Mary Ellen Rudin, one of the pioneers of set-theoretical topology, passed away this week. She was 88.

Born Mary Ellen Estill in Hillsboro, Texas in 1924, Rudin studied under Robert Lee Moore at the University of Texas: Moore’s method involved exposing students to unsolved problems and active research from the word go. While this turned out well for Rudin, she hated the feeling of being manoeuvred and was conscious that the method wasn’t for everyone: “he was destructive,” she said, “to anyone who didn’t fit exactly into his pattern.”

She completed her PhD in topology in 1949 and moved to Duke University in Durham, North Carolina, where her mathematical world opened up: it was impossible, she thought, that anyone would pay her for doing maths. It was here she met Walter Rudin; they married in 1953 and moved to Rochester, New York.

Their solution to the two-body problem was more or less the traditional one: Walter found senior jobs and Mary Ellen followed with the kids, before more junior jobs were found for her. This apparently suited her, allowing her to do her teaching and research unimpeded by such inconveniences as committees and furthering her career.

Brilliantly, she was promoted from temporary part time lecturer at the University of Wisconsin to full professor in 1971 without being asked; a one-step promotion from the lowest academic position available to the highest. Around the same time, she discovered the Dowker space, 20 years after Dowker conjectured it was impossible. Her example has cardinality $\aleph_{\omega}^{\aleph_0}$ and is “generally not well-behaved”.

This was a classical example of her famous ability to construct examples and counter-examples. Her work centred on set-theoretical topology; she considered the implications of Moore’s point set theory, and found solutions to several unsolved problems on the topology of manifolds. She also proved the first Morita conjecture in 1986.

After retiring, Rudin attempted to (I quote, because I’m a folk topologist^{1}) characterise the Hausdorff continuous images of compact linearly ordered spaces, confirming Nikiel’s conjecture that they are precisely the compact Hausdorff monotonically normal spaces.

Rudin received at least four honorary doctorates, was vice-president of the AMA, governer of the MAA, fellow of the AAAS and elected to the Hungarian Academy of Science.

A quote from Steve Watson to sum up her work:

Reading the articles of Mary Ellen Rudin, studying them until there is no mystery takes hours and hours; but those hours are rewarded, the student obtains power to which few have access. They are not hard to read, they are just hard mathematics, that’s all.

### More reading

Mary Ellen Rudin at the MacTutor History of Maths Archive

Mary Ellen Rudin’s Noether lecture biography

- three dimensions and the truth [↩]

Dear Colin,

I accidentally stumbled upon this web site while searching for something else. I was sorry to learn that Mary Ellen Rudin had passed away recently (and also George E. P. Box). I met the Rudins at a “party” during the academic year 1968-69 when I was finishing up my Ph.D. in Electrical Engineering at UW. Until I read your article above, I had no idea that she was “only” a part-time lecturer at the time — her bearing was so regal!

Now that I have discovered your web site, I plan to visit it regularly. All the best.

Sagar