Celebratio Mathematica

Mary El­len Es­till Rud­in, Grace Chisholm Young Pro­fess­or Emer­ita of Math­em­at­ics at the Uni­versity of Wis­con­sin–Madis­on and pree­m­in­ent set-the­or­et­ic to­po­lo­gist, died at her home in Madis­on, Wis­con­sin, on March 18, 2013. Mary El­len was born Decem­ber 7, 1924, in Hills­boro, Texas, south of Dal­las–Fort Worth, a small town whose roster of not­able nat­ives also in­cludes Madge Bel­lamy, a film act­ress of the 1920s and 1930s best known for the hor­ror movie clas­sic White Zom­bie.

When she was six, Mary El­len’s fam­ily moved to the even smal­ler town of Leakey (LAY-key) situ­ated in the Texas hill coun­try in a canyon carved out by the Frio and Nue­ces Rivers. Her moth­er, Irene Shook Es­till, had taught high school Eng­lish. Her fath­er, Joe Jef­fer­son Es­till, was a civil en­gin­eer with the Texas High­way De­part­ment, and the fam­ily had moved around as his pro­jects dic­tated un­til, soon after their ar­rival at Leakey, the De­pres­sion hit. As there was no money to build new roads, the fam­ily stayed there throughout Mary El­len’s school years while her fath­er did sur­vey­ing work. Her broth­er, Joe Jef­fer­son Es­till Jr., was ten years young­er; the two sib­lings al­ways got along fam­ously des­pite their age dif­fer­ence. In those days, reach­ing Leakey from the out­side world re­quired trav­el­ing fifty miles up a one-lane dirt road and ford­ing the Frio River sev­en times. Chil­dren walked to school or rode there on horse­back.

In 1941 Mary El­len was one of five gradu­ates in her high school class. That fall she headed off to Aus­tin to en­roll at the Uni­versity of Texas and was dir­ec­ted to the table with the shortest line of pro­spect­ive stu­dents, where Robert L. Moore sat re­gis­ter­ing stu­dents for math­em­at­ics courses. Im­pressed with her cor­rect us­age of “if/then” and “and/or,” Moore signed Mary El­len up for a tri­go­no­metry course. She was sur­prised to dis­cov­er the next day that he was the pro­fess­or for the class. Every single semester dur­ing her en­tire eight years at the Uni­versity of Texas, from day one un­til she gradu­ated with her doc­tor­al de­gree in 1949, she at­ten­ded a course taught by Moore [e3]. Moore’s meth­od of teach­ing, which es­chewed form­al lec­tures, in­stilled in Mary El­len a lifelong deep con­fid­ence in solv­ing prob­lems and con­jec­tures, though she nev­er used the meth­od in her own teach­ing. As she later put it in an in­ter­view with Al­bers and Re­id [e1], at the end of her fresh­man cal­cu­lus course, “I’m not sure I knew the de­riv­at­ive of \( \sin x \) was \( \cos x \), but I could prove all sorts of the­or­ems about con­tinu­ity and dif­fer­en­ti­ab­il­ity and so on!” Mary El­len of­ten be­moaned the fact that she knew so little math­em­at­ics and felt cheated that she had not been ex­posed to ba­sic sub­jects such as al­gebra and ana­lys­is.

At Texas she was a mem­ber of a ter­rif­ic co­hort of Moore gradu­ate stu­dents, in­clud­ing Richard An­der­son, Ed Bur­gess, R. H. Bing, and Ed­win Moise, that went on to shape gen­er­al to­po­logy and leave its mark on the math­em­at­ic­al com­munity. In her doc­tor­al thes­is, Mary El­len con­struc­ted a counter­example to a well-known con­jec­ture us­ing a tech­nique now called “build­ing a Pix­ley–Roy space” after the two math­em­aticians who later gave a more sim­pli­fied de­scrip­tion of it. At the time she wrote her thes­is, she had nev­er read a single math­em­at­ics pa­per. She main­tained an aver­sion to read­ing re­search pa­pers throughout her ca­reer, loved talk­ing about math­em­at­ics and shar­ing her bounty of ideas with any­one who would listen, and was an avid col­loqui­um go­er (but al­ways with pen­cil and pa­per just in case her in­terest in the sub­ject waned).

After Mary El­len earned her PhD in 1949, Moore re­ferred her to Duke Uni­versity, which then had a wo­men’s col­lege un­der pres­sure to hire a fe­male math­em­atician. At Duke she met Wal­ter Rud­in. Wal­ter had ar­rived there in 1945 from Eng­land, where he had spent the war years in the Roy­al Navy after flee­ing Aus­tria. Hav­ing con­vinced a dean that he should be ad­mit­ted as a ju­ni­or even though he had nev­er fin­ished high school, four years later, in 1949, Wal­ter com­pleted his PhD. He left Duke in 1950 for a two-year C. L. E. Moore In­struct­or­ship at MIT and fol­low­ing that for the Uni­versity of Rochester, but Mary El­len and Wal­ter con­tin­ued to see each oth­er at the winter and sum­mer Joint Math­em­at­ics Meet­ings. In Au­gust 1953 they were mar­ried at the home of her par­ents in Hou­s­ton. While at Duke, Mary El­len proved a con­jec­ture of Ray­mond Wilder, an early Moore stu­dent, and Wilder ap­plied for an NSF grant to en­able her to vis­it him at the Uni­versity of Michigan. When she wired Wilder that she was get­ting mar­ried and go­ing to the Uni­versity of Rochester, some­how he man­aged for the grant to be trans­ferred from Michigan to Rochester. The Uni­versity of Rochester came up with a part-time po­s­i­tion for her on short no­tice, and she con­tin­ued her re­search. Daugh­ter Cath­er­ine ar­rived in Ju­ly 1954, and daugh­ter Elean­or in Decem­ber 1955, so part-time teach­ing suited the newly ex­pan­ded fam­ily.

The Rud­ins were on leave from Rochester vis­it­ing Yale for the aca­dem­ic year 1958–59 when R. H. Bing phoned Wal­ter to in­vite him to give a sum­mer course at the Uni­versity of Wis­con­sin. Wal­ter de­clined be­cause he already had Sloan Fel­low­ship fund­ing for the sum­mer but heard him­self ask­ing, “But how about a real job?” [e2]. Bing, who was math­em­at­ics de­part­ment chair at the time, ar­ranged an in­ter­view a few weeks later. In 1959 the Rud­in fam­ily moved to Madis­on and pur­chased a re­cently built home de­signed by Frank Lloyd Wright that con­sisted of ba­sic­ally one large room with 14-foot ceil­ings and a huge num­ber of win­dows (rumored to be 137). Sons Robert (Bobby)1 and Charles (Charlie) were born in Madis­on in 1961 and 1964. Al­though Wal­ter re­treated to the quiet of his study to do math­em­at­ics, Mary El­len de­scribed her own mode of work as “I lie on the sofa in the liv­ing room with my pen­cil and pa­per and think and draw little pic­tures and try this thing and that thing….It’s a very easy house to work in. It has a liv­ing room two stor­ies high, and everything else opens onto that….I have nev­er minded do­ing math­em­at­ics ly­ing on the sofa in the middle of the liv­ing room with the chil­dren climb­ing all over me” [e1].

Madis­on turned out to be ex­actly the right kind of place for them — the right kind of city and the right kind of math­em­at­ics de­part­ment [e2]. Mary El­len con­tin­ued as a part-time lec­turer who su­per­vised gradu­ate stu­dents and en­gaged in es­sen­tially full-time re­search un­til 1971, when, in Wal­ter’s words [e2], “The anti-nepot­ism rules, which were ac­tu­ally nev­er a law, had fallen in­to dis­rep­ute,” and she was pro­moted from part-time lec­turer to full pro­fess­or. Mary El­len was some­what du­bi­ous about the pro­fess­or­ship be­cause of the teach­ing and com­mit­tee work it en­tailed, but Wal­ter felt it was best, es­pe­cially for the chil­dren, in case something should hap­pen to him. One of my earli­est re­col­lec­tions of Mary El­len is shar­ing an el­ev­at­or with her in the mid-1970s, where she showed me a prin­tout with the small re­tire­ment sum she had ac­cu­mu­lated since com­ing to Wis­con­sin, a real­ity check the ever-ex­pand­ing ranks of ad­juncts and part-timers teach­ing math­em­at­ics today are also bound to face.

Mary El­len was known for her ex­traordin­ary abil­ity to con­struct in­geni­ous counter­examples to out­stand­ing con­jec­tures, many quite com­plic­ated. She was the first to con­struct a Dowker space, thereby dis­prov­ing a long-stand­ing con­jec­ture of Hugh Dowker that such spaces couldn’t pos­sibly ex­ist. Years be­fore this note­worthy ac­com­plish­ment, in 1963 her solu­tion to one of the Dutch Prize Prob­lems had been re­cog­nized by the Nieuw Archief voor Wiskunde (the Math­em­at­ic­al So­ci­ety of the Neth­er­lands). In later years she was named a Fel­low of the Amer­ic­an Academy of Arts and Sci­ences and of the Amer­ic­an Math­em­at­ic­al So­ci­ety, be­came a mem­ber of the Hun­gari­an Academy of Sci­ences, and re­ceived four hon­or­ary Doc­tor of Sci­ence de­grees. She gave an in­vited lec­ture at the In­ter­na­tion­al Con­gress of Math­em­aticians in Van­couver in 1974 and the No­eth­er Lec­ture of the As­so­ci­ation for Wo­men in Math­em­at­ics at the Joint Math­em­at­ics Meet­ings in 1984. In 1990 she was awar­ded the R. H. Bing Prize for sig­ni­fic­ant over­all con­tri­bu­tions to math­em­at­ics. She served as vice pres­id­ent of the AMS 1980–81; as MAA gov­ernor 1973–75; and on a vast num­ber of AMS, MAA, and na­tion­al com­mit­tees, in­clud­ing the ed­it­or­i­al boards of the No­tices and of To­po­logy and its Ap­plic­a­tions. Per­haps iron­ic­ally, she chaired the AMS Com­mit­tee on Aca­dem­ic Free­dom, Ten­ure, and Em­ploy­ment Se­cur­ity. In her hon­or, El­sevi­er es­tab­lished the Mary El­len Rud­in Young Re­search­er Award Fund to cel­eb­rate her achieve­ments and to re­cog­nize her leg­acy in en­cour­aging tal­en­ted young re­search­ers in to­po­logy. This award was form­ally an­nounced at the 47th Spring To­po­logy Meet­ing a week after her death, though she had giv­en her ap­prov­al of it earli­er. The in­aug­ur­al prize was awar­ded in Septem­ber 2013 to Lo­gan C. Hoehn of Nip­iss­ing Uni­versity, Canada, a math­em­at­ic­al des­cend­ant of Mary El­len.

Mary El­len nev­er stopped think­ing about math­em­at­ics and work­ing on prob­lems. She was a main­stay of the South­ern Wis­con­sin Lo­gic Col­loqui­um and couldn’t wait to tell me about her “fab­ulous week­end” when the col­loqui­um hos­ted the As­so­ci­ation for Sym­bol­ic Lo­gic meet­ing in April 2012. The talks were fant­ast­ic, she re­por­ted; she met lots of old friends and, of course, par­ti­cip­ated in all the so­cial gath­er­ings.

The Rud­ins wel­comed math­em­aticians, Wright afi­cion­ados, and stu­dents from all over the world to their unique home. The door was al­ways open — lit­er­ally; it was nev­er locked. As Mary El­len once said to me, “People just open the door and say ‘Hello, we’re here.’ ” To which daugh­ter Cath­er­ine quickly ad­ded, “And most of the time we know them.” The Rud­ins en­ter­tained of­ten and hos­ted every­one with a gra­cious, re­laxed style. I re­mem­ber a Thanks­giv­ing when, with her cus­tom­ary cheer­ful­ness, Mary El­len an­nounced to the gath­er­ing that din­ner would be delayed, as the tur­key, which was be­ing cooked out­side be­cause the oven wasn’t work­ing, had been on fire.

Mary El­len was lar­ger than life, and her repu­ta­tion for res­cues al­most as le­gendary as her counter­examples. On more than one oc­ca­sion she saved a child from the deep end of a pool or from crash­ing ocean waves. At an AMS sum­mer math­em­at­ics in­sti­tute in Col­or­ado, a horse sud­denly took off at a gal­lop, with the young rider who had slipped from the saddle dangling off to one side. Mary El­len charged after them on horse­back, cor­ralled the run­away horse, and righted the girl, the daugh­ter of the Rud­ins’ long­time friend Yale math­em­atician Shizuo Kak­utani, Michiko Kak­utani, now a Pulitzer Prize-win­ning lit­er­ary crit­ic for the New York Times.

For well over twenty years, ex­cept for the five years that Linda Roth­schild was in the de­part­ment, Mary El­len and I were the only wo­men math­em­at­ics fac­ulty mem­bers at Wis­con­sin. Mary El­len’s pas­sion for math­em­at­ics was con­ta­gious, her sup­port and en­cour­age­ment to all ex­traordin­ary. She meant so much to so many; it was in­spir­ing to be a part of her re­mark­able life. She was so ac­cept­ing, so warm and wel­com­ing, so genu­ine, so fiercely in­de­pend­ent. She would nev­er think to tell any of us that she had been taken to the hos­pit­al by am­bu­lance in the middle of the night, ex­cept when it oc­curred to her she had left the house in just her night­gown with no shoes or money and no way to get back home. After Wal­ter’s death, sev­er­al of us would get to­geth­er reg­u­larly for din­ner, and she would want to drive. “We’ll pick you up,” I’d tell her. “Oh, ok,” she would reply. “I’ll be ready”. And she al­ways was.