#### by Judith Roitman

She claimed that she did most of her work on what she called her theorem-proving couch, and other mathematicians joked about how they wished they had couches which could prove theorems, but it wasn’t just theorems. She created examples — some easy, some difficult, and some which were breathtaking, almost audacious. Her theorems and examples cut a wide swath through a world that, when she began, was known as point-set topology and which relatively soon, in large part because of the kind of work she did and the kind of influence she had on others, came to be known as set-theoretic topology.

The difficult, breathtaking, audacious examples came about because, to
her, complexity, intrinsic complexity, came easily. Her work is, as
Steve Watson
[e2]
wrote in the 1993 Festschrift to honor her seventieth
birthday, “just hard mathematics, that’s all.” To pick one example:
She looked at an arbitrary Suslin tree __\( T \)__ and saw not just an __\( L \)__-space
out of its branches, which everyone else saw, but an __\( S \)__-space
constructed out of triples in
__\[ \omega \times \omega_1 \times T \]__ whose
neighborhoods came from not quite subtrees related to each other in an
intertwined fashion so complex that, working through it, you think,
“This can’t possibly work.” But it does
[1].
Yet, as is evident in
the brief description of this construction in her 1975 CBMS notes
[2],
she did not see her __\( S \)__-space from a Suslin tree as particularly
difficult. That is what I mean by breathtaking and audacious.

Aside from her results, there was her influence. There were three
aspects to this: she brought people together, she encouraged anyone
who was interested, and she knew where we should be looking: in
particular, her 1975 *Lectures on Set Theoretic Topology*
[2],
from
the 1974 CBMS Regional Conference in Laramie, set the agenda for
decades.

Her hospitality and warm presence were both legendary and a major part of her influence. Consider how I met her. I was a graduate student at Berkeley wanting to use set theory to do topology and thus wanting to spend time in Madison. Arrangements were made. As soon as I arrived, I called Mary Ellen, per her instructions. She apologized that she could not help me get settled right away because her father had just died and she had to leave town for his funeral. Would I be okay for the next couple of days until she could get back? I am still astonished at the kindness of this gesture from a major mathematician to a very new graduate student barely past quals.

There were so many gestures like that to so many people, helping to form and nurture a community, a floating crew which would meet up in Prague, Warsaw, the Winter School, the Spring Topology Conference….It was an extraordinarily fertile time. I remember one summer in the mid-1970s when a number of us converged simultaneously on Madison for an impromptu summer-long seminar that met several times a week. Every meeting began with Mary Ellen asking, “Who proved a theorem last night?” and at every meeting several hands were raised.

Along with her warmth was an immense good cheer born of deep integrity and an unblinking sense of reality. When my first baby died of meningitis, Mary Ellen wrote the words that I turned to again and again, telling me how it was for her when her son Bobby was born with Down syndrome, and the doctors laid out a hopeless future for him (the hopelessness of which — Mary Ellen and Walter being who they were, refusing to pay attention to what was then accepted wisdom — did not come to pass): “Your life will never be quite the same again.” There was tremendous comfort in those words.

Much about Mary Ellen was symbolized to me by the kitchen radio, an AM radio, already very old when I first noticed it. I asked Mary Ellen years later why they didn’t have a newer, better model, and she said, “Because it still works.” A few years ago I noticed that the radio was gone. What happened to it? “It stopped working.” This radio was, for me, a symbol of Mary Ellen’s and Walter’s basic decency and solid values: no matter how many features the new radios have, you don’t get rid of your old one if it’s still working.

Mary Ellen was, of course, a woman mathematician at a time when there were few women mathematicians. She belonged, with Julia Robinson, Emma Lehmer and others, to what she called the housewives’ generation: women who did substantial mathematics outside the academy, with only occasional ad hoc positions. I think of those women as exhibiting enormous strength of character. I think they thought of themselves as simply doing mathematics. As F. Burton Jones wrote in the Festschrift volume [e1], “Wherever Mary Ellen was there was some mathematics.”

Feminist that I was, I would try to engage Mary Ellen about how the mathematical community treated women, with her as exhibit, if not A, then at least E or F. She was not interested. “The best way to help women in mathematics is to do mathematics!” she roared at me, pounding the breakfast table at the 1974 Vancouver ICM. Yet she went out of her way to meet with young women and encourage them, and she told me many years after Vancouver that she had come to realize that when young she had protective blinders: she simply didn’t notice the differences in how she was treated, so she wasn’t hurt by them.

The last time I saw Mary Ellen was about a year after Walter died. By then she was using a walker and had moved into the guest bedroom off the living room to avoid the stairs. But she was still spending time every day thinking about mathematics simply because she loved it so much, working in Walter’s old office on a huge table that I think was made out of a door plank. We went through the photos and reminiscences that people had sent her in homage to Walter, and her great no-nonsense good cheerfulness was still there, remembering all the times they had shared. There was a call about Bobby’s care, and she excused herself to deal with it. She was going to meet with friends for lunch. Her life was full, her affect was vital, and I could not imagine that this would be the last time I would see her. But it was.