1944, mathematics was still only one of several subjects she had taken. At this stage she was not certain what subject she wanted to pursue in her graduate studies. However when offered an instructorship in mathematics she began research on topology under R L Moore 's supervision for her doctorate. She received her Ph.D. in 1949 and Moore arranged an instructorship for her at Duke University in Durham, North Carolina. She began teaching at Duke in 1949. She found her work so fantastically wonderful that :

... it still seems impossible that anyone would pay me for doing this.

There was a mathematics research student Walter Rudin at Duke University who Mary Ellen Estill became very close to and they married in 1953. Walter Rudin was appointed to the University of Rochester and Mary Ellen left her post at Duke and went with her husband to Rochester. Mary Ellen Rudin got a part-time appointment at the University of Rochester:

I was a mathematician, and I always thought of myself as a mathematician. I always had all the goodies that go with being a mathematician. I had graduate students, I had seminars, I had colleagues who loved me. I never had committees. 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.

While Walter and Mary Ellen worked at Rochester, two of their children were born: Catherine in 1954; Eleanor in 1955. Mary Ellen was not working for the money, however, but for the love of mathematics :

I spent more money than most on childcare. It would have been cheaper for me to stay at home.

Her colleagues at Rochester were working on different areas of mathematics from those that Mary Ellen had become an expert in but that did not bother her; she was happy to work in any area of mathematics :

Wherever I was, I went to look for the mathematicians, and I did whatever the mathematicians were doing.

In 1958 they moved to Madison when Walter was appointed to the University of Wisconsin. In 1959 Mary Ellen began a part-time appointment at the University of Wisconsin as a lecturer. During the next few years her third and fourth children were born: Jefferson in 1961; and Charles Michael in 1964. In 1971 she was promoted from lecturer to full professor, going in one step from the bottom point of the academic ladder to the top:

The guilt feelings in the mathematics department were such that nobody even asked me if I wanted to be a professor. I was simply presented with this full professorship.

To begin to understand why the Mathematics Department at the University of Wisconsin should have felt guilty that by 1971 Mary Ellen Rudin was still only a lecturer, we need to take a look at her remarkable mathematical achievements. First, however, let us note that others had recognised her accomplishments long before Wisconsin for, in 1963, the Mathematical Society of the Netherlands awarded her its Prize of Nieuwe Archief voor Wiskunk.

In a 1988 interview Rudin explained her mathematical interests:

... from the beginning, it was the set-theoretic aspects of topology which interested me most. I liked finite and infinite combinatorics. ... I'm basically a problem solver.

To Rudin, mathematics is pattern recognition:

I draw little pictures and try this thing and that thing. I'm interested in how ideas fit together. Actually I'm very geometric in my thinking. I'm not really interested in numbers.

She began publishing after completing her doctoral thesis. In 1950 the paper Concerning abstract spaces was published in the Duke Mathematical Journal. It looked at the implications, and relations to various alternatives, of an axiom system for point set theory proposed by R L Moore in 1932. She continued to look at spaces satisfying a subset of R L Moore 's axioms in Separation in non-separable spaces published in 1951. Her 1952 paper A primitive dispersion set of the plane provided a positive solution to an unsolved problem contained in R L Wilder 's book Topology of manifolds (1949). Also in 1952 the paper Concerning a problem of Souslin's continued her examination of the implications of R L Moore 's axiom systems, this time motivated by a 1920 problem due to Souslin.

The above papers were all published under her maiden name of Mary Ellen Estill, but beginning with Countable paracompactness and Souslin's problem in 1955, she published under her married name of Mary Ellen Rudin. Having looked at some of her earliest papers let us note that she is best known for her ability to construct counter-examples. Perhaps one of the most famous of these example was produced in 1970 when Rudin, using box products, constructed an example of a normal Hausdorff space whose Cartesian product with an interval is not normal.

In August 1974 Rudin gave a series of lectures on set theoretic topology at the CBMS Regional Conference held at the University of Wyoming, Laramie. The notes of these lectures were published by the American Mathematical Society in the following year. In the lectures she surveyed what were then the recent results connecting set theory with the problems of general topology. In particular her many impressive results are put in context in this useful survey.

In 1981 Rudin became the first holder of the Grace Chisholm Young Professorship at Wisconsin. She remained at the University of Wisconsin for the rest of her career, being made professor emeritus. Over the last few years, however, Rudin has produced some very deep mathematical papers. She began publishing a sequence of four papers in 1998 aimed at characterizing the Hausdorff continuous images of compact linearly ordered spaces. These confirm a conjecture by J Nikiel that they are precisely the compact Hausdorff monotonically normal spaces.

Rudin has received many honours for her work, including at least four honorary doctorates, and will continue to receive further awards. She was elected Vice-President of the American Mathematical Society in 1980-81, she has been Governor of the Mathematical Association of America , elected a Fellow of the American Academy of Arts and Science , and elected to the Hungarian Academy of Science. Invited to be the Emmy Noether Lecturer for the Association for Women in Mathematics, she lectured on Paracompactness.

When asked how she managed to combine being a full-time mother with being a full-time mathematician, she replied:

I have never minded doing mathematics lying on the sofa in the middle of the living room with the children climbing all over me. 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.

Source:School of Mathematics and Statistics University of St Andrews, Scotland