Celebratio Mathematica

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.