# 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!