# Celebratio Mathematica

## Dusa McDuff

### Interview with Dusa McDuff

#### by Donald J. Albers

Dusa Mc­Duff is a highly ac­com­plished math­em­atician who works in sym­plect­ic geo­metry, a re­l­at­ively re­cent and some­what eso­ter­ic branch of math­em­at­ics. She says, “Sym­plect­ic geo­metry is an even-di­men­sion­al geo­metry. It lives on even-di­men­sion­al spaces and meas­ures the sizes of two-di­men­sion­al ob­jects rather than the one-di­men­sion­al lengths and angles that are fa­mil­i­ar from Eu­c­lidean and Rieman­ni­an geo­metry.”

Mc­Duff claims that if it had not been for Miss Cob­ban, her high school math teach­er who taught her geo­metry and cal­cu­lus, she might not have be­come a math­em­atician. She did know that she had to do something to im­press her fath­er, a ge­net­i­cist and de­vel­op­ment­al bio­lo­gist, and ful­fill the am­bi­tion of her moth­er. She also felt that she needed to live up to her grand­moth­er, Am­ber, who as “Dusa” had a scan­dal­ous af­fair with the fam­ous au­thor H. G. Wells.

Her math­em­at­ic­al suc­cess is shown both by her elec­tion in 1994 as a Fel­low of the Roy­al So­ci­ety of Lon­don, the second fe­male math­em­atician to be so honored after Dame Mary Cartwright’s elec­tion al­most fifty years earli­er, and also by her later elec­tions to mem­ber­ships in the Na­tion­al Academy of Sci­ences (U.S.) and the Amer­ic­an Academy of Arts and Sci­ences. She now holds an en­dowed pro­fess­or­ship at Barn­ard Col­lege, a col­lege of Columbia Uni­versity.

Her PhD thes­is in func­tion­al ana­lys­is from Cam­bridge Uni­versity was pub­lished in the An­nals of Math­em­at­ics, one of the most pres­ti­gi­ous math­em­at­ics journ­als in the world, a rare event for any doc­tor­al thes­is. A short time later she went to Mo­scow where she came un­der the in­flu­ence of the fam­ous math­em­atician I. M. Gel­fand. Over the next six months she learned much from him and re­turned to Cam­bridge de­term­ined to work in a new field. In the in­ter­view that fol­lows, Mc­Duff de­scribes the dif­fi­culties in shift­ing fields, in­clud­ing the spe­cial prob­lems that a wo­man en­coun­ters in suc­ceed­ing as a math­em­atician.

MP: Thanks very much, Dusa, for meet­ing in your MSRI [Math­em­at­ic­al Sci­ences Re­search In­sti­tute] of­fice today to chat about your­self and how you be­came a math­em­atician. Let’s start at the be­gin­ning. I un­der­stand you were born in Oc­to­ber of 1945 in Lon­don, and moved to Scot­land when you were a child.

Mc­Duff: Yes. My fath­er, Con­rad Hal (Wad) Wad­ding­ton, got a pro­fess­or­ship at the Uni­versity of Ed­in­burgh in 1947 when I was two. A ge­net­i­cist and de­vel­op­ment­al bio­lo­gist, he worked dur­ing World War II in Patrick Black­ett’s lab de­vis­ing strategies to de­fend against U-boat at­tacks. He told me that this group star­ted the field of op­er­a­tions re­search but couldn’t pub­lish un­til the 1970s be­cause of secrecy laws. When the war ended he traveled ex­tens­ively on war-re­lated work. De­mo­bil­ized in 1947, he took up his po­s­i­tion at Ed­in­burgh as Dir­ect­or of the In­sti­tute of An­im­al Ge­net­ics.

#### Mortonhall — an amazing house

After the war, there was a ser­i­ous hous­ing short­age in Bri­tain. My fath­er’s solu­tion was for every­one con­nec­ted with his lab to live to­geth­er. We moved in­to Mor­ton­hall, a large stone man­sion on the out­skirts of Ed­in­burgh, whose grounds had statues, clipped yew hedges, a large walled kit­chen garden, and stables. The stables had no horses, but I re­mem­ber col­lect­ing the chick­en eggs. Al­though people lived in sep­ar­ate flats and rooms, we ate com­mun­ally, with one din­ing room for the grownups and one for the chil­dren. Ra­tions were shared. Much of the work of the house was done by a house­hold staff that (at least in the later years when I got to know them) in­cluded many dis­placed people from coun­tries like Es­to­nia and Latvia. My fath­er set up the house­hold at Mor­ton­hall al­most as a so­cial ex­per­i­ment; my moth­er, trained as a town plan­ner, was al­ways very in­ter­ested in the in­flu­ence of ar­chi­tec­ture on com­munit­ies.

Al­though these ar­range­ments suited our fam­ily very well since my moth­er worked full time as an ar­chi­tect in the Scot­tish Civil Ser­vice, they made some of the oth­er wives rather un­happy. There were many oth­er ten­sions in Mor­ton­hall. It was dif­fer­ent for the kids, but for the grownups, it was not ne­ces­sar­ily so easy to live that way, partly be­cause there was no es­cape from the lab but partly also be­cause life in Bri­tain at that time was very aus­tere. There was little food, and houses were cold be­cause of lack of fuel. Chil­dren got ra­tioned or­ange juice and milk and oth­er things like cod liv­er oil, but grownups didn’t.

#### Squabbles over porridge

Edith Si­mon, one of the wives, wrote a nov­el about life in Mor­ton­hall called The House of Strangers. One of the few things in it that rang ab­so­lutely true was stor­ies of the grownups at the break­fast table squab­bling over the por­ridge. There was a por­ridge ro­ta­tion and sci­ent­ists are not ne­ces­sar­ily good cooks. They took the pre­cious oat­meal and made por­ridge that was lumpy, or weak, or burnt, or too salty. Then they had to share their mea­ger but­ter and sug­ar ra­tions and would look to see ex­actly how much their neigh­bor took. It was dif­fi­cult.

MP: It sounds that way.

Mc­Duff: But it was won­der­ful for the kids.

MP: How many kids were in the house?

Mc­Duff: Well, count­ing my­self and my sis­ter Car­rie — I guess six or eight. My moth­er worked from nine to six every day and a half-day on Sat­urday, and couldn’t come home at lunch­time be­cause her job was so far away. My sis­ter and I went to nurs­ery school and had Ir­ish nan­nies. But for a lot of the time we were run­ning around in gangs out­side with very little su­per­vi­sion, able to do what we wanted — climb­ing trees, play­ing hide and seek. I also re­mem­ber talk­ing to the cook in her enorm­ous old fash­ioned kit­chen, the boil­er man as he stoked the base­ment fur­nace, and the garden­er work­ing in the kit­chen garden.

MP: It cer­tainly sounds like a mem­or­able child­hood ex­per­i­ence.

Mc­Duff: Yes.

MP: How long did that last?

Mc­Duff: Five years.

MP: That’s a big chunk of one’s life at that stage. You moved there when you were two.

Mc­Duff: Yes. At that time it was un­usu­al for young chil­dren to go to nurs­ery school.

#### Early interest in math and grandfather’s influence

My moth­er, who cared deeply about our edu­ca­tion, chose a very pro­gress­ive school run by the Par­ent’s Na­tion­al Edu­ca­tion­al Uni­on (PNEU). I used to love school, es­pe­cially do­ing math. I was al­lowed to do whatever math I wanted. By the time I was sev­en, I was way ahead of the oth­ers.

MP: In one of your writ­ings, you men­tion the in­flu­ence of your grand­fath­er on your math­em­at­ic­al de­vel­op­ment. You said that he had done math be­fore turn­ing to the law.

Mc­Duff: My grand­fath­er G. R. (Rivers) Blanco White was the Second Wran­gler at Cam­bridge (i.e., he placed second in his class) in 1904 and even­tu­ally be­came a di­vorce court judge. A private in the First World War, he served in the ar­til­lery, us­ing his math­em­at­ic­al know­ledge to cal­cu­late tra­ject­or­ies.

MP: So, he in­flu­enced you when you were quite young.

Mc­Duff: I met him once when I was four and then again when I was about el­ev­en. We were not a close fam­ily. So, this vis­it when I was about four was very spe­cial. I re­mem­ber him show­ing me the mul­ti­plic­a­tion tables.

MP: Were your math­em­at­ic­al in­terests ap­par­ent be­fore he told you about mul­ti­plic­a­tion tables?

Mc­Duff: Prob­ably. Since I liked math, I cer­tainly knew how to add and mul­tiply. But I had nev­er seen a full ten by ten mul­ti­plic­a­tion table be­fore he showed it to me, ex­plain­ing its vari­ous sym­met­ries and pat­terns, how if you look down the nines column, the num­bers change reg­u­larly, one di­git go­ing up each time and the oth­er go­ing down. He showed me its beauty.

MP: You said that a nice as­pect of the school was that you were able to do as much math as you wanted. Do you re­call what it was about math that was so at­tract­ive to you when you were little?

Mc­Duff: I just loved math­em­at­ics, I don’t really know why. My moth­er was good at math (Rivers was her fath­er), and she was al­ways eager to en­cour­age us in­tel­lec­tu­ally. She told me once that she was thrilled when my “first word” was two words with two ideas. I was a bit pre­co­cious and quick at do­ing some things. I liked the way my sums came out cor­rect. I re­mem­ber do­ing an en­trance ex­am when I was six to get in­to a prop­er school. They asked me to add two and three, or something like that. I said, “This is far too easy.” I did a sum with four di­gits, and all the teach­ers gathered round as­ton­ished.

MP: So, your in­terest in math­em­at­ics was early and strong, and it’s nev­er abated.

Mc­Duff: I’ve had oth­er in­terests. I al­ways wanted to be a math­em­atician (apart from a time when I was el­ev­en and wanted to be a farm­er’s wife) and as­sumed that I would have a ca­reer. Luck­ily I had a very good math teach­er in my high school. I went to the same girls’ school from sev­en to six­teen, the best my par­ents could find in Ed­in­burgh. I des­pised the sci­ence teach­ers be­cause they could not an­swer my ques­tions, but I re­spec­ted the math teach­er Miss Cob­ban; she taught me Eu­c­lid and cal­cu­lus. Oth­er­wise, I don’t know wheth­er I would have be­come a math­em­atician.

MP: What ca­reers did your sib­lings pur­sue?

Mc­Duff: My sis­ter Car­oline Humphrey is Pro­fess­or of So­cial An­thro­po­logy at Cam­bridge Uni­versity and a fel­low of King’s Col­lege. My half-broth­er, Jake Wad­ding­ton, whom I hardly knew while I was grow­ing up, is an as­tro­phys­i­cist.

#### Father thought mathematics was boring

MP: You said that your fam­ily very much val­ued cre­ativ­ity, and yet you al­ways felt that in their view the really cre­at­ive people were males.

Mc­Duff: My par­ents would nev­er have said that ex­pli­citly. Un­usu­ally for the time, I was brought up to think I would have a ca­reer and that wo­men could do just what men do. But my moth­er had also sub­or­din­ated her ca­reer in­terests to those of my fath­er, jus­ti­fy­ing that by the fact of his bril­liance and the needs of her fam­ily. When I be­came a teen­ager, about fif­teen or so, I felt that the kind of in­tel­li­gence I had did not count for much, and what was really cre­at­ive was a more artist­ic kind of tal­ent. I might be very good at reas­on­ing, but that was ul­ti­mately not im­port­ant.

I had some artist­ic in­terests; I played the cello, and I loved read­ing. My boy­friend at the time, Dav­id Mc­Duff, who be­came my first hus­band, was a poet and lin­guist. (He knows an as­ton­ish­ing vari­ety of lan­guages, in­clud­ing Rus­si­an, Finnish, Iceland­ic, and the com­puter lan­guage C++.) We met through mu­sic. I thought that he had a bril­liant, cre­at­ive mind, while I didn’t see my­self as cre­at­ive. For ex­ample, al­though I was quite good at paint­ing as a girl and now get great pleas­ure from go­ing to art gal­ler­ies, my sis­ter was much bet­ter at paint­ing than I was, with a won­der­ful sense of design and col­or. Al­though some people sug­ges­ted that I study to be a cel­list, I de­cided not to be­cause I felt I had more tal­ent as a math­em­atician.

MP: So, al­though you had these strong math­em­at­ic­al in­terests and were do­ing very well at it, there was no ap­par­ent feel­ing by your moth­er and fath­er that math­em­at­ics was a par­tic­u­larly cre­at­ive area?

Mc­Duff: My fath­er didn’t like math­em­at­ics; he thought it was very dry. When I was thir­teen, we had many con­ver­sa­tions about the book he was writ­ing called The Eth­ic­al An­im­al, about the de­vel­op­ment of the mor­al sense in hu­mans through evol­u­tion­ary pro­cesses. He gave me philo­sophy to read, along with The Voy­age of the Beagle and Freud, greatly broad­en­ing my out­look. He prided him­self on be­ing a sci­ent­ist, a philo­soph­er, and an artist. He wrote a book about mod­ern paint­ing, Be­hind Ap­pear­ance, that even today some people find worth­while. He knew Al­fred North White­head and Ber­trand Rus­sell from Cam­bridge in the 1930s, but knew Rus­sell as a philo­soph­er, not as a math­em­atician. His at­ti­tude about math­em­at­ics was that it was bor­ing — though in his later years he was very in­ter­ested in de­vel­op­ing a the­or­et­ic­al ap­proach to bio­logy and was open to the im­port­ance of math­em­at­ics in that con­nec­tion.

My moth­er was an ar­chi­tect. For her, the artist­ic side of it came through design. She was pas­sion­ate about re­search and pure thought (math­em­at­ics did qual­i­fy there!), but she didn’t know enough about math­em­at­ics to em­phas­ize its cre­ativ­ity. I first got to know people who I thought were truly cre­at­ive math­em­aticians when I went to Mo­scow in my third year as a gradu­ate stu­dent. I dis­covered there that math­em­at­ics could grow and de­vel­op. Be­fore I had seen its com­pel­ling beauty, but it was some­how stat­ic; I was un­aware of how it was cre­ated.

#### “I had to do something to impress my father”

MP: When you were at Cam­bridge, you wrote a thes­is that ended up be­ing pub­lished in the “An­nals of Math­em­at­ics”. That isn’t chopped liv­er, as some would say.

Mc­Duff: Right.

MP: It got a fair amount of at­ten­tion in the math­em­at­ic­al com­munity.

Mc­Duff: I wasn’t so aware of that be­cause I changed fields so quickly.

MP: You must have felt very good about it at that time.

Mc­Duff: Yes, but I was totally di­vided. I was deeply in love with Dav­id, a poet, and he was math-phobic. I had a sep­ar­ate life as a math­em­atician, with no math­em­at­ic­al friends. When I was an un­der­gradu­ate at Ed­in­burgh, I didn’t talk to any of the oth­er stu­dents. I didn’t know any of them, ex­cept I re­mem­ber play­ing bridge with them one af­ter­noon.

My only friends, and I had very few, were through Dav­id, and they talked about po­etry, art, and polit­ics. I was learn­ing Rus­si­an and Ger­man to keep up. When I was little, every­body thought I was bril­liant; I got a lot of at­ten­tion for al­ways com­ing out top on ex­ams and that kind of thing. At some point, I de­cided that was ir­rel­ev­ant, and I turned my back on it, try­ing to live a dif­fer­ent life. For one thing, I had to do something that would im­press my fath­er, and math­em­at­ics was not it.

#### “I had to live up to my grandmother Dusa”

Mc­Duff: For an­oth­er thing, I had to live up to my grand­moth­er Dusa. I don’t know if you are aware of that as­pect of the story.

MP: Well, you did men­tion in one of the art­icles that you have writ­ten that she was ap­par­ently very col­or­ful and that she had a long, some­what sen­sa­tion­al af­fair with H. G. Wells. She bore a daugh­ter, Anna-Jane, by him. Wells was a well-known writer then, and cer­tainly his fame per­sists. Ap­par­ently Dusa was the name that Wells gave her.

Mc­Duff: The story that my moth­er told me was that he gave her that nick­name be­cause of her long black snaky hair. Then, later, I read about her in H. G. Wells’ own book, H.G. Wells in Love: Post­script to an Ex­per­i­ment in Auto­bi­o­graphy, a book about all the wo­men with whom he had ser­i­ous af­fairs. One of the chapters is about my grand­moth­er, Am­ber Pem­ber Reeves. (She was the mod­el for his very ap­peal­ing “new wo­man” heroine Ann Veron­ica.) Her fath­er, Pem­ber Reeves, was the Gov­ernor Gen­er­al of New Zea­l­and and then the first dir­ect­or of the Lon­don School of Eco­nom­ics. Wells said that Dusa was her private name for her­self, chosen be­cause she was fas­cin­ated by the im­age of the Me­dusa head held by Perseus in Bern­ini’s bronze statue. I much prefer that ver­sion of the story.

Wherever the name came from, it is some­what puzz­ling. As far as I knew, the name Dusa meant a ter­ri­fy­ing mon­ster that rendered oth­ers power­less. Re­cently, I dis­covered that in Tur­key she is a guard­i­an fig­ure, her head of­ten por­trayed on Athena’s shield; in pre­his­tory she must have been an earth god­dess be­cause Me­dusa is the fem­in­ine form of the name Medon which means ruler. My moth­er nev­er told me about those as­pects of the name.

MP: It’s cer­tainly a dis­tinct­ive name.

Mc­Duff: I felt I had to live up to it. Be­ing called after Me­dusa made me feel unique. The oth­er school­girls made fun of me, pre­tend­ing that, like the myth­ic char­ac­ter, I would turn people to stone if they looked at me. And then, as I real­ized much later, I thought I had to do the equi­val­ent of run­ning off with H. G. Wells: I would not be able to hold my head up if I didn’t.

MP: I have read a bit about your grand­moth­er in “Shad­ow Lov­ers” by An­drea Lynn. She por­trays her as a pro­gress­ive fem­in­ist and im­port­ant au­thor of books on so­cial is­sues, whose ad­mir­a­tion for Wells con­tin­ued for more than thirty years after their af­fair com­menced in 1907. She quotes from a let­ter that she wrote to him in 1939: “What you gave to me all those years ago — a love that seemed per­fect to me, the in­flu­ence of your mind, and Anna-Jane — have stood by me ever since. I have nev­er for a mo­ment felt that they were not worth the price.” I’m be­gin­ning to un­der­stand why you hold her in such high re­gard.

Mc­Duff: At that time, the early 1900s, wo­men were only be­gin­ning to have ca­reers, and it was very hard to have both a fam­ily and a ca­reer. You had to choose. She had a job in the First World War in the Min­istry of La­bour pro­mot­ing wo­men’s em­ploy­ment but had to leave it at the end of the war. She then wrote some nov­els and a book on eco­nom­ics for the Left Book Club as well as help­ing her hus­band “nurse” a con­stitu­ency for the La­bour party (i.e., stand for Par­lia­ment in a hope­less seat). After more war work dur­ing the Second World War, she be­came in­ter­im pres­id­ent of Mor­ley Col­lege (part of Lon­don Uni­versity for adult edu­ca­tion) for a short while un­til an un­mar­ried wo­man could take it over. She served there as Tu­tori­al Lec­turer in Mor­al Sci­ence for many years, giv­ing even­ing courses in psy­cho­logy and writ­ing a book Eth­ics for Un­be­liev­ers that used Freu­di­an prin­ciples to ar­gue for a kind of Con­fucian re­straint. Des­pite all this ac­com­plish­ment (much of which I learnt about later), my fam­ily’s at­ti­tude was that she had not lived up to her po­ten­tial.

MP: Did you ever meet her?

Mc­Duff: Oh yes. I met her sev­er­al times, not very of­ten when I was small, but when I was a teen­ager, I spent a few days in her house. We talked quite a bit then, and we also cor­res­pon­ded for a long while.

MP: What do you re­mem­ber of your per­son­al in­ter­ac­tions with her?

Mc­Duff: My grand­moth­er liked telling slightly risqué stor­ies about the people she knew. She was very good at that! She spoke in in­cred­ibly com­plic­ated well-formed sen­tences of the kind nobody uses now. She knew Lloyd George, Be­atrice and Sydney Webb, and many oth­er politi­cians and so­cial­ists. She once told me a story about Be­atrice Webb get­ting a bee in her blouse at some garden party, which made her lose her poise. Be­atrice was known to be so very cor­rect.

We also talked about what I was do­ing. She liked me. I re­mem­ber one day as I left the room I heard her mut­ter “she’s my fa­vor­ite grand­daugh­ter.” She wouldn’t tell me that to my face. I really en­joyed my re­la­tion­ship with her. I wrote to her, and she reg­u­larly wrote back. As she got older, my moth­er wrote a let­ter to her every week.

MP: Wow. A let­ter a week!

Mc­Duff: People did write let­ters in those days. The tele­phone ex­is­ted, ob­vi­ously, but we used it for prac­tic­al things. We nev­er tele­phoned each oth­er to chat; we wrote let­ters.

MP: I’m con­vinced that your grand­moth­er was a rare per­son. You said that you very much wanted to live up to her. Do you feel you have?

Mc­Duff: Yes, I think so. I cer­tainly have done the best that I could.

#### Mother’s career frustrations

Mc­Duff: I knew that my moth­er al­ways felt frus­trated in her ca­reer. She had great am­bi­tion. In her mind, I had to ig­nore the fact that I was a wo­man and just suc­ceed in my ca­reer. She was taken aback when I had my first boy­friend, Dav­id, be­cause she thought that would be a hindrance.

MP: When your moth­er said that you had to ig­nore the fact that you were a wo­man, was she sug­gest­ing that it was bet­ter to be a man?

Mc­Duff: On my moth­er’s side, I come from a line of strong wo­men, start­ing with my great-grand­moth­er Maud Pem­ber Reeves, who wrote a pi­on­eer­ing book Round About a Pound a Week on the Lon­don poor. Nev­er­the­less, there was def­in­itely a feel­ing in my fam­ily that men were more im­port­ant. When I had my daugh­ter, Anna, the very first thing my moth­er said when I told her was, “Oh, what a pity it’s not a boy!” She thought that boys were bet­ter than girls. My grand­moth­er didn’t have a prop­er ca­reer, and my moth­er didn’t have a full ca­reer, though they were both in­cred­ibly tal­en­ted people. They didn’t do as much as they could have if they had been men. So, there was def­in­itely a feel­ing that to be a wo­man was to be in­feri­or. My de­sire not to be second, to­geth­er with the fact that it is easi­er to earn a liv­ing as a math­em­atician than as a poet, was why I made the liv­ing dur­ing my mar­riage with Dav­id; but it did make things dif­fi­cult, be­cause then I had to do everything. In some ways very self-con­fid­ent, I also had many feel­ings of in­feri­or­ity that took a long time to over­come. There are many con­tra­dic­tions.

MP: Earli­er you said your par­ents greatly em­braced and ap­proved of cre­ativ­ity, and cer­tainly po­ets are thought to be quite cre­at­ive. And you re­ferred to Dav­id as be­ing a truly bril­liant and cre­at­ive per­son.

Mc­Duff: In­deed, in­deed, but even so, people are full of con­tra­dic­tions.

MP: Okay, fair enough. So, she wasn’t that pleased with him. Was your fath­er happy with him?

Mc­Duff: My fath­er didn’t pay much at­ten­tion. He was off in his own world. Any­way, part of the point of try­ing to live up to my grand­moth­er was to do things that my par­ents wouldn’t ap­prove of. You have to un­der­stand that my grand­moth­er didn’t be­have as the people around her thought she should.

I grew up in the 1960s. In the sum­mer of 1961 I was home alone dur­ing the week of the Ber­lin Wall crisis, and I really be­lieved that a nuc­le­ar war would an­ni­hil­ate every­one in a few days. So I joined the Cam­paign for Nuc­le­ar Dis­arm­a­ment. From then on, I too was not will­ing to be or do everything that people ex­pec­ted of me.

MP: You have spoken about the im­port­ance of get­ting your fath­er’s ap­prov­al. Did he live long enough to see you achieve pro­fes­sion­ally at very high levels?

Mc­Duff: Yes, he did. He died in 1975 when I was a lec­turer at York. I heard in­dir­ectly that he was very proud of me, at his fu­ner­al from a close friend of his. As far as I know, his ba­sic at­ti­tude about math­em­at­ics was still that it is too dry, but he was much more open to its value as a lan­guage for sci­ence. To­wards the end of his life, very in­ter­ested in sus­tain­ab­il­ity and en­vir­on­ment­al is­sues, he wrote a book and de­veloped an un­der­gradu­ate course on Tools for Thought, how to un­der­stand sci­entif­ic tech­niques of prob­lem solv­ing. He also or­gan­ized sev­er­al meet­ings on the theme “To­wards a The­or­et­ic­al Bio­logy” to­geth­er with math­em­aticians such as Chris­toph­er Zee­man and René Thom. But by that time I was un­der the in­flu­ence of Gel­fand, who thought that Thom’s ap­proach was shal­low, so my fath­er and I did not even con­nect on that.

MP: Well, it would have taken a bit of time be­fore he would have reached a point where he could un­der­stand what you had ac­tu­ally done.

Mc­Duff: I re­mem­ber one time try­ing to ex­plain to my moth­er what I had done. This was when I was a gradu­ate stu­dent and I’d had my first idea, prov­ing my first the­or­em. Des­pite her will­ing­ness to listen and un­der­stand, she lost the thread of the ideas as I was go­ing through all the needed defin­i­tions — I re­mem­ber we got lost when we got to “group.” It was im­possible for her to un­der­stand at the level she wanted to without years of train­ing.

MP: Let’s get back to your un­der­gradu­ate years at Ed­in­burgh. You said that the stu­dents who were do­ing math­em­at­ics there didn’t seem to be in­ter­ested in what you really re­garded as math­em­at­ics. Were they es­pe­cially util­it­ari­an in their out­look?

Mc­Duff: You have to un­der­stand that I was, you would say, a dread­ful snob. I just didn’t talk to them, so I don’t know what they were in­ter­ested in. On the oth­er hand, we did have a few re­cit­a­tions to­geth­er, and if there had been some­body else who was really in­volved in the classes, then it’s con­ceiv­able I would have talked to them.

MP: They didn’t strike you as in­ter­est­ing.

Mc­Duff: They didn’t strike me as in­ter­est­ing, and that says a lot about me as well as a lot about them.

MP: You are re­fer­ring to stu­dents at Ed­in­burgh. What about Cam­bridge stu­dents?

Mc­Duff: I wasn’t at Cam­bridge for my un­der­gradu­ate work. I won a schol­ar­ship to Cam­bridge, but I didn’t go there. I went to the Uni­versity of Ed­in­burgh be­cause that’s where Dav­id was.

MP: But then you went on to Cam­bridge for gradu­ate work.

Mc­Duff: Yes. As a gradu­ate stu­dent, I did talk to some of the oth­ers, but gradu­ate school in Bri­tain is very dif­fer­ent from what it is in Amer­ica. Much more spe­cial­ized, stu­dents have only three years, though usu­ally with no teach­ing du­ties. Be­cause I had dis­tin­guished my­self at Ed­in­burgh, I was ex­cused from part three of the Cam­bridge Tri­pos.

The Tri­pos is roughly the equi­val­ent of a mas­ter’s de­gree; one takes six lec­ture courses in dif­fer­ent sub­jects, with fi­nal ex­ams at the end of the year. If I had done that, then pre­sum­ably I would have got­ten to know both more math­em­at­ics and more stu­dents. In­stead I im­me­di­ately star­ted work­ing with my ad­visor G. A. Re­id on my dis­ser­ta­tion top­ic, in­ter­act­ing only with the small group of stu­dents in func­tion­al ana­lys­is, none of whom were work­ing on ex­actly the same sub­ject as I was. After my first semester in Cam­bridge, I mar­ried Dav­id, who then came to join me. My life out­side math­em­at­ics was with him, which cut me off from the oth­er stu­dents.

Also, I still was not talk­ing to people. For ex­ample, John Con­way was there. He was this idio­syn­crat­ic per­son who wore no shoes, had six kids…. nev­er talked to him. One end of the Com­mon Room was full of his games, which now I think are fun, but in those days I didn’t want to be in­volved. I was ter­ribly ser­i­ous, see­ing math­em­at­ics as a very high, ab­stract, artist­ic en­deavor; games were not part of it.

#### An encounter with I. M. Gelfand

MP: After two years at Cam­bridge, you went off to Mo­scow for six months.

Mc­Duff: Right.

MP: You ended up work­ing un­der Gel­fand be­cause his was the only name that was fa­mil­i­ar to you be­fore you went there. Is that right?

Mc­Duff: More or less. I hadn’t thought that I had to study with any­body. My ad­visor had not asked: “Well, do you know what you want to do when you get there?” I just hadn’t thought about it; I was very na­ive in many ways. But luck­ily, when they asked me in the stu­dent of­fice at Mo­scow Uni­versity who I wanted as my ad­visor, I said Gel­fand, and that turned out to be great.

MP: Good choice.

Mc­Duff: His was the first name that came to mind, prob­ably be­cause I had writ­ten my un­der­gradu­ate pro­ject on his book on dis­tri­bu­tions.

MP: Tell us about get­ting to know him and the im­pact that he had on you.

Mc­Duff: When I first met him, he asked what I was do­ing, why I was there, and then said that he was much more in­ter­ested in the fact that my hus­band Dav­id was writ­ing a thes­is about the Rus­si­an sym­bol­ist poet In­nokenty Annensky than that I had solved this prob­lem about von Neu­mann al­geb­ras. Nev­er­the­less, he then tried to fig­ure out what he could teach me.

Gel­fand amazed me by talk­ing of math­em­at­ics as if it were po­etry. He tried to ex­plain to me what von Neu­mann had been try­ing to do and what the ideas were be­hind his work. That was a rev­el­a­tion for me — that one could talk about math­em­at­ics that way. It is not just some ab­stract and beau­ti­ful con­struc­tion but is driv­en by the at­tempt to un­der­stand cer­tain ba­sic phe­nom­ena that one tries to cap­ture in some idea or the­ory. If you can’t quite ex­press it one way, you try an­oth­er. If that doesn’t quite work, you try to get fur­ther by some com­pletely dif­fer­ent ap­proach. There is a whole un­der­cur­rent of ideas and ques­tions.

MP: What is the single biggest thing that he gave you? He was clearly a very in­spir­a­tion­al per­son for you.

Mc­Duff: He was the first per­son I had met who saw math­em­at­ics in the way that I ima­gined it. At that point, mar­ried to a poet, I was very ideal­ist­ic. I saw math­em­at­ics with its ab­stract beauty as one way of ex­press­ing hu­man thought and cre­ativ­ity. Gel­fand also saw math­em­at­ics as part of everything else. Wheth­er he was read­ing books to me, or we were listen­ing to mu­sic, for him, that was do­ing math­em­at­ics. At that time in Rus­sia, there were so few out­lets for people’s cre­ativ­ity that many people be­came math­em­aticians who in the West would prob­ably have done oth­er things. We think that math­em­at­ic­al tal­ent is something very spe­cial, pos­sessed by only a few. But many dif­fer­ent kinds of minds can con­trib­ute to math­em­at­ics, and they did so in Rus­sia. That’s one reas­on it was such a vi­brant and broad math­em­at­ic­al cul­ture. In ad­di­tion he used so much math­em­at­ics, while I knew noth­ing. He gave me his re­cent pa­per to read, “Co­homo­logy of the Lie Al­gebra of Vec­tor Fields on a Man­i­fold.” I had been so nar­rowly edu­cated that I didn’t know what co­homo­logy was, what a Lie al­gebra was, what a vec­tor field was, or what a man­i­fold was.

MP: So, he in­spired you to learn a lot of new math­em­at­ics.

Mc­Duff: Yes, he opened my eyes to many things, but I was only in Rus­sia for six months.

MP: A very im­port­ant six months. It sounds as if he spent a lot of time with you.

Mc­Duff: Be­ing a young and very in­ex­per­i­enced math­em­atician from the West, I was a com­plete nov­elty. There were very few vis­it­ors from the West in those days, and Gel­fand was eager to prac­tice his Eng­lish. He tried to help me find a way for­ward, sug­gest­ing many things for me to read. He once said to­ward the end of my time in Mo­scow, when I’d re­ex­pressed one of his res­ults in the lan­guage of sheaves that I was just learn­ing: “Oh, you’re quick.” He real­ized that I could do some math­em­at­ics and gave me a let­ter of re­com­mend­a­tion to help me in the fu­ture. He gave me a vis­ion and he spent time with me. He ob­vi­ously thought I was worth­while, which was very en­cour­aging.

Gel­fand cared deeply about edu­ca­tion. In Rus­sia tal­en­ted young Jew­ish people couldn’t get the edu­ca­tion they wanted and were largely shut out of the uni­versity sys­tem. He found ways to bring math­em­at­ics to them, for ex­ample through even­ing schools that he set up.

MP: He also wrote some very ele­ment­ary and in­nov­at­ive books on al­gebra and tri­go­no­metry.

Mc­Duff: He grew up in the provinces, ex­cluded be­cause he was Jew­ish and poor. He de­voted con­sid­er­able en­ergy to cre­at­ing op­por­tun­it­ies for tal­en­ted young people, in­vit­ing them to his sem­in­ar and try­ing to make the ideas ac­cess­ible.

#### Changing fields — not easy

MP: After those six months in Rus­sia, had your math­em­at­ic­al in­terests shif­ted?

Mc­Duff: When I came back to Cam­bridge, I was work­ing in a com­pletely dif­fer­ent field.

MP: That falls in­to what some people in sports would call the guts ball cat­egory — shift­ing fields. At that point you had done work, very good work, in func­tion­al ana­lys­is.

Mc­Duff: But I didn’t know where to go with it. If I had gone to France and talked to someone like Dixmi­er, I might have found out what my work in func­tion­al ana­lys­is was re­lated to and where it might lead; but my thes­is ad­visor didn’t really know. I had no clue, and Gel­fand was in­ter­ested in oth­er things. So, what was I to do but try an­oth­er area of math­em­at­ics? It wasn’t easy; I was start­ing again and didn’t really have a frame­work. Gel­fand sug­ges­ted that I work with Frank Adams, but Adams was just in the pro­cess of mov­ing to Cam­bridge and didn’t know any­thing about me. He sug­ges­ted to me that I study al­geb­ra­ic K-the­ory, which I did, but it didn’t help me get my foot­ing in this new field.

After sub­mit­ting my PhD upon my re­turn from Rus­sia, I spent two more years in Cam­bridge as a Sci­ence Re­search Coun­cil postdoc, ba­sic­ally learn­ing on my own ex­cept that I talked to some to­po­lo­gists. I took a course on four-man­i­fold to­po­logy from Cas­son, went to won­der­ful lec­ture courses by Adams on Quil­len’s work on ho­mo­topy groups of spheres, and read a vari­ety of books: Mil­nor on Morse the­ory; Lang and Serre on num­ber the­ory. At that stage, I was still learn­ing pass­ively, not work­ing on any prob­lems.

Since I had no du­ties, Dav­id and I were able to spend sev­er­al months each spring in my par­ents’ place in Tuscany. This was a peas­ant cot­tage, built of stone with no run­ning wa­ter or elec­tri­city, in the middle of an olive grove owned by Aleksander Zyw, a paint­er friend of the fam­ily. We spent idyll­ic months there. After each day’s work, we would walk up the hill to drink wine with Aleksander and his Scot­tish wife Leslie and talk about paint­ing, olive trees, and life in gen­er­al.

Back in Cam­bridge for the second year of my postdoc, I gave birth to Anna. At the end of that year, the de­part­ment paid for me to go to a K-the­ory con­fer­ence at the Bat­telle In­sti­tute in Seattle, where I met Graeme Segal. We got to know each oth­er and star­ted work­ing to­geth­er. I did the equi­val­ent of a second PhD with him, fi­nally get­ting back in­to re­search by work­ing on prob­lems he sug­ges­ted. For a long time, feel­ing totally in­ad­equate be­cause of my ig­nor­ance, I had just been try­ing to learn things with no sense of where the ques­tions are, what I might con­trib­ute. If I’d con­tin­ued on my own, it’s not clear to me that I would have found a way back.

MP: So after your postdoc at Cam­bridge, you took a po­s­i­tion at the Uni­versity of York. How did that hap­pen?

Mc­Duff: There were very few jobs in the U.K. that year (1972), just four I be­lieve, and I was lucky enough to get one. Some years later, my Cam­bridge ad­visor said, “What a pity you didn’t ap­ply for that lec­ture­ship at Cam­bridge….” Why didn’t he sug­gest it at the time?

I left Cam­bridge be­cause there were no lec­ture­ships that year, and the only pos­sible fel­low­ship was at Gir­ton, where the salary wasn’t enough to sup­port a hus­band and child. I wasn’t eli­gible for one of the bet­ter-pay­ing fel­low­ships, say at Trin­ity, be­cause they were re­served for men.

Al­though there wasn’t overt pre­ju­dice at Cam­bridge when I was a gradu­ate stu­dent, the Cam­bridge sys­tem wasn’t set up for wo­men to have a ca­reer. I was some­what an­om­al­ous, sup­port­ing a child and hus­band, and I couldn’t sur­vive on a very small fel­low­ship from Gir­ton. So I left.

MP: So you went off to York.

Mc­Duff: York, yes. At that time, I had a nine-month-old child, my first teach­ing job, and a hus­band who re­fused to do any­thing around the house.

MP: You were busy cop­ing with lots of re­spons­ib­il­it­ies.

Mc­Duff: And I was try­ing to do math­em­at­ics, so I was very busy.

MP: Well, I think a nine-month-old child would be more than enough to oc­cupy your time.

Mc­Duff: Dav­id did look after Anna, I have to say, but he wouldn’t change her nap­pies; I had to drive home five miles every lunch­time for that. He said they were too geo­met­ric (they did have to be fol­ded). We also couldn’t af­ford good dis­pos­able nap­pies. I washed them in a ma­chine, and hung them out to dry in the garden.

MP: My wife and I are greatly en­joy­ing our first grand­child, and I have got­ten real in­sights in­to how much ef­fort goes in­to caring for a baby.

Mc­Duff: It really is a lot of work. It’s also hard to do math­em­at­ics when your time is chopped up in­to little pieces.

#### MIT and Graeme Segal — a turning point

MP: So, after your Rus­si­an ex­per­i­ence, you came to feel you could do re­search again.

Mc­Duff: Slowly, very slowly. I very much en­joyed be­ing at York, teach­ing for the first time. Feel­ing less in­tim­id­ated once out of Cam­bridge, I or­gan­ized sem­inars with oth­er young fac­ulty and learnt with them. We were al­lowed to carry through some ideas about chan­ging the struc­ture of the un­der­gradu­ate pro­gram, in­tro­du­cing a choice of courses and stu­dent pro­jects in­to the last year. I con­tin­ued work­ing closely with Segal, mostly via let­ters, com­plet­ing a pa­per on con­fig­ur­a­tion spaces of pos­it­ive and neg­at­ive particles.

In 1974–75, I was in­vited to MIT as a vis­it­ing as­sist­ant pro­fess­or. While there I real­ized how far away I was from be­ing the math­em­atician I wanted to be, but I also real­ized that I could do something about it. I be­came more aware of the rel­ev­ance of fem­in­ist ideas. Be­fore I’d thought that I was bey­ond all that since I already earned the liv­ing, but I’ve slowly learnt that these mat­ters go much deep­er. In those days, I was still a fol­low­er, not in­ter­act­ing with any­one on a basis of equal­ity. I had most in­ap­pro­pri­ate role mod­els, either sirens such as Lou An­dreas Sa­lomé or suf­fer­ers such as the Rus­si­an poet’s wife Nadezhda Man­del­stam — neither of much help in be­com­ing a cre­at­ive math­em­atician. It was also harder than it is today for a young wo­man to in­ter­act with oth­er (male) math­em­aticians in a purely pro­fes­sion­al way as a stu­dent or col­league; there were too few of us.

That year, for the first time, I met oth­er fe­male stu­dents of math­em­at­ics to whom I could re­late. I also had a math­em­at­ic­al idea again, the first real idea since my thes­is, which grew in­to a joint pa­per with Segal on the Group Com­ple­tion The­or­em. (Again we col­lab­or­ated by mail, since he was in Mo­scow and Ox­ford.) The year at MIT was cru­cial in build­ing up the re­search side of my ca­reer. I woke up and real­ized that I could af­fect my life.

MP: It seems that the in­flu­ence of Gel­fand, Segal, and your MIT ex­per­i­ence were key factors in your de­vel­op­ment as a re­search math­em­atician.

Mc­Duff: Be­cause I had a child, was very busy, and had changed fields, it would have been very easy for me not to suc­ceed as a re­search math­em­atician. I read a very in­ter­est­ing book1 20 years ago about wo­men in aca­demia that showed how small but key things de­term­ined wheth­er wo­men re­mained in the academy or were, as they said, “de­flec­ted” by ad­vice they re­ceived, in­con­veni­ently timed moves they had to make to ac­com­mod­ate their hus­band’s ca­reer, or an ill­ness. If you’re an out­sider, it is al­most im­possible to func­tion. For mar­gin­al­ized people, as wo­men were at that time, it’s not only a ques­tion of mer­it but also one of luck. I had tal­ent and per­sever­ance, but I was also lucky.

MP: Nev­er un­der­es­tim­ate the value of luck, but it takes more than that to suc­ceed in re­search.

Mc­Duff: For me it’s been a long steady haul.

MP: So, in what was to be year three at York, you went to MIT.

Mc­Duff: Right.

MP: Did you simply learn of this ap­point­ment that was re­served for wo­men and de­cide to ap­ply?

Mc­Duff: At that stage I would nev­er have ap­plied; I was in­vited to come. MIT was look­ing for wo­men, and I ima­gine that I. M. Sing­er had heard about me from Gel­fand.

While there, I real­ized that in­stead of be­ing en­vi­ous of oth­er people’s op­por­tun­it­ies, I could ar­range them for my­self. I ap­plied to the In­sti­tute for Ad­vanced Study and got in. There was a job com­ing up in War­wick. I didn’t have to be at York; I could ap­ply to War­wick. It was that kind of thing.

MP: It sounds like something of an awaken­ing. So, you went to War­wick for two years.

Mc­Duff: Yes. I was very happy there.

MP: War­wick was a very young uni­versity at that point.

Mc­Duff: York was also a “new uni­versity,” as they were called. But War­wick had more in­ter­na­tion­al con­nec­tions and pos­sib­il­it­ies be­cause of the Math­em­at­ic­al In­sti­tute set up by Zee­man.

MP: In the early 1970s, were all Cam­bridge col­leges still single sex?

Mc­Duff: I felt ex­cluded from Cam­bridge for that reas­on. There were one or two oth­er wo­men float­ing around the de­part­ment, but they were pretty mar­gin­al. The few fe­male gradu­ate stu­dents typ­ic­ally got mar­ried and left the field after their PhD. There was a seni­or wo­man in stat­ist­ics, but I did not know her. Gir­ton had wo­men math­em­aticians, Dame Mary Cartwright for ex­ample. But al­though I was form­ally a mem­ber of that col­lege, it had no pro­vi­sion for mar­ried stu­dents, and I nev­er went there. My one in­ter­ac­tion with Mary Cartwright was when I was a school­girl ap­ply­ing to Cam­bridge; I had tea with the Mis­tress of Gir­ton Col­lege, who just happened to be the dis­tin­guished math­em­atician Mary Cartwright. I don’t re­mem­ber know­ing that she was a math­em­atician. She handed me a cup of tea in a del­ic­ate cup. It was a form­al oc­ca­sion, not a math­em­at­ic­al one.

MP: You said that, dur­ing this peri­od, your hus­band Dav­id was something of a house dad.

Mc­Duff: After fin­ish­ing his PhD, he didn’t want a reg­u­lar job, in­stead trans­lat­ing po­etry from many lan­guages. He was not at all do­mest­ic.

MP: So in 1975, after be­ing at MIT, you went back to York, and that co­in­cided, roughly, with your sep­ar­a­tion from Dav­id.

Mc­Duff: Right.

MP: And then on to War­wick in 1976.

Mc­Duff: That was a very good place for me. I could well have stayed there for the long haul, but I moved to Stony Brook in 1978 for per­son­al reas­ons I’ll talk about later. The two in­sti­tu­tions are alike in many ways, not quite at the cen­ter of things but rich with op­por­tun­it­ies.

#### Isolation

MP: You fre­quently speak of be­ing isol­ated in your writ­ing.

Mc­Duff: Right.

MP: Many people con­tin­ue to be­lieve that math­em­at­ics is a single-per­son sport and not a team sport. You seem to be sug­gest­ing very strongly that in­ter­ac­tions with oth­er math­em­aticians are very im­port­ant.

Mc­Duff: I think they are. I talked about this with my hus­band, Jack Mil­nor, re­cently, be­cause he is some­body who al­most al­ways works alone; he does talk to people, but not that much. What he said was that when you’re learn­ing a sub­ject, it is vi­tal to talk to oth­ers. You have to grow up in a com­munity, know where the sub­ject is at, and what the in­ter­est­ing prob­lems are. Once you have a gen­er­al frame­work, you can fruit­fully work on your own — though even then it’s of­ten good to talk to oth­ers.

A large part of the prob­lem was my at­ti­tude. If I’d had role mod­els of wo­men chal­len­ging au­thor­ity I might have done bet­ter — to do re­search you have to ask ques­tions. I did not know any­one who was at­tempt­ing to live a sim­il­ar life, and so it took a long time for things to come to­geth­er. The late six­ties was the time of the “Free Uni­versity” in Cam­bridge, lots of far-left polit­ics, very an­ti­au­thor­ity. There were very few adults whom I was will­ing to talk to — Gel­fand and Aleksander Zyw — but not my par­ents or any­one who might have giv­en me sens­ible ad­vice.

I kept my­self apart from most oth­er wo­men since they didn’t seem to share my am­bi­tions. I also isol­ated my­self be­cause of my life with Dav­id; he was not at all so­ci­able either.

MP: You said that Gel­fand opened a num­ber of fields to you. That might have helped with the isol­a­tion prob­lem.

Mc­Duff: Even­tu­ally it did.

MP: He in­tro­duced you to sub­ject mat­ter that he thought you should know and re­vealed the in­ter­con­nec­ted­ness of many of these ideas. A math­em­atician I talked to re­cently said that un­der­scores a de­fect of Amer­ic­an edu­ca­tion in math­em­at­ics. He was talk­ing about it at the un­der­gradu­ate level as well as the doc­tor­al level. He claims that stu­dents get pushed through a num­ber of re­quired courses and very of­ten fin­ish a bach­el­or’s de­gree or an ad­vanced de­gree with only a weak idea of how math­em­at­ic­al sub­jects con­nect. For that reas­on he re­com­mends de­vel­op­ing new sorts of mod­ern cap­stone ex­per­i­ences that bring the ideas to­geth­er. I don’t know if that’s par­tic­u­larly easy. I think it’s easi­er to do it at the un­der­gradu­ate level than at the gradu­ate level. Maybe that’s part and par­cel of edu­ca­tion in Rus­sia.

Mc­Duff: Well, I don’t know what edu­ca­tion in Rus­sia is like now, but the Gel­fand sem­in­ar re­flec­ted his very broad in­terests. His at­ti­tude was that everything was one.

You can’t learn all of math­em­at­ics, but the edu­ca­tion that I got as a gradu­ate stu­dent in Bri­tain was very nar­row. Edu­ca­tion there is still rather nar­row be­cause, at least un­til very re­cently, PhD stu­dents were al­lowed only three years. I think it’s much bet­ter in the States than in Bri­tain. In­stead of start­ing work im­me­di­ately on some thes­is top­ic, stu­dents have one or two years of gen­er­al courses and can then de­cide whom to work with. Even though people may still be spe­cial­ized, they have cer­tainly seen more math­em­at­ics when they fin­ish than I had.

MP: So most new PhDs in Bri­tain are about 24 years old when they com­plete their de­grees.

Mc­Duff: I was 24 when I’d done mine.

MP: In the United States, the av­er­age is closer to 27, a dra­mat­ic dif­fer­ence.

Mc­Duff: It used to be the case in Eng­land that you spe­cial­ized more as an un­der­gradu­ate, so you had a bit more math­em­at­ics com­pleted be­fore start­ing gradu­ate school, but not in Ed­in­burgh be­cause the Scot­tish uni­versity sys­tem was more like the Amer­ic­an. Of course, if you are in a de­part­ment with broad enough in­terests, you can con­tin­ue de­vel­op­ing and grow­ing.

MP: Do you still feel isol­ated?

Mc­Duff: No, I don’t feel isol­ated any­more, but that’s fairly re­cent — really start­ing when I be­came in­ter­ested in sym­plect­ic geo­metry in the mid-1980s.

#### Symplectic geometry

MP: I have to com­pli­ment you on your art­icle on an in­tro­duc­tion to sym­plect­ic geo­metry. It’s the first one that really began to make sense to me. Your ex­pos­i­tion is a gift.

Mc­Duff: Which in­tro­duc­tion was that?

MP: The one you gave at the European Wo­men in Math­em­at­ics Con­fer­ence.

Mc­Duff: Oh, that re­cent one.

MP: As I say, it was a gift.

Mc­Duff: At first I thought you were talk­ing about the book I wrote with Di­et­mar Sala­mon, called In­tro­duc­tion to Sym­plect­ic Geo­metry, whose first chapter is “From Clas­sic­al to Mod­ern.” One of the things I did learn in Ed­in­burgh was very old-fash­ioned clas­sic­al mech­an­ics, spin­ning tops, ca­non­ic­al trans­form­a­tions, and all that. Those are the roots of sym­plect­ic geo­metry, so this chapter star­ted off talk­ing about clas­sic­al mech­an­ics and then dis­cussed Gro­mov’s mod­ern ap­proach to the geo­metry of Eu­c­lidean space.

#### Jack Milnor

MP: Some­where along the line, you en­countered Jack Mil­nor.

Mc­Duff: I met him when I was at the In­sti­tute for Ad­vanced Study in Spring 1976.

MP: Ap­par­ently you and Jack do dis­cuss math­em­at­ics.

Mc­Duff: To some ex­tent. I’ve nev­er col­lab­or­ated with him. But we do talk about math­em­at­ics, and he oc­ca­sion­ally reads things that I write. For ex­ample, he read the art­icle of mine you liked, help­ing me make it un­der­stand­able to some­body who doesn’t know the sub­ject.

MP: I’ve heard more than one math­em­atician say, “Nev­er marry a math­em­atician in the same field, be­cause that can only lead to con­flict.” That was one of the reas­ons for ask­ing that ques­tion, but your fields are suf­fi­ciently dif­fer­ent that math­em­at­ic­al con­flicts are less likely to oc­cur.

Mc­Duff: Well, he’s moved out of to­po­logy in­to dy­nam­ic­al sys­tems. There are re­la­tions between sym­plect­ic geo­metry and dy­nam­ic­al sys­tems, but we don’t talk much about them. He’s won­der­ful when I want to ask ques­tions about to­po­logy. We do in­ter­act about math­em­at­ics, some­what more when we met than now, but I’ve al­ways felt that it’s bet­ter for me to be in­de­pend­ent.

MP: I could have guessed that by now. So, as of the mo­ment, you’re con­tinu­ing to work vig­or­ously in sym­plect­ic geo­metry, not an­ti­cip­at­ing a move in­to some oth­er field.

Mc­Duff: Sym­plect­ic geo­metry is in­cred­ibly rich. Many bril­liant young people have come in­to the field. It now en­com­passes a huge amount of math­em­at­ics and relates to many oth­er areas, so I am not temp­ted to do something com­pletely dif­fer­ent. The ho­mo­topy the­ory I stud­ied as a postdoc is rel­ev­ant, as are many oth­er things I learnt along the way. For ex­ample, I first learnt about con­tin­ued frac­tions in or­der to teach a work­shop for the Stony Brook un­der­gradu­ate Wo­men in Sci­ence pro­gram, but it was a cru­cial in­gredi­ent of my latest work about em­bed­ding el­lips­oids. Of course, there are many oth­er top­ics like mir­ror sym­metry and al­geb­ra­ic geo­metry that I don’t know enough about, but I am more con­fid­ent that I can learn them as needed.

MP: There are all kinds of op­por­tun­it­ies, even full-blown journ­als in sym­plect­ic geo­metry.

Mc­Duff: The Journ­al of Sym­plect­ic Geo­metry is fairly re­cent, I would say, about five years old or so.

MP: That’s young for a journ­al.

Mc­Duff: The field has in­flu­ence. The ideas of Flo­er the­ory, first ex­pressed in sym­plect­ic geo­metry, have now per­meated low-di­men­sion­al to­po­logy, with close con­nec­tions to gauge the­ory and ho­mo­lo­gic­al al­gebra. Via mir­ror sym­metry, we now un­der­stand that sym­plect­ic geo­metry is in some sense the twin of com­plex geo­metry.

#### Dusa McDuff as role model

MP: In 1978 you moved to Stony Brook to be closer to Mil­nor, who was at the In­sti­tute in Prin­ceton, and in 1984 you were mar­ried. At Stony Brook you quickly be­came a full pro­fess­or and de­part­ment head. As de­part­ment head you worked to im­prove the cur­riculum. Tell us about that.

Mc­Duff: I made ef­forts to im­prove the un­der­gradu­ate cur­riculum at Stony Brook by in­tro­du­cing new classes and work­ing to at­tract more ma­jors. I like teach­ing. I was in­volved in cal­cu­lus re­form, teach­ing cal­cu­lus with com­puters, and ex­per­i­ment­ing with new cur­ricula. I haven’t been able to work con­sist­ently at that be­cause it’s just too much to spend a lot of time do­ing that and have a fam­ily and do re­search. (My son, Thomas, was born in 1984.) At Stony Brook I worked with oth­ers to im­prove the un­der­gradu­ate pro­gram, but there is al­ways a huge amount left to do.

MP: Like it or not, you’ve be­come a role mod­el for wo­men in math­em­at­ics. How do you handle that?

Mc­Duff: At some point I had to de­cide wheth­er I’d put more ef­fort in­to do­ing ad­min­is­tra­tion or in­to im­prov­ing teach­ing — get­ting in­volved in a ma­jor way and do­ing it prop­erly, or wheth­er I wanted to con­cen­trate on re­search. There are many prom­in­ent wo­men sci­ent­ists who’ve re­cently be­come deans or uni­versity pres­id­ents. I de­cided I didn’t want to take that route, since what I really cared about was do­ing re­search. That’s also im­port­ant for wo­men, to see that wo­men can ex­cel at re­search. I re­cently moved to Barn­ard partly for that reas­on, since it gives me a vis­ible plat­form on which to be both a wo­man and a re­search math­em­atician.

I al­ways try to en­cour­age young wo­men, in­deed wo­men at all stages. I had very little ad­vice, and talked to very few people early in my ca­reer. Now I talk to people a lot; it’s good to en­cour­age dia­logue. There are many ways of be­ing a suc­cess­ful wo­man math­em­atician. When I gave my ac­cept­ance speech after win­ning the Sat­ter Prize, I said that it would be good for oth­er wo­men to talk about how and why they be­came math­em­aticians, for my story is cer­tainly not the only one. A few months later, the No­tices of the Amer­ic­an Math­em­at­ic­al So­ci­ety pub­lished fas­cin­at­ing auto­bi­o­graph­ic­al ac­counts by six oth­er wo­men. That was very valu­able be­cause it showed wo­men from dif­fer­ent back­grounds, with dif­fer­ent mo­tiv­a­tions and in­terests, and dif­fer­ent ways of con­trib­ut­ing.

MP: Such art­icles ac­tu­ally do lots of good for math­em­at­ics in that they provide a lot of in­form­a­tion, coun­sel­ing as it were, of what it means to be a wo­man in math­em­at­ics and what they’re up against.

Mc­Duff: Now there are sev­er­al very suc­cess­ful pro­grams de­signed for wo­men. People have been try­ing vari­ous ap­proaches, some of which have really worked. For ex­ample, the Neb­raska Con­fer­ence for Un­der­gradu­ate Wo­men and the pro­gram at the In­sti­tute for Ad­vanced Study are both ex­cel­lent. There are still not enough wo­men in the pro­fes­sion for us to take their pres­ence for gran­ted. Any­thing that can bring wo­men to­geth­er and help them meet oth­ers, who are pos­sibly quite dif­fer­ent but fa­cing some of the same is­sues, is to my mind very help­ful.

MP: Some wo­men math­em­aticians I have spoken with be­lieve that em­ploy­ment op­por­tun­it­ies for wo­men math­em­aticians have ac­tu­ally de­clined in re­cent years.

Mc­Duff: It’s still very spotty. There are some really bril­liant young wo­men math­em­aticians now; it is much more ac­cep­ted that wo­men can be good math­em­aticians.

There’s still a lot of hid­den pre­ju­dice, not just about wo­men. There are so many at­trib­utes — ac­cent, col­or, or back­ground — that make one think a per­son couldn’t pos­sibly be a math­em­atician. It takes a long time for the aca­dem­ic cul­ture to change.

Some good de­part­ments have made ser­i­ous ef­forts to over­come this prob­lem. In those that haven’t, there aren’t many wo­men. In gen­er­al, I think the situ­ation is much bet­ter than it was. There are many more op­por­tun­it­ies. Every year there are some wo­men every­body wants to hire. Com­ing here to MSRI is great fun; there are a lot of young wo­men in the pro­gram, which im­proves the at­mo­sphere for every­one.

One can’t be com­pla­cent. Every­body should be en­cour­aged, not just wo­men. The old at­ti­tude used to be that if people are any good they’ll sur­vive, and if they don’t, there are al­ways oth­ers. I dis­agree; we have to care about every­one.

#### Career, family, husband — a lot of juggling

MP: In one of the art­icles you have writ­ten you say that you only sur­vived be­cause of the con­fid­ence that was in­stilled in you by the suc­cess of your work on von Neu­mann al­geb­ras.

Mc­Duff: My up­bring­ing also gave me a lot of con­fid­ence. I felt I could do everything, and I tried to do everything — to have a ca­reer and a fam­ily and a bril­liant hus­band.

But it’s not pos­sible to keep all those balls up in the air at the same time.

MP: It’s dif­fi­cult. I don’t think it’s got­ten easi­er.

Mc­Duff: It’s not got­ten much easi­er, ex­cept that at­ti­tudes to­ward gender is­sues have im­proved. Mar­riage is now more of an equal part­ner­ship, while in the past wo­men and men were ex­pec­ted to play very dif­fer­ent roles. It is less of an an­om­aly for a young wo­man to have the am­bi­tion to suc­ceed as a math­em­atician. In my day it was con­sidered so un­fem­in­ine that I had to spend a lot of en­ergy prov­ing I was a wo­man.

At the be­gin­ning, be­fore I had found my way as a math­em­atician, the fact that I had writ­ten a good PhD thes­is gave me be­lief in my­self. The vis­ib­il­ity of my thes­is also en­abled me to get jobs. No doubt I was known be­cause I was one of the very few wo­men do­ing re­search math­em­at­ics at that time, but I had also shown that there are in­fin­itely many type II$_1$ factors, a ques­tion left open since the found­a­tion­al pa­pers of Mur­ray and von Neu­mann in the 1940s. So that gave me a firm basis on which to build a life.