Celebratio Mathematica

Mary Ellen Rudin

A Tribute to Mary Ellen Rudin

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.

István Juhász, A. Hajnal, Mary Ellen, and Michael Starbird at the ICM in Vancouver in 1974.

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.


[1] M. E. Rud­in: “A nor­mal hered­it­ar­ily sep­ar­able non-Lindelöf space,” Ill. J. Math. 16 : 4 (1972), pp. 621–​626. MR 309062 Zbl 0241.​54013 article

[2] M. E. Rud­in: Lec­tures on set the­or­et­ic to­po­logy (Lara­m­ie, WY, 12–16 Au­gust 1974). CBMS Re­gion­al Con­fer­ence Series in Math­em­at­ics 23. Amer­ic­an Math­em­at­ic­al So­ci­ety (Provid­ence, RI), 1975. Re­prin­ted in 1980. MR 367886 Zbl 0318.​54001 book