Celebratio Mathematica

Mary Ellen Rudin

Mary Ellen Rudin

by Claudia Henrion

Mary El­len Rud­in’s1 life presents a fas­cin­at­ing ex­ample of how rad­ic­ally ex­pect­a­tions can change in the course of one gen­er­a­tion. Her story il­lus­trates some of the dra­mat­ic shifts that have taken place in wo­men’s vis­ion of them­selves, their work, and their fam­il­ies.2 Mary El­len is a kind, gen­er­ous per­son and a very tal­en­ted math­em­atician. She mar­ried a math­em­atician, had four chil­dren, and was act­ively in­volved in math­em­at­ic­al re­search. Though she is now a full pro­fess­or at the Uni­versity of Wis­con­sin, for most of her work­ing life she did not have a stand­ard pro­fess­or­ship at a re­search in­sti­tu­tion. She de­scribes her­self as an “am­a­teur math­em­atician” — a la­bel that is per­haps mis­lead­ing, for it does not con­vey the fact that she has pub­lished more than eighty art­icles in set-the­or­et­ic to­po­logy, and is in­ter­na­tion­ally re­cog­nized as a first-class math­em­atician. In fact, her repu­ta­tion in the math­em­at­ics com­munity be­came so strong that the Uni­versity of Wis­con­sin was suf­fi­ciently em­bar­rassed by her status as a lec­turer that they sud­denly pro­moted her from lec­turer to full pro­fess­or in 1971. She was forty-sev­en years old.

At the Uni­versity of Wis­con­sin, Mary El­len be­came a kind of math­em­at­ic­al moth­er, help­ing to es­tab­lish a strong and flour­ish­ing lo­gic and set the­ory com­munity. People from all over the world would travel there in or­der to be part of the stim­u­lat­ing, ex­cit­ing, and sup­port­ive en­vir­on­ment. She con­tin­ues to be pro­duct­ive in pub­lish­ing art­icles in new and dif­fi­cult areas of set-the­or­et­ic to­po­logy. However, for Mary El­len, be­ing a moth­er and wife is just as im­port­ant as be­ing a math­em­atician. As she says, she came from the “house­wives’ gen­er­a­tion.” There was no ques­tion in her mind that she would have chil­dren, and that she would fol­low her hus­band wherever his ca­reer would take them.

In­deed, Mary El­len feels that her situ­ation was in many ways ideal — she had all the ad­vant­ages of a math­em­at­ic­al life: a pro­fes­sion­al com­munity, the op­tion to teach when she wanted to, the stim­u­la­tion of gradu­ate stu­dents, the re­sources of a first-rate lib­rary, and an of­fice. Yet she was not weighed down with ad­min­is­trat­ive re­spons­ib­il­it­ies and time-con­sum­ing meet­ings. The in­form­al­ity of her po­s­i­tion al­lowed her to shape her work around her fam­ily. She could ad­just to the ever-chan­ging needs of her chil­dren and de­vote whatever free time she had to re­search. “I didn’t have to prove to any­body that I was a math­em­atician, and I didn’t have to do all the grungy things that you have to do in or­der to have a ca­reer as a math­em­atician. The pres­sure was en­tirely from with­in. I did lots of math­em­at­ics, but I did it be­cause I wanted to do it and en­joyed do­ing it, not be­cause it would fur­ther my ca­reer.”3

Mary El­len was able to in­teg­rate these dif­fer­ent roles of her life smoothly, which en­abled her to con­tin­ue to be pro­duct­ive as a re­search math­em­atician when most oth­er wo­men of her gen­er­a­tion did not. But as she points out in an in­ter­view pub­lished in More Math­em­at­ic­al People, the situ­ation for young wo­men today is quite dif­fer­ent: they see them­selves as pro­fes­sion­als.

If you do something pro­fes­sion­ally, it’s harder for you to quit. You stay with it in hard times. The young wo­men today are much more pro­fes­sion­al. We were am­a­teurs…. We did what we did be­cause we loved it. And some of us were lucky. For us, things worked out, and we did very well. Some were not so lucky, and they just dropped out along the way. But the young wo­men math­em­aticians today are think­ing in terms of a ca­reer from the be­gin­ning. It’s true that they want a full-time job. They want to do all the re­search in the world. They want to have a hus­band and chil­dren. They want to have a home. We wanted everything too — in spades — but the one thing we didn’t de­mand, in fact it nev­er oc­curred to us, was a ca­reer. The fact that they are think­ing in terms of a ca­reer means that when it’s a ques­tion of wash­ing the socks or do­ing math­em­at­ics, they will of­ten do math­em­at­ics. I think it was easi­er to quit do­ing math­em­at­ics in our day.4

Giv­en Mary El­len’s vis­ion of her­self as a moth­er and house­wife, how did she find her way in­to math­em­at­ics? And what kept her go­ing?

Early training

Mary El­len Rud­in had a rather un­usu­al child­hood and early train­ing in math­em­at­ics. In both cases she was quite isol­ated from main­stream cul­ture. She grew up in a little town in south­w­est Texas. It was a very isol­ated com­munity, at an alti­tude of about 3,000 feet, tucked in a canyon formed by the Frio River and moun­tains on all sides.

In those days you entered the town by go­ing fifty miles up a dirt road — you had to ford the river sev­en times to get there…. My fath­er was there to build a new road, but the De­pres­sion hit and the State High­way De­part­ment nev­er com­pleted the road while we lived there…. It was a real moun­tain com­munity. Many kids came to school on horse­back. We had a well and an elec­tric pump, which gave us run­ning wa­ter, but most people didn’t have run­ning wa­ter or any of the things you think of as be­ing per­fectly stand­ard. Yet it was won­der­ful. There were miles of wild coun­try and beau­ti­ful trees along the river. Every­where there was a beau­ti­ful view.

We had a very good school, and there were some very bright kids. We also had a lot of time to de­vel­op games. We had few toys. There was no movie house in town. We listened to things on the ra­dio. That was our only con­tact with the out­side world. But our games were very elab­or­ate and purely in the ima­gin­a­tion. I think ac­tu­ally that that is something that con­trib­utes to mak­ing a math­em­atician — hav­ing some time to think and be­ing in the habit of ima­gin­ing all sorts of com­plic­ated things.5

Grow­ing up, she was not in­ter­ested in math­em­at­ics (or any one par­tic­u­lar thing) more than any­thing else; she cer­tainly had no idea that she would be­come a math­em­atician. When she began col­lege at the Uni­versity of Texas, Aus­tin, there­fore, she simply fol­lowed her par­ents’ guid­ance and de­cided to pur­sue a gen­er­al edu­ca­tion; in her first term she took a broad range of courses. However, as fate would have it, on her first day at re­gis­tra­tion she wandered over to the math­em­at­ics table, where there were very few people, and began talk­ing with “an old white-haired gen­tle­man” who asked her a lot of ques­tions in­volving the use of terms such as if and then, and and or, to see if she used them cor­rectly from a math­em­at­ic­al point of view. As it turned out, the man she spoke with was R. L. Moore, a math­em­atician fam­ous for his un­con­ven­tion­al teach­ing style, and for the num­ber of math­em­aticians he pro­duced. That con­ver­sa­tion was to shape the course of her life. When she walked in­to her cal­cu­lus class the next day, it was Moore who was teach­ing it. She went on to take many more courses with him, and she ul­ti­mately ma­jored in math­em­at­ics. In fact, Moore was the only math­em­at­ics pro­fess­or she stud­ied with un­til her seni­or year. However, even then she still had no idea what she would do with her math­em­at­ics de­gree — be­ing a high school teach­er was the only thing she could ima­gine, and it was not what she wanted to do. But Moore had oth­er plans in mind. She was in­vited to stay at the Uni­versity of Texas for gradu­ate school. She ac­cep­ted the of­fer, and R. L. Moore be­came her gradu­ate ad­visor.

I’m a math­em­atician be­cause Moore caught me and de­man­ded that I be­come a math­em­atician. He schooled me and pushed me at just the right rate. He al­ways looked for people who had not been in­flu­enced by oth­er math­em­at­ic­al ex­per­i­ences, and he caught me be­fore I had been sub­jec­ted to in­flu­ence of any kind. I was pure, unadul­ter­ated. He al­most nev­er got any­body like that.6

Moore’s meth­ods were un­usu­al and con­tro­ver­sial. He had a very com­pet­it­ive and ad­versari­al style, which was sim­ul­tan­eously meant to weed out the weak­er mem­bers and boost the con­fid­ence of the sur­viv­ors.

I was al­ways con­scious of be­ing man­euvered by him. I hated be­ing man­euvered. But part of his tech­nique of teach­ing was to build your abil­ity to with­stand pres­sure from out­side — pres­sure to give up math­em­at­ic­al re­search, pres­sure to change math­em­at­ic­al fields, pres­sure to achieve non-math­em­at­ic­al goals. So he man­euvered you in or­der to build your ego. He built your con­fid­ence that you could do any­thing. No mat­ter what math­em­at­ic­al prob­lem you were faced with, you could do it. I have that total con­fid­ence to this day.7

In ad­di­tion to de­vel­op­ing their con­fid­ence, Moore taught his stu­dents to be highly self-suf­fi­cient. In class, he would simply put defin­i­tions on the board and give stu­dents po­ten­tial the­or­ems to work on. Some of the the­or­ems were true, oth­ers false, but the stu­dents had to dis­cov­er which were which on their own. They were dis­cour­aged from read­ing journ­als or con­sult­ing oth­er people; they were ex­pec­ted to work com­pletely in­de­pend­ently. In fact, Moore had his own unique math­em­at­ic­al lan­guage, which made it even more dif­fi­cult for his stu­dents to learn from out­side sources. He wanted them to fo­cus on their own ideas, their own in­sights, their own in­tu­itions — in a sense cre­at­ing math­em­at­ics from scratch. At the time Mary El­len wrote her thes­is, she had nev­er seen a single math­em­at­ics pa­per.

Though the kind of in­de­pend­ence they de­veloped was a sig­ni­fic­ant as­set, there were cer­tainly prob­lems with his meth­ods as well. Many stu­dents were turned off by the ex­treme de­gree of com­pet­i­tion. Oth­ers grew frus­trated by the fact that their math­em­at­ic­al train­ing made them so isol­ated from what was go­ing on in the field more gen­er­ally. In fact, Mary El­len does not use his meth­ods in her own classes. When asked how she felt later about her math­em­at­ic­al edu­ca­tion, she said:

I really re­sen­ted it, I ad­mit. I felt cheated be­cause, al­though I had a Ph.D., I had nev­er really been to gradu­ate school. I hadn’t learned any of the things that people or­din­ar­ily learn when they go to gradu­ate school. I didn’t know any al­gebra, lit­er­ally none. I didn’t know any to­po­logy. I didn’t know any ana­lys­is — I didn’t even know what an ana­lyt­ic func­tion was. I had my con­fid­ence built, and my con­fid­ence was plenty strong. But when my stu­dents get their Ph.D.’s, they know everything I can get them to learn about what’s been done. Of course, they’re not al­ways as con­fid­ent as I was.

Al­though Moore’s primary goal was to in­still con­fid­ence and in­de­pend­ence in his stu­dents, what de­veloped in the pro­cess was a very strong com­munity among his stu­dents, which proved to be tre­mend­ously help­ful in their ca­reers and math­em­at­ic­al de­vel­op­ment. “We have all been very close to each oth­er for our en­tire ca­reers. That is, we were a team. We were a team against Moore and we were a team against each oth­er, but at the same time we were a team for each oth­er. It was a very close fam­ily type of re­la­tion­ship.”8

This math­em­at­ic­al fam­ily played an im­port­ant role in prac­tic­al ways: help­ing her to get jobs, grants, and re­cog­ni­tion. In­deed, when Mary El­len fin­ished gradu­ate school, she nev­er ap­plied for a job; she was simply in­formed by Moore that she had a po­s­i­tion at Duke, and it was as­sumed that she would take it. “Moore simply told me that I’d be go­ing to Duke the next year. He and J. M. Thomas, who was a pro­fess­or at Duke, had been on a train trip to­geth­er. Duke had a wo­men’s col­lege which was sort of pres­sur­ing them to hire a wo­man math­em­atician. So Moore told Thomas, ‘I’ve got the very best, and I’ll ship her to you next Septem­ber.’ ”9 He did, and Mary El­len went.

In a sim­il­ar vein, near the end of her po­s­i­tion at Duke, one of her fel­low Moore stu­dents, R. L. Wilder, ar­ranged for her to go to the Uni­versity of Michigan and even ap­plied for a grant for her. He was im­pressed with her math­em­at­ic­al abil­ity and was hop­ing to work with her there. However, Mary El­len de­cided at the last mo­ment to do something dif­fer­ent, namely to marry Wal­ter Rud­in, who was then at the Uni­versity of Rochester. In ac­cord with the tra­di­tions of the time, Mary El­len nev­er ques­tioned that she would fol­low her hus­band. Wilder, there­fore, simply ar­ranged for her grant to be trans­ferred to the Uni­versity of Rochester.

Marriage, motherhood, and mathematics

Over the course of the next dec­ade, Mary El­len Rud­in had four chil­dren. Two of them came in the first two years after she got mar­ried. “I was very busy and very happy as a moth­er, and cer­tainly ex­pec­ted to be a moth­er, and wanted to be a moth­er very much.” It would not have been un­usu­al to stop do­ing math­em­at­ics at that point — rais­ing four chil­dren was a full-time oc­cu­pa­tion, and there was no in­cent­ive to have a ca­reer out­side of the home. What, then, en­abled her to con­tin­ue on this path, even when many oth­er even very gif­ted wo­men did not?

To some ex­tent her early math­em­at­ic­al train­ing con­trib­uted to this com­mit­ment, not only by help­ing her to de­vel­op a highly autonom­ous work style and provid­ing a com­munity which pro­pelled her along a math­em­at­ic­al path, but also through the un­der­ly­ing mes­sages con­veyed by R. L. Moore about what con­sti­tutes suc­cess and fail­ure.

Moore had warned Mary El­len about his earli­er wo­men stu­dents. One wrote a “fant­ast­ic thes­is” but then im­me­di­ately went off to China as a mis­sion­ary. The oth­er was “very in­flu­en­tial as a teach­er and ad­min­is­trat­or,” but did not con­tin­ue in re­search. Mary El­len says that Moore “viewed his two earli­er wo­men stu­dents as fail­ures and he didn’t hes­it­ate to tell me about them in great de­tail so I would real­ize that he didn’t want to have an­oth­er fail­ure with a wo­man.” In the con­text of oth­er con­ver­sa­tions he would subtly work on her — steer­ing her to a life of math­em­at­ics. On one oc­ca­sion when she men­tioned something about hav­ing a hus­band someday, he re­spon­ded, “Hus­band! But, Miss Es­till, I thought that you were go­ing to be a math­em­atician.” But as Mary El­len says, “Al­though he may have had his doubts, I nev­er saw any con­tra­dic­tion in be­ing both a house­wife and a math­em­atician — of the two I was more driv­en to be a house­wife.”10

But oth­er factors also played an im­port­ant role in her con­tin­ued com­mit­ment to math­em­at­ics. Like Fan Chung, Mary El­len had sig­ni­fic­ant help in rais­ing her chil­dren. The Rud­ins’ nanny, Lila Hil­gen­dorf, was in many ways a second moth­er to the chil­dren:

She cared for the chil­dren and did some house­clean­ing. When I would walk in­to the house, she would walk out; and when I had to go, she was there. We had that re­la­tion­ship un­til she died this year. She was ab­so­lutely the best moth­er I ever saw, and my chil­dren just ad­ored her. One thing that she did for me was ab­so­lutely fant­ast­ic. The first week­end after my re­tarded child was born, she said, “Oh, I just have to have him for the week­end!” And he went to her house for the week­end for the rest of her life. Ac­tu­ally he lived at her house the last sev­er­al years. So when people ask me how it is, in my po­s­i­tion to have four chil­dren, I have to say that when you’ve got Lila, it’s easy. I am afraid that few wo­men will ever have such an easy, non-pres­sured ca­reer as mine.11

Of course, cent­ral to this ar­range­ment was the fact that they had the eco­nom­ic re­sources to hire such a nanny. They were able to live com­fort­ably on Wal­ter’s salary, even with do­mest­ic help. And Mary El­len did not need to work to make ends meet; hence she could de­vote her free time to re­search.

But equally im­port­ant was the fact that both Mary El­len and her hus­band felt com­fort­able hir­ing do­mest­ic help. As Mary El­len points out. “I think there are a fair num­ber of wo­men in my day who had the po­ten­tial to be math­em­aticians, but who didn’t be­come math­em­aticians be­cause it didn’t seem right to have someone help you with your chil­dren.” Caring for the chil­dren was, after all, seen as a wife’s primary re­spons­ib­il­ity. And even if a wo­man felt com­fort­able with such ar­range­ments, of­ten her hus­band did not. Wal­ter, however, both un­der­stood and sup­por­ted Mary El­len’s de­sire to do re­search. Hir­ing help seemed like a nat­ur­al solu­tion.

In Ravenna Hel­son’s study of cre­at­ive wo­men math­em­aticians, there were very few things that the dif­fer­ent wo­men she in­ter­viewed had in com­mon. One un­ex­pec­ted find­ing, however, was that most of the wo­men she stud­ied were mar­ried to Cent­ral European Jews. Many of these men, like Wal­ter, had had nan­nies when they were young. Hence do­mest­ic help seemed nor­mal; they re­cog­nized that “the per­son who changes your di­apers doesn’t ne­ces­sar­ily de­term­ine what you do in life. It doesn’t de­term­ine one’s val­ues.” Fur­ther­more, they came from a cul­tur­al mi­lieu that cel­eb­rated in­tel­lec­tu­al wives — hav­ing a wife who was a math­em­atician was there­fore seen as an as­set, not a prob­lem.

Mary El­len and Wal­ter’s mar­riage was a sig­ni­fic­ant factor in en­abling her to stay act­ively en­gaged in math­em­at­ics in oth­er ways as well. Be­cause Wal­ter is a highly re­spec­ted math­em­atician, it has been fairly easy for Mary El­len to in­teg­rate in­to the math­em­at­ic­al com­munity. Both the Uni­versity of Rochester and the Uni­versity of Wis­con­sin were glad to have her teach; she could use lib­rar­ies and oth­er re­sources, and she was giv­en an of­fice and in­vited to sem­inars. Cer­tainly Mary El­len’s tal­ent and her ties to the Moore fam­ily helped, but if she had had no dir­ect con­nec­tion to these uni­versit­ies, it is un­likely that they would have giv­en her such a warm re­cep­tion. This kind of com­munity sup­port has been quite im­port­ant in sus­tain­ing her math­em­at­ic­ally.

The whole com­munity sup­port — fam­ily and oth­er math­em­aticians’ sup­port — are needed in or­der to be a math­em­atician. You may be able to get along without some of it, up to a point, but it cer­tainly makes it more prob­able that you will be an ef­fect­ive math­em­atician if you have it. It al­lows you to fo­cus on your math­em­at­ics prob­lems. If you look at the math­em­aticians from the nine­teenth cen­tury, like Grace Chisolm Young, Emmy No­eth­er, Sofia Ko­va­levskaia, they were people who had to com­pletely up­set the com­munity around them. They were strong enough to do it. But I’m sure there were in­fin­itely many more po­ten­tial math­em­aticians who would have been glad to pur­sue math­em­at­ics if they had the op­por­tun­ity to go to school, and so­cial ac­cept­ance for what they were do­ing. It was hard; I think none of them were really happy wo­men in some sense. Each of them had a cer­tain kind of sup­port, which per­haps was all they cared about. But their com­munity of sup­port was in the middle of a hos­tile en­vir­on­ment. It is help­ful if the en­vir­on­ment isn’t hos­tile.

Be­ing mar­ried to a math­em­atician had oth­er be­ne­fits as well. The Rud­ins could travel around the world to­geth­er to at­tend con­fer­ences, or give talks, and these trips were in­vari­ably both math­em­at­ic­ally stim­u­lat­ing and ex­cit­ing va­ca­tions. It was not un­usu­al for one of them to give a lec­ture in the morn­ing, and then be out on the beach in the af­ter­noon. The walls of their house are covered with pic­tures of the their trips to places such as Hawaii, New Zea­l­and, and China. They think of their col­leagues, friends, and stu­dents as their math­em­at­ic­al fam­ily — one that ex­tends across the globe.

Al­though be­ing mar­ried to Wal­ter helped cre­ate the kind of sup­port­ive en­vir­on­ment that Mary El­len points out is quite help­ful, she and Wal­ter do not ac­tu­ally do math­em­at­ics to­geth­er, or even talk with each oth­er about their res­ults. They are in dif­fer­ent fields, and have dif­fer­ent work styles. Nor do they feel the need to share that part of them­selves with each oth­er. “Every­body should have something [of their own]. I have plenty of things to share with people. I don’t have to share all of my math­em­at­ics with them, too.” In ad­di­tion, she and Wal­ter have very dif­fer­ent ways of think­ing about math­em­at­ics and work­ing on prob­lems. Mary El­len de­scribes her­self as a prob­lem solv­er rather than a the­ory build­er; it is a style that lends it­self to her field of to­po­logy. Wal­ter, on the oth­er hand, is more con­cerned with build­ing struc­tures, a skill that is par­tic­u­larly use­ful in his field of ana­lys­is.

Moreover, Mary El­len’s way of do­ing math­em­at­ics is highly in­di­vidu­al­ist­ic. She likes work­ing alone be­cause she thinks quite dif­fer­ently than most oth­er math­em­aticians she knows — she is very visu­ally ori­ented. As she says, she can­not fol­low a proof or an ar­gu­ment without pa­per and pen­cil in hand; she re­lies on pic­tures to help visu­al­ize an idea. “I don’t learn math­em­at­ics with my ears.” As a res­ult, there are very few col­leagues or stu­dents with whom she can sit down and do math­em­at­ics spon­tan­eously. More typ­ic­ally, a stu­dent will come in with a prob­lem, they will dis­cuss it briefly, she might make a sug­ges­tion or two, but then they go off and work on it sep­ar­ately. The next time they come to­geth­er, she will have a few more sug­ges­tions. Both her nat­ur­al style and her early train­ing con­trib­ute to her pref­er­ence for work­ing alone.

Iron­ic­ally, while Mary El­len is ac­cus­tomed to work­ing alone in one sense, she is of­ten far from alone in an­oth­er. It is not un­usu­al for her to work at home — not in a study with her door closed, but rather sit­ting on her couch in the middle of the liv­ing room, sur­roun­ded by chil­dren.12

It’s a very easy house to work in. It has a liv­ing room two stor­ies high, and everything else sort of opens in­to that. It ac­tu­ally suits the way I’ve al­ways handled the house­hold. I have nev­er minded do­ing math­em­at­ics ly­ing on the sofa in the middle of the liv­ing room with the chil­dren climb­ing all over me. I like to know, even when I am work­ing on math­em­at­ics, what is go­ing on. I like to be in the cen­ter of things, so the house lends it­self per­fectly to my math­em­at­ics…. I feel more com­fort­able and con­fid­ent when I’m in the middle of things, and to do math­em­at­ics you have to feel com­fort­able and con­fid­ent.

For some people, the dis­trac­tions of home make it im­possible to do cre­at­ive math­em­at­ic­al work. But Mary El­len has an amaz­ing abil­ity to work even in the midst of do­mest­ic activ­ity. Part of what en­ables her to do this is the grit and de­term­in­a­tion that are a nat­ur­al part of her work style. She is the kind of per­son who simply can­not let a prob­lem go once it has taken hold of her. She de­scribes what she does when she gets stuck on a prob­lem:

I am apt to hit it dir­ectly on the head, again and again and again and again. I find it very dif­fi­cult to give it up. I don’t try to find an easi­er prob­lem else­where. I know math­em­aticians who do that. Some people are very good at go­ing side­ways, or go­ing for a par­tial solu­tion, but I nev­er want to turn aside. I want to go for­ward and go for the gold. I struggle with my­self to put a prob­lem away, when I have looked at it a thou­sand times and drawn the same pic­ture a thou­sand times and got­ten no idea. But I find it very pain­ful to put something away. I can’t let go.

This kind of in­tense de­term­in­a­tion and fo­cus is ex­tremely use­ful in main­tain­ing the drive to do re­search even through the in­ev­it­able struggles and frus­tra­tion that arise in work­ing on math­em­at­ics.

Clearly, then, there were many factors that con­trib­uted to Mary El­len’s abil­ity to con­tin­ue as an act­ive re­search math­em­atician, even as she raised four chil­dren and cre­ated a home life. In the end, however, Mary El­len ar­gues that while all the ex­tern­al factors such as eco­nom­ics, do­mest­ic help, and com­munity and fam­ily sup­port are im­port­ant, they alone will not sus­tain you. You should do math­em­at­ics only “if you really want to, and only if you en­joy work­ing hard on hard prob­lems, and only if you find it tre­mend­ously sat­is­fy­ing to solve dif­fi­cult ques­tions.”

Is this a viable model today?

Some would ar­gue that while Mary El­len Rud­in’s situ­ation was in many ways ideal, it is no longer a vi­able op­tion for most wo­men en­ter­ing math­em­at­ics today. First, few fam­il­ies can sur­vive on one per­son’s in­come. The mod­el of the hus­band as bread­win­ner and wife as home­maker is no longer an eco­nom­ic pos­sib­il­ity for many fam­il­ies. Mary El­len’s ar­range­ment is even less an op­tion for wo­men who are single or self-sup­port­ing.

Second, many wo­men find it dif­fi­cult to be ac­cep­ted by the math­em­at­ics com­munity if they are not seen as pro­fes­sion­al. While the la­bel “am­a­teur” math­em­atician may have been an hon­or­able one when wo­men were not ex­pec­ted to do any­thing oth­er than do­mest­ic work, it is no longer a la­bel that would meet with such ac­cept­ance. Such a des­ig­na­tion would now have neg­at­ive con­nota­tions, and would make it dif­fi­cult, for ex­ample, to re­ceive grants, awards, jobs, and re­cog­ni­tion.

Third, it is not only how wo­men are per­ceived by their col­leagues that is at stake, it is also a mat­ter of how wo­men per­ceive them­selves in re­la­tion to their work. Wo­men are raised with the ex­pect­a­tion that they will be just like men in the com­mit­ment to their work — they ex­pect to have equal op­por­tun­it­ies and equal treat­ment. Hence, many wo­men would feel un­com­fort­able de­fin­ing them­selves as am­a­teurs. They see them­selves, and ex­pect to be seen, as pro­fes­sion­als.

Non­ethe­less, Mary El­len’s mod­el is an im­port­ant one, and should not be dis­missed too quickly as no longer rel­ev­ant. It is an ex­ample of a wo­man who was able to suc­cess­fully com­bine mar­riage, moth­er­hood, and math­em­at­ics. She was able to stay act­ive and pro­duct­ive as a re­search­er. She had four chil­dren and was act­ively in­volved in rais­ing them, and she did not feel that she had to deny the do­mest­ic side of her life. Per­haps most im­port­ant, she was very happy.

Is it pos­sible, there­fore, to modi­fy her mod­el to meet the needs of con­tem­por­ary wo­men, and in­creas­ingly of men as well? Is it not pos­sible, for ex­ample, for math­em­aticians to be part-time for cer­tain seg­ments of their ca­reer, and still be defined as pro­fes­sion­als? Is it ne­ces­sary to main­tain such a de­gree of sep­ar­a­tion between work and fam­ily in or­der to be taken ser­i­ously as a math­em­atician? Is it ne­ces­sary to re­leg­ate fam­ily to a less­er pri­or­ity in or­der to be defined as a real math­em­atician? Cer­tainly Mary El­len Rud­in sug­gests a dif­fer­ent way of look­ing at these ques­tions. She would ar­gue that main­tain­ing some con­nec­tion to re­search at all times, even when chil­dren are young, is very im­port­ant, but as her life il­lus­trates, there are many ways to do this.