Celebratio Mathematica

Dusa McDuff

Some autobiographical notes

by Dusa McDuff

I grew up in a house in which cre­ativ­ity was very much val­ued but, des­pite the achieve­ments of the wo­men in the fam­ily, males were seen to be more truly cre­at­ive than fe­males and it has taken me a long time to find my own cre­at­ive voice. My life as a young math­em­atician was much harder than it needed to be be­cause I was so isol­ated. I had no role mod­els, and my first at­tempts at in­vent­ing a life style were not very suc­cess­ful. One im­port­ant way of com­bat­ing such isol­a­tion is to make both the achieve­ments of wo­man math­em­aticians and the dif­fer­ent ways in which we live more vis­ible. I’ll try to do my part by telling you something of my life.

I grew up in Ed­in­burgh, Scot­land, though my fam­ily was Eng­lish. My fath­er was a pro­fess­or of ge­net­ics who trav­elled all over the world and wrote books on philo­sophy and art as well as on de­vel­op­ment­al bio­logy and the uses of tech­no­logy. My moth­er was an ar­chi­tect, who was also very tal­en­ted, but who had to make do with a civil ser­vice job since that was the best po­s­i­tion which she could find in Ed­in­burgh. Her hav­ing a ca­reer was very un­usu­al: none of the oth­er fam­il­ies I knew had moth­ers with pro­fes­sion­al jobs of any kind. There were oth­er wo­men on my moth­er’s side of the fam­ily who led in­ter­est­ing and pro­duct­ive lives. I iden­ti­fied most with my ma­ter­nal grand­moth­er since I had her name: Dusa was a nick­name giv­en to her by H. G. Wells. She was most not­able for cre­at­ing a great scan­dal in the Lon­don of her time by run­ning away with H. G. (this was be­fore she mar­ried my grand­fath­er), but she later wrote books, on Con­fucian­ism for ex­ample, and was act­ive in left-wing polit­ics. Her moth­er (my great grand­moth­er) was also dis­tin­guished: in 1911 she wrote a book about the work­ing class poor in Lon­don which I was pleased to find be­ing used in Stony Brook as a text-book. In dis­cuss­ing the wo­men in my fam­ily I should also men­tion my sis­ter, who was the first West­ern an­thro­po­lo­gist al­lowed to go on a field trip to So­viet Cent­ral Asia, and is now a Fel­low of King’s Col­lege, Cam­bridge, with a lec­ture­ship at the uni­versity.

I went to a girls’ school and, al­though it was in­feri­or to the cor­res­pond­ing boys’ school, it for­tu­nately had a won­der­ful maths teach­er. I al­ways wanted to be a math­em­atician (apart from a time when I was el­ev­en when I wanted to be a farm­er’s wife), and as­sumed that I would have a ca­reer, but I had no idea how to go about it: I didn’t real­ise that the choices which one made about edu­ca­tion were im­port­ant and I had no idea that I might ex­per­i­ence real dif­fi­culties and con­flicts in re­con­cil­ing the de­mands of a ca­reer with life as a wo­man.

When, as a teen­ager, I be­came more aware of my fem­in­in­ity, I re­belled in­to do­mest­icity. I gladly star­ted cook­ing for my boy­friend; I stayed in Ed­in­burgh as an un­der­gradu­ate to be with him in­stead of tak­ing up my schol­ar­ship to Cam­bridge; and when I mar­ried I took his name. (My moth­er had kept her maid­en name for pro­fes­sion­al pur­poses.) I did even­tu­ally go to Cam­bridge as a gradu­ate stu­dent, this time fol­lowed by my hus­band. There I stud­ied func­tion­al ana­lys­is with G. A. Re­id and man­aged to solve a well-known prob­lem about von Neu­mann al­geb­ras, con­struct­ing in­fin­itely many dif­fer­ent factors of type “\( \mathrm{II}_1 \)”. This was pub­lished in the An­nals of Math­em­at­ics, and for a long time was my best work.

After this, I went to Mo­scow for six months since my hus­band had to vis­it the archives there. In Mo­scow, I had the great for­tune to study with Is­rael M. Gel’fand. This was not planned: it happened that his was the only name which came to mind when I had to fill out a form in the In­ot­del of­fice. The first thing that Gel’fand told me was that he was much more in­ter­ested in the fact that my hus­band was study­ing the Rus­si­an Sym­bol­ist poet In­nokenty Annensky than that I had found in­fin­itely many type \( \mathrm{II}_1 \) factors, but then he pro­ceeded to open my eyes to the world of math­em­at­ics. It was a won­der­ful edu­ca­tion, in which read­ing Pushkin’s Moz­art and Sa­lieri played as im­port­ant a role as learn­ing about Lie groups or read­ing Cartan and Ei­len­berg. Gel’fand amazed me by talk­ing of math­em­at­ics as though it were po­etry. He once said about a long pa­per brist­ling with for­mu­las that it con­tained the vague be­gin­nings of an idea which he could only hint at and which he had nev­er man­aged to bring out more clearly. I had al­ways thought of math­em­at­ics as be­ing much more straight­for­ward: a for­mula is a for­mula, and an al­gebra is an al­gebra, but Gel’fand found hedge­hogs lurk­ing in the rows of his spec­tral se­quences!

When I came back to Cam­bridge, I went to Frank Adams’s to­po­logy lec­tures, read the clas­sics of al­geb­ra­ic to­po­logy, and had a baby. At the time, al­most all the col­leges in Cam­bridge were for men only, and there was no pro­vi­sion at all for mar­ried stu­dents. I was very isol­ated, with no one to talk to, and found that after so much read­ing I had no idea how to be­gin to do re­search again. After my postdoc, I got a job at York Uni­versity. I was the fam­ily bread­win­ner and house­keep­er and di­aper changer (my hus­band said that di­apers were too geo­met­ric for him to man­age). At about this time I star­ted work­ing with Graeme Segal, and es­sen­tially wrote a second Ph.D. with him. As this was near­ing com­ple­tion, I re­ceived an in­vit­a­tion to spend a year at M.I.T. to fill a vis­it­ing slot which they had re­served for a wo­man. This was a turn­ing point. While there I real­ised how far away I was from be­ing the math­em­atician I felt that I could be, but also real­ised that I could do something about it. For the first time, I met some oth­er wo­men whom I could re­late to and who also were try­ing to be­come math­em­aticians. I be­came much less pass­ive: I ap­plied to the In­sti­tute for Ad­vanced Study and got in, and even had a math­em­at­ic­al idea again, which grew in­to a joint pa­per with Segal on the group-com­ple­tion the­or­em. When back home, I sep­ar­ated from my hus­band and, a little later, ob­tained a lec­ture­ship at War­wick. After two years at War­wick, I took an (un­ten­ured) as­sist­ant pro­fess­or­ship at Stony Brook, so that I could live closer to Jack Mil­nor in Prin­ceton. I went to Stony Brook sight un­seen. I knew no one there, and have al­ways thought my­self ex­tremely lucky to have landed in such a fine de­part­ment, al­though very fool­hardy to have giv­en up a ten­ured job for an un­ten­ured one.

After that, I had to do the work that every­one has to do to be­come an in­de­pend­ent math­em­atician, build­ing up on what one knows and fol­low­ing one’s ideas. I spent a long time work­ing on the re­la­tion between groups of dif­feo­morph­isms and the clas­si­fy­ing space for fo­li­ations: this grew out of my study of Gel’fand–Fuchs co­homo­logy in Mo­scow and my work with Segal on clas­si­fy­ing spaces of cat­egor­ies. I still worked very much in isol­a­tion and there are only a few people who are in­ter­ested in what I did, but it was a ne­ces­sary ap­pren­tice­ship. I had some ideas, and gained con­fid­ence in my tech­nic­al abil­it­ies. Of course, I was in­flu­enced by the clar­ity of Jack Mil­nor’s ideas and ap­proach to math­em­at­ics, and was helped by his en­cour­age­ment. I kept my job in Stony Brook, even though it meant a long com­mute to Prin­ceton and a week­end re­la­tion­ship, since it was very im­port­ant to me not to com­prom­ise on my job as my moth­er had done. After sev­er­al years, I mar­ried Jack and had a second child.

For the past eight years or so, I have worked in sym­plect­ic to­po­logy. Here again I have been very lucky. Just after I star­ted get­ting in­ter­ested in the sub­ject, it was re­vital­ised with new ideas from sev­er­al sources. Most im­port­ant to me was Mikhail Gro­mov’s work on el­lipt­ic meth­ods. I took ad­vant­age of a sab­bat­ic­al to spend the spring of 1985 at I.H.E.S. in Par­is so that I could learn about Gro­mov’s tech­niques, and the work I did then has been the found­a­tion of all my re­cent re­search. At the time, our child was a few months old. So I worked rather short days, but found it easy to cope since we had enough money to pay for good day care. Even­tu­ally he brought the fam­ily to­geth­er. We didn’t want to make him com­mute, and Jack did not like be­ing left with him for the best part of each week. So Jack took a job at Stony Brook, where we are now en­joy­ing life in one house. In con­clu­sion, I think that there is quite an ele­ment of luck in the fact that I have sur­vived as a math­em­atician. I also got real help from the fem­in­ist move­ment, both emo­tion­ally and prac­tic­ally. I think things are some­what easi­er now: there is at least a little more in­sti­tu­tion­al sup­port of the needs of wo­men and fam­il­ies, and there are more wo­men in math­em­at­ics so that one need not be so isol­ated. But I don’t think that all the prob­lems are solved.