Celebratio Mathematica

Margaret H. Wright

Interview with Margaret Wright

by Allyn Jackson

Margaret Wright.
Photo courtesy of the Simons Foundation.

Mar­garet H. Wright has been a lead­ing fig­ure in nu­mer­ic­al ana­lys­is for more than forty years. Born in Cali­for­nia in 1944, she earned a bach­el­or’s de­gree in math­em­at­ics (1964) and a mas­ter’s de­gree in com­puter sci­ence (1965) from Stan­ford Uni­versity. For six years she worked as a pro­gram­mer at GTE Sylvania. Seek­ing more in­de­pend­ence and autonomy in her ca­reer, she re­turned to Stan­ford to earn a PhD in com­puter sci­ence in 1976, un­der the dir­ec­tion of Gene Gol­ub and Wal­ter Mur­ray. She then worked for 12 years as a re­search as­so­ci­ate in the Sys­tems Op­tim­iz­a­tion Labor­at­ory that George Dantzig had foun­ded at Stan­ford. In 1988, Wright took a po­s­i­tion as a re­search­er at AT&T Bell Labs, a place she called “para­dise.” In 2001, in the midst of grow­ing un­cer­tainty about the fu­ture of Bell Labs, she moved to the Cour­ant In­sti­tute of Math­em­at­ic­al Sci­ences at New York Uni­versity (NYU), where today she is the Sil­ver Pro­fess­or of Com­puter Sci­ence.

Wright’s work, which has fo­cused primar­ily on op­tim­iz­a­tion, unites the­or­et­ic­al prowess, tech­nic­al com­mand, and real-world im­ple­ment­a­tion. She has been at the cen­ter of ma­jor de­vel­op­ments in ap­plied math­em­at­ics, in­clud­ing the in­teri­or-point re­volu­tion in lin­ear pro­gram­ming.

While Wright de­scribes her­self as “bor­ing” and a “goody two-shoes”, she ex­udes an easy­going cha­risma. That qual­ity, to­geth­er with her stature in re­search, a high level of per­son­al in­teg­rity, and a dis­arm­ing sense of hu­mor, has made her a trus­ted and be­loved lead­er in a host of ad­min­is­trat­ive ca­pa­cit­ies, in­clud­ing as the head of the Sci­entif­ic Com­put­ing Re­search De­part­ment at Bell Labs, as chair of the Com­puter Sci­ence De­part­ment at NYU, and as pres­id­ent of the So­ci­ety for In­dus­tri­al and Ap­plied Math­em­at­ics (SIAM).

Among her hon­ors are the Award for Dis­tin­guished Pub­lic Ser­vice from the Amer­ic­an Math­em­at­ic­al So­ci­ety (2002) and the John von Neu­mann Lec­ture Prize from SIAM (2019). She was elec­ted to the Amer­ic­an Academy of Arts and Sci­ences and to both the U.S. Na­tion­al Academy of En­gin­eer­ing and the U.S. Na­tion­al Academy of Sci­ences.

The fol­low­ing in­ter­view with Wright, con­duc­ted in Septem­ber and Oc­to­ber 2019, has been ed­ited and con­densed.

Math and sanitation

Jack­son: I want to start with some re­cent his­tory. In Ju­ly this year you re­ceived the von Neu­mann Prize and presen­ted the prize lec­ture at ICIAM [In­ter­na­tion­al Con­gress of In­dus­tri­al and Ap­plied Math­em­at­ics] in Valen­cia, Spain.1 You talked about a prob­lem you worked on that came from the De­part­ment of San­it­a­tion of the City of New York. Can you tell me about that prob­lem and what the out­come was?

Wright: In Oc­to­ber 2018, a per­son work­ing in in­form­a­tion tech­no­logy at the New York De­part­ment of San­it­a­tion emailed Russ Caflisch, the dir­ect­or of Cour­ant, and sketched out an “op­tim­iz­a­tion” prob­lem. Russ asked if I wanted to help, and I thought, Why not? It would be like my days at Bell Labs, where I had really en­joyed work­ing on real-world prob­lems.

The prob­lem was this. The De­part­ment of San­it­a­tion has sev­er­al thou­sand em­ploy­ees. Each san­it­a­tion work­er has a “home sta­tion,” and these are spread over the five bor­oughs. Of­ten em­ploy­ees want to change their home sta­tion. There are peri­ods a few times a year when they can re­quest this change by filling in a pa­per form and list­ing in or­der of pref­er­ence three home sta­tions they would like to move to. Then the de­part­ment re­as­signs people if pos­sible.

The ab­so­lute pri­or­ity for re­as­sign­ment is seni­or­ity, which is a unique in­teger for each per­son; you can’t have two people with the same seni­or­ity. Also, a work­er who does not wish to move can­not be forced to do so. The de­part­ment’s high-level policy, broadly speak­ing, is to re­as­sign people in pri­or­ity or­der, sub­ject to avail­ab­il­ity. However, there is a com­plic­a­tion when someone of lower pri­or­ity moves to a po­s­i­tion that has been re­ques­ted by a high­er-pri­or­ity per­son, thus free­ing up a pre­vi­ously oc­cu­pied po­s­i­tion. In such a case, fur­ther it­er­a­tions of the as­sign­ment pro­cess are re­quired.

At first this felt like a prob­lem in op­tim­iz­a­tion, but it’s ac­tu­ally a match­ing prob­lem. So I star­ted read­ing the lit­er­at­ure about match­ing prob­lems of this kind, and met on sev­er­al oc­ca­sions (for “fun”) with col­leagues from the De­part­ment of San­it­a­tion. This match­ing prob­lem is some­times called “hous­ing with sit­ting ten­ants.” There is an al­gorithm that solves the prob­lem, with a great name, “You Re­quest My House, I Get Your Turn” (YRM-IG­YT).2 (It is also called “Top Trad­ing Cycles” in the eco­no­met­rics lit­er­at­ure). It starts by go­ing down the list in pri­or­ity or­der. When it’s your turn, sup­pose someone wants your house. Then they get your turn — they are moved up the pri­or­ity list. Vari­ous prop­er­ties of this al­gorithm can be proved. Us­ing it ini­tially seemed ideal for the San­it­a­tion De­part­ment, but then I found some ex­amples where the al­gorithm pro­duced an an­swer that did not do what the de­part­ment wanted.

Un­for­tu­nately, this doesn’t have a great happy end­ing, like “Math­em­atician comes in, solves prob­lem, every­one is happy.” The YRM-IG­YT al­gorithm, nice as it was, does not really solve the prob­lem; the De­part­ment of San­it­a­tion de­veloped a new, re­lated al­gorithm. This phe­nomen­on — need­ing to ad­just the math­em­at­ic­al prob­lem to match real­ity — is fa­mil­i­ar when you are work­ing on real-world prob­lems. And it was very en­joy­able for me to work with the De­part­ment of San­it­a­tion team.

Jack­son: And it’s nice that the De­part­ment of San­it­a­tion felt they could reach out to the math­em­aticians.

Wright: Yes. When I talked to the per­son who had writ­ten to Russ, I asked about this. The per­son said, “Well, Cour­ant is a fam­ous math in­sti­tute. We have a prob­lem. It’s math.”

I also want to say that, in many real-world prob­lems, find­ing an al­gorithm is only the first step. Next you have to write “bul­let-proof code,” as we say. Of­ten people who are on the more the­or­et­ic­al side don’t think about that. They just say, here’s an al­gorithm, end of story. Writ­ing good code is es­sen­tial.

A very American life

Jack­son: The De­part­ment of San­it­a­tion work was a re­cent chapter in the story of your life. Let’s go back to the be­gin­ning, to the first chapter. Where in your mind does the story of your life be­gin?

Wright: I have not had a very ex­cit­ing life! It’s very Amer­ic­an. I was born in San Fran­cisco, be­cause my moth­er was a doc­tor and she wanted me to be born in a cer­tain hos­pit­al in San Fran­cisco where she had done her train­ing. We lived in an ag­ri­cul­tur­al town, Han­ford, Cali­for­nia, where the pop­u­la­tion was about 10,000. It’s prob­ably not much big­ger than that now.

I didn’t like liv­ing in a small town. It was too much of every­body know­ing what every­body else was do­ing. Not that as a child I did any­thing bad! But I have a strong sense of pri­vacy. We lived in Han­ford un­til I was ten, which is when my par­ents split up. Then my mom and the kids moved to Tuc­son.

My birth­day is in Feb­ru­ary, and the cutoff date for go­ing to kinder­garten was March 1st. So I was one of the young­est chil­dren in kinder­garten. At that time kids were al­lowed to skip grades in Cali­for­nia, though later it was con­sidered bad psy­cho­lo­gic­ally for them. I skipped fourth grade in Han­ford, so that for most of my time in school and col­lege, I was al­most two years young­er than every­body else.

Jack­son: Your moth­er be­came a doc­tor at a time when there were very few wo­men be­com­ing doc­tors. What was her story?

Wright: She said that half of the stu­dents in her med­ic­al school class were wo­men. She got her med­ic­al de­gree in 1937. When she went to the 50th class re­union, there were half wo­men! Now, this is only one data point, the Uni­versity of Cali­for­nia Med­ic­al School. But she thought the worst dis­crim­in­a­tion against wo­men star­ted after World War II. When she was in med­ic­al school, there wasn’t a lot of “wo­men are in­feri­or” feel­ing — and she did say proudly that she’d been num­ber one in her class. So she nev­er talked about the struggle of be­ing a wo­man.

Jack­son: How did she juggle ca­reer and fam­ily when you were grow­ing up?

Wright: She had three chil­dren. My dad was also a doc­tor. He was a gen­er­al prac­ti­tion­er of a kind they don’t have any­more — he did sur­gery, he de­livered ba­bies. I re­mem­ber as a child, I would hear the phone ring at 2 AM, and my dad would get up and rush out to de­liv­er a baby. My mom’s spe­cialty was “eye, ear, nose and throat,” a spe­cialty that doesn’t ex­ist any­more. She did not have those last-minute emer­gen­cies, which would have been very dif­fi­cult with three chil­dren.

I’ve thought about this, giv­en how things are now, when wo­men are so tor­men­ted about do­mest­ic ar­range­ments if they have a chal­len­ging ca­reer. My mom nev­er talked about it at all. We had a very nice wo­man who was from Iowa who came to stay with us after school. There was an­oth­er per­son who would oc­ca­sion­ally come in for ma­jor house clean­ing. It sounds idyll­ic, doesn’t it?

Jack­son: It sounds great! Did your par­ents en­cour­age you a lot in school, did they in­sist on per­fect home­work? What were they like in that re­gard?

Wright: Well — this goes with me be­ing a bor­ing per­son — I al­ways did so well in school, and so did my broth­ers, that no one ever said any­thing. I was al­ways either the top stu­dent or the next-to-top stu­dent.

Jack­son: What did you want to be when you grew up? Did you dream about be­ing a sing­er, or an as­tro­naut, something like that?

Wright: No! As I said, I am a very bor­ing per­son! My dad kept say­ing to my broth­ers and me, “One of you has to be a doc­tor.” I am not ex­actly a re­bel­li­ous per­son, but I thought: I don’t know about that! My uncle was a law­yer. My fam­ily was not as­so­ci­at­ing with pro­fess­ors and aca­dem­ics and re­search­ers, or with en­gin­eers or sci­ent­ists. What adults did I know who had in­ter­est­ing-sound­ing jobs? Doc­tor and law­yer. That’s it.

A high school coun­selor once said to me, “I see you have got­ten all As in bio­logy and chem­istry. Have you thought that you might do something in those areas? You could be a nurse.” Now, I am go­ing to be ac­cused of elit­ism! Nurs­ing is a per­fectly good pro­fes­sion. But I said: “My mom is a doc­tor, and if I were go­ing to be in medi­cine, that’s what I would want to be.” The coun­selor was shocked. She said, “Okay, but what about hav­ing a fam­ily?” I said, “Well, my mom man­aged to do it.”

I knew I was go­ing to go to col­lege. I didn’t worry about it at all, in con­trast to kids today. Wo­men were not ad­mit­ted to the Ivy Leagues at that time — this would have been in 1959-1960. My par­ents had both gone to UC Berke­ley. Al­though they wer­en’t to­geth­er when I was in high school, they both were of course in­ter­ested in where I would go to col­lege. As a child of a Berke­ley alum, I could get in-state tu­ition at Berke­ley. I knew Stan­ford was a good school, and they ad­mit­ted wo­men.

So I ap­plied to Stan­ford and Berke­ley, and my “safety school” was the Uni­versity of Ari­zona, be­cause we were in Tuc­son. This is go­ing to be a very ob­nox­ious com­ment, but if you were in the top three-quar­ters of your high school class, you would get ad­mit­ted to Ari­zona. So I figured I would get in! In the end I got ad­mit­ted to all of them and de­cided to go to Stan­ford, pos­sibly to be dif­fer­ent from my par­ents.

Jack­son: Cost was not an is­sue? Berke­ley would have been es­sen­tially free with in-state tu­ition, and Stan­ford not.

Wright: Yes, and Stan­ford had the stag­ger­ing fig­ure of I think \$1000 a year as tu­ition.

Jack­son: That sounds like noth­ing today!

Wright: Yes, though not at that time. But my par­ents were both doc­tors. They could af­ford it. They said, it will be ex­pens­ive, but okay. That’s how I ended up at Stan­ford, which as it turned out was great. Berke­ley would prob­ably have been okay too.

Jack­son: Yes, both are ex­cel­lent, you couldn’t have gone wrong. But Stan­ford has a dif­fer­ent feel, be­ing a private uni­versity.

Wright: It was dif­fer­ent. A big part of life at the Uni­versity of Ari­zona was sor­or­it­ies and fra­tern­it­ies. I was against them, pos­sibly be­cause I wasn’t a “pop­u­lar” girl. There were the “cool” people, and I was nev­er in that group. The cool girls in high school talked about go­ing to the Uni­versity of Ari­zona and join­ing sor­or­it­ies, and I re­mem­ber think­ing: That sounds really hor­rible. Stan­ford at that time had fra­tern­it­ies, but no sor­or­it­ies.

Jack­son: When you were in high school, did you en­counter the at­ti­tude that girls are not sup­posed to be smart?

Wright: People did say that, if you are a girl and you are too smart, boys won’t like you, and you shouldn’t do bet­ter than every­body else. We played a game in our math class where one stu­dent would stand be­hind the desk of an­oth­er, and the teach­er would ask a ques­tion. Who­ever got the an­swer fast­est would move on to stand be­hind the next chair. I al­ways went all the way around the room. Af­ter­wards people would say, “The boys are not go­ing to like you if you do this.” I re­mem­ber think­ing, Too bad for them!

Jack­son: Good for you! Where did that con­fid­ence come from?

Wright: Well, I’ve thought about that. If I am not sure I can do something well, I am in­sec­ure. I was a nervous wreck be­fore giv­ing the von Neu­mann Lec­ture, as I am be­fore every big talk. But in the con­text of high school, I knew that I was a good stu­dent. If I say I knew I was smart, it sounds ob­nox­ious, but I really did. I just nev­er had any trouble with any­thing in high school.

Of course in col­lege that changes, right? In my fresh­man year at Stan­ford, which was 1960, one of the fresh­men com­mit­ted sui­cide. He had been from a small town in the Mid­w­est. When he left to go to Stan­ford, he went by train. A band came to the sta­tion and played for him, and the may­or of his town made a speech about how proud the town was of him. When he got to Stan­ford, he was totally out of his depth. If you grow up in an en­vir­on­ment where you are al­ways the best and you can main­tain that in your life, good for you. But most people can’t. Cer­tainly at Stan­ford, I knew I wasn’t the best.

Jack­son: It’s much more se­lect­ive, it’s a dif­fer­ent en­vir­on­ment.

Wright: Right. Some stu­dents went to very chal­len­ging prep schools, where they were really pushed aca­dem­ic­ally. That wasn’t hap­pen­ing at Catalina High School, where I went.

Getting the computer to do what you want

Jack­son: What was your in­ten­ded ma­jor when you ar­rived at Stan­ford?

Wright: I had a fab­ulous French teach­er in high school. And I really liked math be­cause it was so neat — and I am us­ing the word “neat” in the sense of tidy. It fit to­geth­er, you could prove things. I felt that was won­der­ful. But I also liked Eng­lish. I’ve al­ways been a big read­er. People would say that I al­ways had my nose in a book.

So when I first went to Stan­ford and had to in­dic­ate my in­terests, I put math­em­at­ics, his­tory, Eng­lish, French. Those were the areas I thought I might ma­jor in. At that time there was a gen­er­al stud­ies re­quire­ment, so for the first two years you had to take Eng­lish, his­tory, sci­ence, math, and so on. That was not a prob­lem for me. The hard part came when I was a ju­ni­or and had to pick a ma­jor. Be­cause my mom had had a job and my par­ents had got­ten di­vorced, I knew from the be­gin­ning that I needed to be able to earn my own liv­ing.

Someone told me that I could get a good job if I ma­jored in math. I re­mem­ber be­ing puzzled. Why would any­one pay me to do math? It’s too much fun! The per­son just said: Trust me. So you can see how com­pletely na­ive I was about the world of schol­ar­ship and aca­demia, or for that mat­ter, work­ing in in­dustry. No one came to Stan­ford and gave talks about how you use math in in­dustry, as is done today. But I just thought, Okay, I’ll ma­jor in math. And what a good choice that was.

Stan­ford had com­puter sci­ence courses, but no com­puter sci­ence ma­jor. A big change in my life came when I took my first com­puter sci­ence course. I es­pe­cially liked that you could make the com­puter do what you wanted. In math, you could prove things, but with the com­puter, you could write a pro­gram to solve a prob­lem, and the solu­tion would come out the way you wanted it to.

Jack­son: How did you pro­gram? Did you use key­punch cards?

Wright: We did. We pro­grammed in a lan­guage called AL­GOL, which still ex­ists, but in minor form. You had to go to the com­put­ing cen­ter and bring your stack of cards. You would punch them on the key­punch ma­chine, and then hand the stack to the per­son at the desk, and they would take it away. You would come back later, and they would give you your out­put.

I took my first com­puter sci­ence course my ju­ni­or year and loved it. If there had been a ma­jor in com­puter sci­ence, I prob­ably would have done that. Don’t get me wrong, I loved math. But the com­puter sci­ence was so great!

Jack­son: Who taught com­puter sci­ence?

Wright: Gene Gol­ub taught the first course, and Cleve Mol­er, who was then a PhD stu­dent, taught the second one.

Jack­son: Two greats in com­puter sci­ence.

Wright: Yes, and both of them were ex­cel­lent teach­ers. This sounds corny, but they con­veyed ex­cite­ment. Com­puter sci­ence was very in­ter­act­ive. I liked that a lot.

Socially noticeable as different — a female, and a math major

Jack­son: When you were an un­der­gradu­ate, were you the only fe­male in your math classes?

Wright: Mostly, yes. I had a dif­fer­en­tial equa­tions class that had 150 stu­dents, and I was the only wo­man. I nev­er dared to miss class be­cause if I did, it was ob­vi­ous that I was not there!

Jack­son: Did that af­fect you? Did you feel out of place?

Wright: Yes, I felt out of place. No one said any­thing, but when you are a minor­ity in any con­text, you do stand out. Also, it was com­mon for un­der­gradu­ates to ask one an­oth­er about their ma­jors. When I said math, they’d say, “I al­ways hated math, I was nev­er good in math” — in an in­dig­nant way, as if it was my fault that they didn’t like math! Of­ten this brought the con­ver­sa­tion to a screech­ing halt. If you were, say, a his­tory ma­jor, people could ask which coun­try, or which peri­od. With math, people didn’t know what to say. So my be­ing so­cially no­tice­able as dif­fer­ent did hap­pen, and it still hap­pens.

When I went to gradu­ate school to get my mas­ter’s and later my PhD, there were not very many wo­men, but it was cer­tainly not a case of one out of a big num­ber. There were a small num­ber.

Jack­son: How did you de­cide to go on for a mas­ter’s at Stan­ford, and did you think about go­ing dir­ectly for a PhD?

Wright: I needed to get a job when I gradu­ated. By the time I got my mas­ter’s, I could get the de­gree in com­puter sci­ence, and I knew there were pro­gram­mers who got paid. So I got a mas­ter’s in com­puter sci­ence, but I also took sev­er­al nu­mer­ic­al ana­lys­is courses, and that’s really what I was in­ter­ested in.

There was no one in my fam­ily who had done an aca­dem­ic PhD, so I had no idea what that meant. I re­garded pro­fess­ors with awe. I couldn’t pic­ture my­self be­ing a pro­fess­or.

Jack­son: Did you have any wo­men pro­fess­ors at Stan­ford?

Wright: Def­in­itely not in math or com­puter sci­ence. I don’t re­mem­ber any wo­men pro­fess­ors on the tech­nic­al side. Think­ing about it in ret­ro­spect, I am sure that it af­fected me. I nev­er thought, “I can’t pos­sibly do this”; I was just in­ter­ested in oth­er things. I nev­er had what you might call a ment­or. No pro­fess­or ever said, “Are you in­ter­ested in re­search? Maybe you could think about gradu­ate school” — which is what we pro­fess­ors do now. But I didn’t ex­pect that. Stu­dents now have more of an ex­pect­a­tion that someone will be sup­port­ive. So it’s dif­fer­ent now — it’s much bet­ter!

Jack­son: After your mas­ter’s, you got a job at Sylvania [in Moun­tain View, Cali­for­nia], which makes me think of light bulbs. But I don’t think you were work­ing on light bulbs.

Wright: It was GTE Sylvania, and GTE stands for Gen­er­al Tele­phone and Elec­tron­ics. They made elec­tron­ic equip­ment. They had a group that wrote com­puter pro­grams for sim­u­la­tions, al­though they didn’t call them sim­u­la­tions. For ex­ample, one of the pro­jects I worked on was ship photo re­cog­ni­tion. I sus­pect it might have had a mil­it­ary pur­pose. They would get pho­tos of ships and scan them in, in some way, and we were sup­posed to say what kind of ship it was. That sounds pretty mod­ern, right?

They needed com­puter pro­grams to per­form the sim­u­la­tion and com­pute an es­tim­ate of how wide the ship was, or of oth­er meas­ure­ments. These were lin­ear least-squares prob­lems, and there was a brand-new tech­nique called quasi-New­ton meth­ods that had been de­veloped by Fletch­er and Pow­ell in Eng­land.3 I wrote FOR­TRAN codes that did that. And I found it ut­terly fas­cin­at­ing.

This was team­work, and it had good and bad as­pects. It was really fun to talk to the oth­er people and learn from them. But there was also the “You’re not in charge” feel­ing, so if I wanted to do something a cer­tain way, oth­ers might say, “No, we have to do it this way.” I think that’s fairly typ­ic­al for team­work. It’s rare that every­one agrees. I worked there for six years. I learned a lot, not so much about tech­nic­al top­ics, but about the real world, about get­ting a pro­ject done, what you had to do when it had to be ready in a month. I really liked that.

Moving on to a PhD

Jack­son: At this time, you got mar­ried and had a daugh­ter.

Wright: That’s right. I got mar­ried in 1965. I had to get a job, be­cause my hus­band was a law stu­dent at Stan­ford and his tu­ition needed to be paid. The tu­ition was tiny com­pared to now. Be­ing a pro­gram­mer paid pretty well, and I wanted to work. At that time, liv­ing to­geth­er without be­ing mar­ried was com­pletely frowned upon. So we got mar­ried, and we had a daugh­ter in 1968.

Dur­ing our daugh­ter’s early years, I wanted to work part-time — 20 hours, or two and a half days, per week. This was amaz­ingly easy to ar­range with Sylvania. I did not ap­pre­ci­ate at the time how en­lightened this was on their part. Child care was, of course, an im­port­ant is­sue, but we were ex­tremely lucky to find a young moth­er with a daugh­ter who was ba­sic­ally the same age as our daugh­ter. This won­der­ful wo­man was happy to have a part-time job that in­cluded spend­ing the day with her child, hav­ing a play­mate of the same age, and be­ing paid. So that ar­range­ment — which could not have been bet­ter — las­ted un­til our daugh­ter star­ted kinder­garten. Then, again by good for­tune, and be­cause we were will­ing, in fact happy, to pay a reas­on­able salary, we hired a ded­ic­ated “older” wo­man — prob­ably slightly young­er than I am now! — who would come to the house when our daugh­ter fin­ished school and re­main un­til I got home. She was able to con­tin­ue work­ing for us es­sen­tially all the way through high school.

Even­tu­ally I thought about re­turn­ing to Stan­ford to get a PhD be­cause at Sylvania I was get­ting fed up with hav­ing oth­er people tell me what to do and also with the blatant dis­crim­in­a­tion against wo­men, which was com­mon at the time. I was un­sure what I needed to do, but when I con­tac­ted a Stan­ford pro­fess­or, he said that be­cause I had been a mas­ter’s stu­dent, I could re­turn as a PhD stu­dent without ac­tu­ally ap­ply­ing. I really should not have been al­lowed to do that. I should have been forced to take the GREs!

As a res­ult, I re­turned to Stan­ford in 1971 as a PhD stu­dent, plan­ning to work in nu­mer­ic­al ana­lys­is, with Gene Gol­ub. Gene loved hav­ing vis­it­ors, and one in­ter­est­ing vis­it­or after an­oth­er vis­ited Stan­ford thanks to him. While I was a PhD stu­dent, Philip Gill came from Eng­land for a short vis­it. He had worked on op­tim­iz­a­tion at the Na­tion­al Phys­ic­al Labor­at­ory, which is something that prob­ably doesn’t ex­ist any­more — a gov­ern­ment re­search lab with a per­man­ent staff who were ba­sic­ally free to do whatever they wanted. The next year, Wal­ter Mur­ray, who was a close col­league of Philip’s from NPL, also vis­ited and taught an ele­ment­ary nu­mer­ic­al ana­lys­is class. I was Wal­ter’s teach­ing as­sist­ant.

In Eng­land at that time, and even today, stu­dents spe­cial­ize at a much earli­er age than in the U.S. Math­em­at­ics un­der­gradu­ates in Eng­land ar­rive already know­ing a lot of math­em­at­ics. That’s what Wal­ter was used to. At Stan­ford, the stu­dents who took the un­der­gradu­ate in­tro­duc­tion to nu­mer­ic­al ana­lys­is of­ten didn’t know much math­em­at­ics. Some had barely had cal­cu­lus. Wal­ter as­sumed they knew all about in­teg­ra­tion, ana­lys­is, dif­fer­en­tial equa­tions — and they didn’t. The stu­dents would come to see me as the TA, and of course I was sym­path­et­ic, be­cause I knew that they didn’t have the right back­ground. I would say to Wal­ter, “You really can’t as­sume they know this.” And he would say, “They should know that!” And I would say, “They don’t know it — be­lieve me, they don’t!” Two gradu­ate stu­dents were also tak­ing the class — two gradu­ate stu­dents mixed with around 60 un­der­gradu­ates. The gradu­ate stu­dents kept telling Wal­ter the class was too slow and too easy. Wal­ter would say to me, “Look, they are telling me it’s too easy!” And I said, “Talk to the oth­er stu­dents!” Not sur­pris­ingly, the un­der­gradu­ates were afraid to say any­thing to him.

Jack­son: That’s not easy for you as a TA and a gradu­ate stu­dent to go to the pro­fess­or and say, “You’re not do­ing your course right.”

Wright: Well, Wal­ter is a very friendly, in­form­al per­son. But I don’t think he ever fully ap­pre­ci­ated the lack of math­em­at­ic­al know­ledge of the un­der­gradu­ates.

A year or two later, the de­part­ment cre­ated the For­sythe Award for Stu­dent Con­tri­bu­tions to Teach­ing, and I was the first re­cip­i­ent. I’m sorry if this sounds like brag­ging, but I was pretty proud of it. It was named after George For­sythe, who had been the found­ing chair of the com­puter sci­ence de­part­ment — a won­der­ful man. The cita­tion said something tact­ful like “for con­tri­bu­tions in be­ing a teach­ing as­sist­ant for a vis­it­or.”

When Wal­ter went back to Eng­land, Gene Gol­ub, to whom I will al­ways be grate­ful, sug­ges­ted I go to the NPL and said he would sup­port me on his grant. I am amazed, look­ing back on it now, that he could use his grant to send me to Eng­land for six months. I don’t know how happy fund­ing agen­cies would be about that today! So my little fam­ily and I went to Eng­land. And it was really great.

The NPL was a won­der­ful place. I had been warned that people wer­en’t go­ing to be friendly, they would be “stiff up­per lip” Brit­ish people. They wer­en’t any­thing like that. They were very friendly and con­stantly in­vit­ing us over to din­ner. And I got a lot of work done on my thes­is. That was in 1974–75.

Jack­son: Were there wo­men at the NPL?

Wright: Yes, there were. Were they at the same level as Wal­ter and Philip? No. They were usu­ally pro­gram­mers.

When people there wrote pa­pers, they would give their names with only ini­tials. In­stead of Philip E. Gill, as it would usu­ally be in the U.S., it would be P. E. Gill. But if one au­thor was the pro­gram­mer, and the pro­gram­mer was a wo­man, then they would put her first name, for ex­ample P. E. Gill and Gwen Peters. I asked why they did not give every­body’s first name. That led to a lively dis­cus­sion! I was only a vis­it­or, only a stu­dent. I had no power. But I kept ask­ing, what is this?

Jack­son: Can you tell me about the top­ic of your PhD thes­is?

Wright: Wal­ter had an idea, which he had worked on in his thes­is, about two classes of meth­ods for non­lin­early con­strained op­tim­iz­a­tion. One was pen­alty func­tion meth­ods, the oth­er was bar­ri­er func­tion meth­ods. In a sense they are com­ple­ment­ary.

If you are try­ing to min­im­ize some func­tion, and you have con­straints, one way to solve the con­strained prob­lem is to trans­form it in­to a prob­lem that has no con­straints (i.e., an un­con­strained prob­lem). One way to do that is to cre­ate a new func­tion by com­bin­ing the one you are try­ing to min­im­ize with the con­straints.

With a pen­alty meth­od, the new func­tion pen­al­izes you if the con­straints aren’t sat­is­fied. So, for ex­ample, if you have a con­straint \( x = 1 \), you would add something that pen­al­izes you when \( x \) is not equal to 1. Un­der fairly gen­er­al con­di­tions, you can show that the min­im­izers of the pen­alty func­tion con­verge to the solu­tion.

Bar­ri­er meth­ods are sort of the op­pos­ite. Here you have an in­equal­ity con­straint, for ex­ample, \( x \ge 1 \). Start­ing at a point where the con­straint is sat­is­fied, you min­im­ize a new func­tion that com­bines the ori­gin­al func­tion with a “bar­ri­er” func­tion that be­comes in­fin­ite as you get closer and closer to the con­straint \( x \ge 1 \).

In his thes­is, Wal­ter had proved vari­ous res­ults about pen­alty func­tions, and he thought I could work on bar­ri­er func­tions. That’s what my thes­is was about. He didn’t know that at this time bar­ri­er meth­ods were con­sidered to be in­her­ently flawed. The flaw is that, broadly speak­ing, when you take something that’s fi­nite and add things to it that gradu­ally be­come in­fin­ite, you cre­ate something ill-con­di­tioned. So, al­though bar­ri­er meth­ods were very pop­u­lar in the 1960s, by 1975 oth­er meth­ods had come along that seemed to be bet­ter and didn’t suf­fer from in­her­ent ill-con­di­tion­ing.

Still, I was happy with my thes­is. At this time I wanted to stay in the Bay Area, for per­son­al reas­ons. George Dantzig had cre­ated a re­search group in the Stan­ford op­er­a­tions re­search de­part­ment, and I was hired there in a soft-money po­s­i­tion. Things at the NPL were not go­ing well — they were be­ing forced more and more to work on pro­jects and get grants. So Philip and Wal­ter were in­ter­ested in mov­ing, and George Dantzig was able to ob­tain fund­ing to hire them too.

Dantzig: Small, sweet, smart

Jack­son: George Dantzig is a huge name in your field. Can you tell me about him?

Wright: He is one of the sweetest and smartest people I have ever known. He was quite small in terms of height, very soft-spoken. I nev­er heard him raise his voice. And he was just a de­light. He is the called the fath­er of lin­ear pro­gram­ming and won all kinds of awards for his math­em­at­ic­al con­tri­bu­tions.

One of his dreams was to have an or­gan­iz­a­tion, which he called the Sys­tems Op­tim­iz­a­tion Labor­at­ory (SOL), to deal with very large real-world prob­lems. George had writ­ten a couple of pa­pers ur­ging that such a place be cre­ated.4 He had to rely on gov­ern­ment grants, so he could nev­er really get the huge or­gan­iz­a­tion that he wanted. But he star­ted with hav­ing a few people who were work­ing on op­tim­iz­a­tion and try­ing to solve real-world prob­lems. That was his dream. I was very lucky to be­come a teeny part of that.

When the Stan­ford OR de­part­ment hired me to work at SOL, some people there thought my job would be to take someone else’s al­gorithm and write a pro­gram that car­ried it out. But I thought that I was go­ing to come up with new al­gorithms! It was def­in­itely a mis­match. But George just said, “Fine, Mar­garet, you can work on that.” And he was the one with the money.

Jack­son: He un­der­stood that you were cap­able of do­ing that.

Wright: He didn’t say that ex­pli­citly, but I op­tim­ist­ic­ally as­sumed that was what he thought.

Mi­chael Saun­ders, who is ori­gin­ally from New Zea­l­and, had fin­ished his PhD in com­puter sci­ence at Stan­ford a few years earli­er. He worked on the nu­mer­ic­al as­pects of lin­ear pro­gram­ming, and his work is rightly fam­ous. He then re­turned to New Zea­l­and for a few years. Philip and Wal­ter and I, who knew Mi­chael well, were hop­ing he would come back to Stan­ford, and that we four would be to­geth­er. That’s what even­tu­ally happened. This was around 1979. We were then called — I wouldn’t say “af­fec­tion­ately”! — the Gang of Four.

I’ve drif­ted in this con­ver­sa­tion away from Dantzig, but I can tell you that as a hu­man be­ing, he was amaz­ing. People would come to Stan­ford to the OR de­part­ment and say they wanted to meet “the fam­ous Pro­fess­or Dantzig.” One time it was a group from Ja­pan, all dressed up in suits. Maybe they were people from a busi­ness that used lin­ear pro­gram­ming. George came in­to my of­fice and said, “There is a group here and they want to meet me. I can’t face it. Can I just sit in here for a while?” He couldn’t take the “this is the fam­ous Pro­fess­or Dantzig” thing, be­cause he was ba­sic­ally shy. Of course I said, “Yes, you can hide in my of­fice un­til they go away!”

The media go wild for algorithms

Jack­son: Dantzig was the founder of the sim­plex meth­od. There is a 2004 pa­per on the sim­plex meth­od by Spiel­man and Teng5 in which they said something sort of puzz­ling. They wrote: “In spite of half a cen­tury of at­tempts to un­seat it, the sim­plex meth­od re­mains the most pop­u­lar meth­od for solv­ing lin­ear pro­grams. However, there has been no sat­is­fact­ory the­or­et­ic­al ex­plan­a­tion of its ex­cel­lent per­form­ance.” Oth­er meth­ods seemed like they might end up be­ing bet­ter than sim­plex, but sim­plex has con­tin­ued to be used and be very ef­fect­ive. Can you com­ment on this?

Wright: Yes, I can, and I’ll bring in my own know­ledge of bar­ri­er func­tions.

The­or­et­ic­al com­puter sci­ence de­veloped a huge amount of very im­port­ant the­ory, in­clud­ing the ideas of poly­no­mi­al-time, NP-com­plete, ex­po­nen­tial-time, etc. The idea grew that a poly­no­mi­al-time al­gorithm would al­ways be bet­ter than an al­gorithm with, say, worst-case ex­po­nen­tial time.

For years people be­lieved that the sim­plex meth­od must be worst-case ex­po­nen­tial, but there was no ex­ample. Then, in the 1970s, Klee and Minty gave an ex­ample where, on a prob­lem with \( n \) vari­ables, the sim­plex meth­od takes \( 2^{n-1} \) steps.6 That was the worst case. But people who routinely solved large lin­ear pro­grams had ob­served that in prac­tice sim­plex be­haves like a poly­no­mi­al-time meth­od — in prac­tice it takes \( 2n \) or \( 3n \) it­er­a­tions. It’s very puzz­ling, a huge gap between the­ory and prac­tice.

For at least a dec­ade people tried to find a poly­no­mi­al-time al­gorithm for lin­ear pro­gram­ming. Sev­er­al at­tempts turned out to be wrong. This all changed in 1979. Le­onid Khachiy­an, in the So­viet Uni­on, was work­ing on vari­ous al­gorithms for non­lin­ear prob­lems that had been de­veloped earli­er in the So­viet Uni­on. He came up with what turned out to be a poly­no­mi­al-time lin­ear pro­gram­ming al­gorithm.7 It was a big story on the front page of the New York Times.8 Re­mem­ber, the So­viet Uni­on was our en­emy — and they had this al­gorithm. The press went wild and pub­lished stor­ies about how the Rus­si­ans would be able to crack our codes, which was com­plete non­sense.9

Re­port­ers were call­ing George of course, be­cause they wanted his com­ments. He didn’t want to talk to them, so one of them got me. The re­port­er asked, “Can you tell me in simple terms what a poly­no­mi­al-time al­gorithm is?” I said, “Do you know what a poly­no­mi­al is?” He said no, so I said, “Okay, let’s take \( x^2 \) and \( x^3 \)…”. And he said, “That’s too hard! I think poly­no­mi­al-time means really, really fast.” I said, “Ac­tu­ally it doesn’t mean really, really fast.” He said, “Well, that’s what I’m go­ing to put in my story!” He missed his chance to have the defin­i­tion of a poly­no­mi­al!

Lots of people, in­clud­ing the Gang of Four, star­ted im­ple­ment­ing Khachiy­an’s al­gorithm and run­ning it on a vari­ety of lin­ear pro­grams. Sim­plex was al­ways much, much faster. We knew the Klee–Minty ex­ample showed that sim­plex was ex­po­nen­tial-time in the worst case, but on a stand­ard­ized test set of lin­ear pro­gram­ming prob­lems, Khachiy­an’s al­gorithm was slower. This was a case where the “fast” al­gorithm in the­ory, Khachiy­an’s, was slower than the “slow” al­gorithm. You’ll still meet people from the­or­et­ic­al com­puter sci­ence who will say, “Isn’t there a poly­no­mi­al-time al­gorithm from Khachiy­an that’s al­ways faster than the sim­plex meth­od?” You just have to throw up your hands!

Then in 1984, Nar­en­dra Kar­markar of Bell Labs an­nounced a poly­no­mi­al-time al­gorithm for lin­ear pro­gram­ming that was sup­posedly 50 times faster than the sim­plex meth­od on every prob­lem. That’s a dra­mat­ic state­ment. That was also on the front-page of the New York Times, as Ron Gra­ham says, “above the fold.”10

Jack­son: Was Ron Gra­ham be­hind the huge pub­li­city for Kar­markar’s work?

Wright: I would guess so. Ron is a great math­em­atician, a great sci­ent­ist. At the time he was a high-level man­ager in the Math­em­at­ics Re­search Cen­ter at Bell Labs. And he is a mas­ter of pub­li­city. He can take an ap­par­ently dry top­ic in math­em­at­ics and gen­er­ate a huge amount of pub­lic in­terest in it.

There were news art­icles all over, in­clud­ing in Time magazine, all fea­tur­ing the 28-year-old Nar­en­dra Kar­markar. By the way, Khachiy­an had also been 28 when he an­nounced his al­gorithm, so people were talk­ing about “the ma­gic age, 28.”

George was fas­cin­ated to learn about Kar­markar’s work (and also about Khachiy­an’s) be­cause George loved lin­ear pro­gram­ming. So he in­vited Kar­markar to speak at Stan­ford. But Kar­markar was be­ing very cagey. He said the al­gorithm was AT&T pro­pri­et­ary, so he could not give de­tails. In his talk, he wrote a few equa­tions on the board and just made a few com­ments.

Now, the Gang of Four — Philip, Wal­ter, Mi­chael, and I — no­ticed that the equa­tions Kar­markar wrote down had the same format as the equa­tions in a bar­ri­er meth­od. One of us said, “That looks like a bar­ri­er func­tion.” People have asked us which one of us figured that out. But it was a group thing. I did my thes­is on bar­ri­er meth­ods, Wal­ter gave me my thes­is prob­lem, Philip knew all about it, Mi­chael knew all about it. Any one of us could have said this, and we don’t re­mem­ber who it was. But it got said: This looks like a bar­ri­er func­tion.

So we and John Tom­lin (of Ket­ron) star­ted work­ing on this. Kar­markar’s meth­od, which is called an in­teri­or-point meth­od, was be­ing presen­ted as something brand-new. Claims were be­ing made that Kar­markar’s meth­od was con­sist­ently much faster than the sim­plex meth­od on large lin­ear pro­grams. On the oth­er hand, re­mem­ber­ing what had happened with Khachiy­an’s meth­od, many ex­perts in lin­ear pro­gram­ming be­lieved that the sim­plex meth­od would al­ways be faster.

In the midst of this con­tro­versy, in Au­gust 1985 I gave a talk at the Math­em­at­ic­al Pro­gram­ming Sym­posi­um, a ma­jor con­fer­ence in op­tim­iz­a­tion held that year at MIT, about our work on Kar­markar’s meth­od. Now, how did I hap­pen to give the talk? People have asked me that many times: “You’re the one people used to mis­take for the pro­gram­mer! How did you get to give this talk?” The an­swer is that Wal­ter was ori­gin­ally in­vited to give this talk, and then something came up and he couldn’t go. Mi­chael and Philip then agreed that I should give the talk, which we worked on to­geth­er late in­to the night be­fore.

The room was packed. I said that we had shown, first, that there was an equi­val­ence between Kar­markar’s in­teri­or-point meth­od and bar­ri­er meth­ods.11 Most of the audi­ence had nev­er heard of bar­ri­er meth­ods be­cause they had gone out of style, and this res­ult was a sur­prise to many. But the nu­mer­ic­al res­ults were what aroused the strongest emo­tion. In our ex­tens­ive com­pu­ta­tion­al tests on a large suite of lin­ear pro­grams, re­cog­nized as a “fair” com­par­is­on, the res­ults were split — some­times the Kar­markar meth­od was faster, some­times sim­plex was faster. Why was this dra­mat­ic? Be­cause the sim­plex de­votees in the audi­ence were up­set that a “non­lin­ear” meth­od (Kar­markar) could be com­pet­it­ive with the sim­plex meth­od. And the Kar­markar fans were ab­so­lutely con­vinced that his new al­gorithm must al­ways be faster than the sim­plex meth­od. So neither group was happy. Many audi­ence mem­bers came up to me af­ter­ward and star­ted yelling and com­plain­ing. It was quite ex­cit­ing.

What about today? Bob Bixby, from Rice Uni­versity, is one of the world’s lead­ing ex­perts on com­pu­ta­tion­al lin­ear pro­gram­ming. I see Bob about once a year, and I ask him, “Which is bet­ter, sim­plex or bar­ri­er?” And the an­swer is: sim­plex is bet­ter some of the time, and bar­ri­er is bet­ter some of the time.

So that quo­ta­tion from the Spiel­man–Teng pa­per is still true. And no one knows ex­actly which meth­od is bet­ter for which lin­ear pro­gram­ming prob­lem. In oth­er parts of nu­mer­ic­al ana­lys­is, we know that if a prob­lem is of a cer­tain type, you should use Meth­od A, and if it’s of an­oth­er type you should use Meth­od B. But not for lin­ear pro­gram­ming.

Jack­son: It’s still not un­der­stood.

Wright: I still meet people who say, “Well surely no one uses the sim­plex meth­od any­more.” And I say, “Yes, they do!”

For com­plete­ness, I have to men­tion that that pa­per of Spiel­man and Teng, which is on smoothed ana­lys­is of al­gorithms, is fant­ast­ic. They prove that, in the con­text of smoothed ana­lys­is, the sim­plex meth­od is poly­no­mi­al-time. Both of them have been showered with hon­ors, de­servedly so, for that ana­lys­is.

The interior-point revolution

Jack­son: AT&T said that Kar­markar’s work was pro­pri­et­ary. How did you find out enough about it to work out the equi­val­ence to bar­ri­er meth­ods?

Wright: Kar­markar’s early talks were typ­ic­ally titled something like, “The New Age of Lin­ear Pro­gram­ming,” and al­most nev­er con­tained any equa­tions. So when he spoke at Stan­ford, he was asked many ques­tions and wrote a few sparse equa­tions on the board. But one of these was the equa­tion for find­ing the next step in the it­er­a­tion defined in his meth­od. That’s the one that looked like the equa­tions that came up in bar­ri­er meth­ods. It’s a di­ag­on­al mat­rix and each di­ag­on­al ele­ment is 1 over the squared val­ues of the con­straints. That made us think that his meth­od was con­nec­ted with bar­ri­er meth­ods. Soon there­after, he pub­lished a pa­per that in­cluded a few equa­tions.

So we talked about it and worked through it. It’s not dif­fi­cult, I have to say. One of the things that was stated fre­quently at the be­gin­ning of the pub­li­city was that no one would un­der­stand the math­em­at­ics of this for ten years. Well, it doesn’t take very long to fig­ure it out, once you know it’s there. It wasn’t deep, new math­em­at­ics. Now, once it was known, Nes­ter­ov and Nemirovskii, two people ori­gin­ally from the So­viet Uni­on, wrote a beau­ti­ful book about the the­ory of bar­ri­er meth­ods.12 That was deep math­em­at­ics.

To com­plete the circle in a way, in 1996 Kurt An­streich­er wrote a pa­per about SUMT, Se­quen­tial Un­con­strained Math­em­at­ic­al Tech­nique.13 SUMT refers to a class of meth­ods (pen­alty and bar­ri­er func­tions) and to a widely used soft­ware pack­age dat­ing from the 1960s. His pa­per proved that SUMT is a poly­no­mi­al-time al­gorithm for lin­ear pro­gram­ming. People had spent years des­per­ately try­ing to find poly­no­mi­al-time meth­ods, and this one was there all the time. They just didn’t have the right per­spect­ive.

In­teri­or-point meth­ods are now a whole field, and re­search on bar­ri­er meth­ods led to the field of semi­def­in­ite pro­gram­ming. Kar­markar’s work really changed op­tim­iz­a­tion in a big way.14

Jack­son: Can you tell me more about the im­pact of the equi­val­ence between bar­ri­er meth­ods and Kar­markar’s in­teri­or-point meth­ods?

Wright: Giv­en the date of his PhD, Kar­markar would not have been taught about bar­ri­er meth­ods, whose hey­day was in the 1960s. As I men­tioned, by the mid-1970s they were con­sidered fatally flawed. When I fin­ished my thes­is on bar­ri­er meth­ods in 1976, Wal­ter and I wrote a pa­per about a bar­ri­er meth­od. This was my first ex­per­i­ence try­ing to get a pa­per pub­lished. One of the ref­er­ees wrote: “I can’t be­lieve any­one would waste their time on a use­less meth­od that is not worth wor­ry­ing about.” That was of course very dev­ast­at­ing to me, that this per­son com­pletely dis­missed this part of my thes­is. When Kar­markar’s res­ults came in 1984, no one was think­ing about bar­ri­er meth­ods. Once people star­ted think­ing about them, the floodgates opened.

Bar­ri­er meth­ods had been pro­posed in the 1960s ori­gin­ally for non­lin­early con­strained op­tim­iz­a­tion. After Kar­markar’s work was con­nec­ted to bar­ri­er meth­ods, people star­ted to look for gen­er­al­iz­a­tions, such as op­tim­iz­a­tion sub­ject to con­straints in­volving a mat­rix — for ex­ample, the mat­rix must be pos­it­ive semi­def­in­ite. This activ­ity con­tin­ues today.

People used to teach lin­ear pro­gram­ming and the sim­plex meth­od, and that was it. Today, if you don’t teach New­ton’s meth­od and bar­ri­er meth­ods, you are not do­ing a good job. It’s part of the field now.

Let me just say that George Dantzig, bless his heart, was very ex­cited about all the de­vel­op­ments around in­teri­or-point meth­ods. He was quoted as say­ing something like, “I’d give 20 years of my life to be around as a young per­son now and work on this.” It would have been a whole new out­look for him.

From theorems to algorithms to software

Jack­son: The Gang of Four did everything. You proved the­or­ems, you de­signed al­gorithms, you wrote soft­ware. It is un­usu­al to have four people work­ing so closely.

Wright: It was un­usu­al. We agreed we would write all our pa­pers with all four names, in al­pha­bet­ic­al or­der. Philip Gill of course favored that! I said, “I’m go­ing to change my name to Aard­vark, then I’ll get to be first!”

But there was no oth­er way to do it. We all knew that if we tried for every pa­per to ask, Who did the ma­jor­ity of the work?, then we would all hate each oth­er pretty soon. We thought that keep­ing the four names, al­ways in the same or­der, was a very good policy, but it some­times led to mis­un­der­stand­ings out­side the Gang.

Jack­son: Do you have a fa­vor­ite ex­ample of some work the Gang of Four did, in which you proved the­or­ems, came up with al­gorithms, and then wrote soft­ware?

Wright: There is a class of meth­ods called se­quen­tial quad­rat­ic pro­gram­ming (SQP) meth­ods, in which a non­lin­early con­strained prob­lem is solved by con­struct­ing a se­quence of quad­rat­ic pro­grams (quad­rat­ic ob­ject­ive, lin­ear con­straints). In con­trast, pen­alty and bar­ri­er func­tions gen­er­ate a se­quence of un­con­strained prob­lems. Bob Wilson, of the Stan­ford busi­ness school, pro­posed SQP meth­ods for con­vex pro­gram­ming in his PhD thes­is in 1963. At that time, people said that such a meth­od would nev­er work and would be far too ex­pens­ive. But we wanted to de­vel­op some the­ory about SQP meth­ods and also to write code, be­cause pro­gram­ming them was tricky. So the Gang of Four worked to­geth­er on that. The code is called NPSOL, for “Non­lin­ear Pro­gram­ming Solu­tion” or “Non­lin­ear Pro­gram­ming at SOL”. If you think writ­ing pa­pers to­geth­er is com­plic­ated, writ­ing code to­geth­er is al­most im­possible! But we man­aged. Stan­ford set up a pro­ced­ure through which people could li­cense NPSOL, and it be­came very widely used and gen­er­ated roy­al­ties.

Jack­son: Where did NPSOL end up get­ting used?

Wright: Com­pan­ies that use op­tim­iz­a­tion, like Boe­ing and oil com­pan­ies, were prob­ably the biggest cus­tom­ers. Jet Propul­sion Labor­at­ory also used it. It was ba­sic­ally free for aca­dem­ic pur­poses, and the price was reas­on­able through the Stan­ford li­cens­ing agree­ment.

Jack­son: In 1981, you, Philip Gill, and Wal­ter Mur­ray wrote the now-clas­sic book Prac­tic­al Op­tim­iz­a­tion.15 What was the mo­tiv­a­tion be­hind that book?

Wright: What of­ten happened is that people would want to use NPSOL, and then one of us would have to give them lec­tures about op­tim­iz­a­tion. So after we had worked on NPSOL, one of us said that we should write a book sum­mar­iz­ing our ex­per­i­ences.

Mi­chael didn’t want to work on the book be­cause he had too many oth­er things to do — and prob­ably be­cause he knew how many ar­gu­ments we would have! The rest of us did not fully grasp how hard it was go­ing to be, so we went ahead.

Did you know that this was the second book ever pub­lished with \( \mathrm{\TeX} \)?

Jack­son: No, I didn’t know that.

Wright: [Don­ald] Knuth’s was the first, of course. I heard about \( \mathrm{\TeX} \) be­cause I went to a lot of talks in the com­puter sci­ence de­part­ment. I thought we should do the book in \( \mathrm{\TeX} \) be­cause we didn’t have a good sec­ret­ary to do tech­nic­al typ­ing. Us­ing \( \mathrm{\TeX} \) was dif­fi­cult then: you had to cre­ate the text, com­pile it, wait to print it all (slowly) on a roll of pa­per, cor­rect mis­takes, and re­peat — a te­di­ous pro­cess. But it was worth it be­cause we were in con­trol.

For the cam­era-ready copy, we were very lucky. There was a high-res­ol­u­tion print­er in the com­puter sci­ence de­part­ment called the Al­pha­type. Print­ing on the Al­pha­type was ex­pens­ive and com­plic­ated, but we knew a help­ful un­der­gradu­ate who agreed (with Knuth’s per­mis­sion) to print our pages out in the middle of the night. I re­cently read a let­ter writ­ten by Knuth about the early days of \( \mathrm{\TeX} \), in which he de­scribed how he was “pleas­antly sur­prised” to dis­cov­er pages from Prac­tic­al Op­tim­iz­a­tion near the Al­pha­type. He did not know at the time who was writ­ing those pages!

It was very ex­cit­ing to be early users of \( \mathrm{\TeX} \); we could nev­er have done the book without it. Knuth should win every prize in the world for cre­at­ing \( \mathrm{\TeX} \) and en­han­cing the work of writers.

Jack­son: And giv­ing it out for free, from the very be­gin­ning.

Wright: Yes, ab­so­lutely.

Bell Labs: Open doors, open discussions

Jack­son: To re­turn to the timeline — you worked for twelve years at the Sys­tems Op­tim­iz­a­tion Lab. Then in 1988 you moved to Bell Labs. I’m won­der­ing how you made that trans­ition.

Wright: At some point I star­ted think­ing I should leave SOL, be­cause I felt that no one out­side Stan­ford knew who I was. There were the four of us work­ing to­geth­er, which was great, but I thought, in 20 years do I still want to be do­ing this? We did not want to change to hav­ing single-au­thored pa­pers. Wal­ter was a re­search pro­fess­or, and the rest of us were re­search as­so­ci­ates. At the time at Stan­ford, only one per­son per de­part­ment could be a re­search pro­fess­or. We talked to the chair of the OR de­part­ment and asked if we could all be re­search pro­fess­ors. He said it was im­possible, and that was that.

So you can see, our situ­ation posed this op­tim­iz­a­tion prob­lem, of mak­ing us all in­di­vidu­ally happy while main­tain­ing the struc­ture we had set up. It just wasn’t go­ing to work. Leav­ing was heart­break­ing, but in the end it was a good thing.

I’ve talked to young wo­men who were in the same ex­act situ­ation, mean­ing they have a re­search soft-money po­s­i­tion that they really like, but they are not go­ing to get pro­moted at their uni­versity. It doesn’t both­er them at the be­gin­ning, and it both­ers them later. That is what happened to me. And it wasn’t clear at all that the OR de­part­ment cared about hav­ing wo­men fac­ulty. Stan­ford around that time made a big pub­lic an­nounce­ment that they’d hired six wo­men in the en­gin­eer­ing school. I think only one of those six got ten­ure. It’s not dis­sim­il­ar to the way things still are. They say, “We care deeply about this” — it’s like when you make a call and you get a ma­chine and it says “Your call is very im­port­ant to us.” You think, If it were very im­port­ant, a per­son would an­swer the phone!

When I thought about leav­ing SOL, I made some dis­creet in­quir­ies, and in the end I in­ter­viewed ser­i­ously at Wis­con­sin, in the com­puter sci­ence de­part­ment, and at Bell Labs. I had of­fers from both. Wis­con­sin was won­der­ful. I ag­on­ized over this. Should I go to this great uni­versity, or should I go to an in­dus­tri­al lab, which I had no ex­per­i­ence of? Fi­nally I said, I’ll see what Bell Labs is like. And it was in­deed won­der­ful.

My of­fer came in 1986, and I asked to stay a few months at Stan­ford be­cause Philip, Wal­ter, and I were try­ing to fin­ish our second book.16 It took a lot longer than that. Fi­nally, in Feb­ru­ary of 1988, on Pres­id­ent’s Day hol­i­day, I went to Bell Labs. I knew people there, so it wasn’t like go­ing in­to a com­pletely un­known situ­ation. And I had taken leave from Stan­ford, so I could go back if I wanted. Still, it was scary. But once I was at Bell Labs, I real­ized that this was the place for me.

At that point, my daugh­ter was 20 and a col­lege stu­dent. My hus­band and I had broken up. So it seemed like a good time to go, in the sense that I wasn’t dis­rupt­ing any­body else’s life.

Jack­son: What did you ex­per­i­ence of the le­gendary at­mo­sphere of Bell Labs?

Wright: How can I say this? I am ba­sic­ally a goody two-shoes. I try to fol­low the rules, prob­ably too much so. I’m kind of a nerd — not a wild and crazy nerd but a goody two-shoes nerd. I was im­me­di­ately struck by how dif­fer­ent things were at Bell Labs.

Not long after I ar­rived, a vis­it­or was giv­ing a talk to a small audi­ence, maybe 15 people. I have to say, the speak­er was totally bor­ing. About five minutes in­to the talk, a couple of the Bell Labs people just got up and left. They didn’t try to sneak out dis­creetly, they just got up and left. I was shocked! I stayed, of course. Af­ter­wards, I said, “I can’t be­lieve that people walked out.” One of my col­leagues, who is not a nasty, mean per­son, said, “The talk was bor­ing, they have bet­ter things to do, they just left. What’s the prob­lem?” At Stan­ford it was much more po­lite. You just wouldn’t walk out of a talk.

Every once in a while there would be a meet­ing where a top man­ager would speak and people from the sci­entif­ic end, from Bell Labs, were in­vited. And they gave that man­ager a hard time! They’d say, “Wait a minute, this is a really stu­pid idea! Why are you do­ing this?” No one seemed to mind it. Lively ques­tion­ing was al­ways en­cour­aged at Bell Labs — it took me a while to get used to be­ing free to speak out.

People’s doors were al­ways open. Col­leagues would come in with an idea, write something on the board and say, “What do you think?” We didn’t do that at Stan­ford, be­cause the Gang of Four were work­ing to­geth­er, so we ten­ded to talk to each oth­er. There was al­ways the pos­sib­il­ity that stu­dents would come by and want to ask ques­tions about home­work, so my door was closed at least half the time. At Bell Labs, the doors were open, and people were al­ways avail­able for a tech­nic­al dis­cus­sion.

There were 14 per­cent wo­men among the mem­bers of tech­nic­al staff. I no­ticed early on a dif­fer­ence in ap­proach between men and wo­men. Sev­er­al of the men would drop by and say, “I’ve got this great idea, isn’t it ter­rif­ic?” The wo­men ten­ded to be much more guarded. Sev­er­al of my fe­male col­leagues no­ticed the same thing, we talked about it, and even­tu­ally agreed that it’s okay to be openly pos­it­ive about one’s own work. So be­ing at Bell Labs made me a bit more out­go­ing. The “good little girl” does not al­ways get re­cog­nized.

A method from the vegetable research station

Jack­son: Can you ex­plain what dir­ect-search meth­ods are, and in par­tic­u­lar what the Neld­er–Mead al­gorithm is?

Wright: First I’ll tell you about a wire­less pro­ject I worked on called WISE. That was one of the most fun things I worked on at Bell Labs.

In the Com­put­ing Sci­ence Re­search Cen­ter at Bell Labs, people’s job was to do good re­search. It was not to con­trib­ute ex­pli­citly to the com­pany’s bot­tom line. We were sup­posed to pub­lish, go to con­fer­ences, give talks, etc. But if we did want to talk to people who had real prob­lems to solve, Bell Labs was very happy about and wel­comed that.

My dir­ect­or at the time, Ravi Sethi, happened to talk to an AT&T ex­ec­ut­ive who worked on wire­less sys­tems. The ques­tion was where to put wire­less base sta­tions in a build­ing, in or­der to op­tim­ize cov­er­age. This was 20 years ago, be­fore, for ex­ample, cell phones were in wide use. Ravi talked about this prob­lem to me and oth­ers in Bell Labs, in­clud­ing Bri­an Kernighan, a well-known com­puter sci­ent­ist; Dav­id Gay, who also worked in op­tim­iz­a­tion; Steve For­tune, who worked in com­pu­ta­tion­al geo­metry; and Re­in­aldo Valen­zuela, a wire­less en­gin­eer. It took sev­er­al meet­ings be­fore we figured out how to for­mu­late what was needed and what skills were re­quired. The as­so­ci­ated pro­ject needed, of course, to have a cute name, so it was called WISE (“wire­less sys­tems en­gin­eer­ing”).

The ob­vi­ous first ques­tion: How do you define cov­er­age? And how do you cal­cu­late it? You need to cal­cu­late the power that’s re­ceived at any giv­en point in the build­ing. Steve real­ized that you need to use the struc­ture of the build­ing, be­cause walls are made of vari­ous ma­ter­i­als, and ra­dio waves are gov­erned by phys­ic­al laws de­scrib­ing how waves bounce off ob­jects and re­flect. Steve worked on that, and Bri­an worked on writ­ing bril­liant code and design­ing the user in­ter­face, be­cause they wanted to be able to show cus­tom­ers ex­actly what cov­er­age they would get.

What about the op­tim­iz­a­tion? Well, this was a very com­plic­ated func­tion, as you can ima­gine. Here’s a build­ing, here’s a pic­ture of the walls, here are some ra­dio waves boun­cing around. You can’t just write down a for­mula. When you use com­pu­ta­tion­al geo­metry to cal­cu­late the power that’s re­ceived, it doesn’t come out to be a nice, dif­fer­en­ti­able func­tion. That was the key point. We needed to op­tim­ize it, but we didn’t have a math­em­at­ic­al form for the func­tion.

I had nev­er pre­vi­ously been in­ter­ested in op­tim­iz­a­tion meth­ods that don’t use de­riv­at­ives, i.e., you are op­tim­iz­ing a func­tion that you can cal­cu­late, but you do not have its de­riv­at­ives. When I gave a talk about this work at the 1995 Dun­dee Meet­ing in Nu­mer­ic­al Ana­lys­is, I tried to in­tro­duce a dis­tinc­tion between what I called mod­el-based meth­ods and dir­ect-search meth­ods. With a mod­el-based meth­od, you make a math­em­at­ic­al mod­el of the ob­ject­ive func­tion, and then you use the de­riv­at­ive of the mod­el to ap­prox­im­ate the de­riv­at­ive of the func­tion. What I called dir­ect-search meth­ods were those that do not “in their heart” cal­cu­late de­riv­at­ives. I ac­tu­ally wrote that in a pa­per!17

The WISE pro­ject led me to the Neld­er–Mead meth­od, a dir­ect-search meth­od that does not build a mod­el of the func­tion. It has a cer­tain set of ma­nip­u­la­tions that it per­forms on the points you’ve ob­served, or where you’ve eval­u­ated the func­tion. Neld­er and Mead, sadly no longer with us, were stat­ist­i­cians in the UK. They worked at the Na­tion­al Ve­get­able Re­search Sta­tion, which is a name that many people find hil­ari­ous! But when you think about the im­port­ance of stat­ist­ics in ag­ri­cul­ture, it makes sense.

Neld­er and Mead pub­lished their meth­od in 1965 and called it “the sim­plex meth­od.”18 Ap­par­ently they either didn’t know about the Dantzig sim­plex meth­od or didn’t think it was im­port­ant to say theirs was dif­fer­ent. So that is of­ten con­fus­ing.

It’s in­ter­est­ing that the Neld­er–Mead meth­od was pub­lished in The Com­puter Journ­al, a very pres­ti­gi­ous journ­al. At that time, you could pub­lish pa­pers that said — and this is what Neld­er and Mead ba­sic­ally did — “We have thought of this meth­od, here is an ex­ample, and it works well on these prob­lems.” Peri­od. No proof, no lemma, no the­ory. But their meth­od was in­cred­ibly ef­fect­ive and worked really well. It was (and is still) widely used and ex­tremely pop­u­lar. Oth­ers had writ­ten about it, but as far as I could find, ex­ist­ing the­ory was not about the ori­gin­al meth­od, but rather about mod­i­fied ver­sions.

Be­ing a math­em­atician, I thought there’s got to be some the­ory about the ori­gin­al meth­od, we just need to find it. So in ad­di­tion to de­vel­op­ing a spe­cial­ized ver­sion of Neld­er–Mead that we used for WISE, I hoped to prove, if pos­sible, some res­ults about the ori­gin­al meth­od. Jeff Lagari­as, a bril­liant math­em­atician who was at Bell Labs, and I star­ted to talk about it.

One of the great things about Bell Labs, as it then was, was that you could walk up one flight of stairs, or over to an­oth­er build­ing, and there would be a lead­ing world ex­pert in the area you were in­ter­ested in. And you were en­cour­aged to talk to each oth­er. That’s why I’ve de­scribed Bell Labs as para­dise.

I was a friend of Jeff’s, and we got in­ter­ested in the Neld­er–Mead meth­od. The meth­od can be de­scribed on one piece of pa­per with a few fig­ures. And you think, How hard can this be? Turns out it was hard.

A clever counterexample

Wright: I gave my talk in Dun­dee and said that Jeff and I hoped to prove con­ver­gence of Neld­er–Mead for strictly con­vex func­tions. In the audi­ence — I loved what happened! — was Ken McKin­non (from Ed­in­burgh). He raised his hand and said, “I think I have a counter­example to that.” Thank God I didn’t say “we proved this”! I was sur­prised, but I said: Okay. Ken said he would bring it in the next day.

Jack­son: Had he already thought of that counter­example?

Wright: I don’t know. He may have thought of it on the spot; he is very smart. He must be one of the few people in the whole world who taught the Neld­er–Mead meth­od in his op­tim­iz­a­tion class. So he knew it very well.

He came the next day, and by gosh, he had a counter­example, the McKin­non counter­example, as it is known — very clev­er, in two di­men­sions, strictly con­vex, con­tinu­ously dif­fer­en­ti­able. I was ac­tu­ally happy he had done that, al­though I wished we had thought of it!

Jeff and I had some nice res­ults that made the the­ory more tidy. We agreed that we would try to pub­lish two pa­pers in the SIAM Journ­al on Op­tim­iz­a­tion: Ken’s pa­per with the counter­example, and then a pa­per by Jeff and me, plus Paul Wright and Jim Reeds, who also worked at Bell Labs and who had talked to us about the prob­lem.19

Des­pite the counter­example, Neld­er–Mead works well in prac­tice. The ques­tion re­mained, What can you say about the Neld­er–Mead meth­od?

Bjorn Poon­en was a sum­mer in­tern in the Math Cen­ter at Bell Labs, and Jeff talked to him about Neld­er–Mead. Bjorn said he thought we could give a con­ver­gence proof for Neld­er–Mead for two-di­men­sion­al prob­lems that sat­is­fy cer­tain very strict con­di­tions. Then I left Bell Labs, Bjorn went to Berke­ley, and we still had not writ­ten this pa­per. It took a long time, and most of the delay was my strug­gling to try to fig­ure out one thing that I hoped we could prove. I nev­er could fig­ure that out, so fi­nally we wrote a pa­per.20

Jack­son: That ap­peared much later, in 2012.

Wright: Yes, much later. It ap­plies to an ex­tremely lim­ited prob­lem set: two vari­ables, strictly con­vex, bounded level sets, twice-con­tinu­ously dif­fer­en­ti­able, pos­it­ive def­in­ite Hes­si­an. That does not fit prac­tic­al prob­lems, does it? It didn’t help any­body solve real-world prob­lems, but it was a miss­ing piece in the the­ory, and that’s why it was im­port­ant.

I kept try­ing to un­der­stand the Neld­er–Mead meth­od. I still haven’t suc­ceeded. You can run so many prob­lems on it, not just in two di­men­sions, and it will work bril­liantly. I know there is some math­em­at­ic­al prop­erty that, if we could only find it, would ex­plain how it does so well.

At the SIAM meet­ing at Stan­ford in 1997, I de­cided to or­gan­ize a ses­sion where George Dantzig and John Neld­er would talk about the two sim­plex meth­ods. We took a great pic­ture of Dantzig and Neld­er to­geth­er. It has a cer­tain sweet­ness, be­cause George Dantzig was fairly short and John Neld­er was very tall.

Ro­ger Mead had been at the Uni­versity of Read­ing in the UK. When I gave a talk there, nat­ur­ally I wanted to meet him. He had re­tired and had no idea that his meth­od had 20,000 cita­tions! Today it has more than 30,000!21

John Nelder (left) and George Dantzig, at the 1997 SIAM meeting at Stanford.
Photo courtesy of Margaret Wright.

Jack­son: Your pa­per with Lagari­as and Poon­en uses meth­ods from dis­crete dy­nam­ic­al sys­tems. Does that come out of left field, the use of dis­crete dy­nam­ic­al sys­tems here?

Wright: No one else had taken this view, so yes! That was Jeff’s in­sight. You can look at the pic­tures that go with Neld­er–Mead — for ex­ample, there are web sites with ap­plets that run Neld­er–Mead, and in some sense they look like dis­crete dy­nam­ic­al sys­tems.

How did Neld­er and Mead think of the meth­od? I asked both of them about this, and they said, “Well, you look at the points, and you see which one is the worst, and then you move away from it to a new point.” That makes sense, right? You do it in a struc­tured way, with a sim­plex in \( n \) di­men­sions, and, there you go. But the moves are not ob­vi­ous.

Jack­son: There is a lot of geo­met­ric in­tu­ition there, maybe based on the con­tact with prac­tic­al prob­lems, like the ones they must have had at the Ve­get­able Re­search Sta­tion.

Wright: It was in­deed in­tu­ition about real-world prob­lems. In the UK in the early 1960s, most of the work in op­tim­iz­a­tion was about meth­ods that were prac­tic­al. Plus Neld­er and Mead both stressed that their main in­terest was stat­ist­ics.

I don’t have good geo­met­ric in­tu­ition. I am ter­rible in three-di­men­sion­al geo­metry, for ex­ample. Steve For­tune used to think it was hil­ari­ous be­cause he would sketch a three-di­men­sion­al fig­ure, and I would say, “I can’t un­der­stand that.”

Jack­son: So what kind of in­tu­ition do you have? How would you char­ac­ter­ize it?

Wright: Al­geb­ra­ic. Lin­ear al­gebra, with a mat­rix that is ill-con­di­tioned, with a sin­gu­lar value de­com­pos­i­tion, where you have the sin­gu­lar vec­tors and the sin­gu­lar val­ues. The ei­gen­decom­pos­i­tion. You are in \( n \) di­men­sions, but you have a mat­rix, and you can look at it and you can fig­ure out what its product with a vec­tor is go­ing to be like. That’s what my in­tu­ition is.

Academia is different

Jack­son: Can you tell me about the cir­cum­stances of your go­ing to NYU?

Wright: Be­cause of the 1995 split of AT&T in­to Lu­cent and NCR, Bell Labs be­came much more fo­cused on busi­ness. This is not to blame any­body. It was just dif­fer­ent. AT&T went from hav­ing very little com­pet­i­tion to hav­ing a lot of com­pet­i­tion. So the people at Bell Labs star­ted be­ing pushed to work on busi­ness-re­lated top­ics. Also, be­cause of the split, the math cen­ter went to AT&T and the com­puter sci­ence cen­ter stayed at Lu­cent. Many of my col­leagues were sud­denly in dif­fer­ent loc­a­tions.

This was a very tense time, 2001, 2002. Be­fore the split, hardly any­body ever left Bell Labs. After the split, every­body wondered, Should we leave? Nearby were New York City, IBM, Rut­gers Uni­versity, and so on, but there wer­en’t enough jobs at the right level for every­one in the com­puter sci­ence cen­ter, which was about 60 people. And we all wanted to stay to­geth­er. We had tre­mend­ous loy­alty to each oth­er. It’s corny to say it, but we loved our cen­ter.

At some point Bri­an Kernighan said he was leav­ing to be a pro­fess­or at Prin­ceton. That was the first chip in the wall. Once word gets out that someone is leav­ing, people start get­ting in touch, and that’s what happened to me. Around that time, I got a call from Dave McLaugh­lin, who was then dir­ect­or of the Cour­ant In­sti­tute. They needed a chair for the com­puter sci­ence de­part­ment. I wasn’t really in­ter­ested in be­ing chair, but that’s what the po­s­i­tion was. Dave is won­der­ful — he said, “Mar­garet, just vis­it us. No com­mit­ment, just come and see.” So I did. I knew people there, and it was a great group. I was very close to go­ing to an­oth­er school, but I thought, I love New York City. It’s the Cour­ant In­sti­tute. I’ll go to NYU.

Jack­son: Was that a dif­fi­cult trans­ition?

Wright: The trans­ition to de­part­ment chair was not dif­fi­cult for me in some sense, be­cause at Bell Labs I had been head of a de­part­ment of six people. But it was dif­fer­ent at NYU. I don’t think I am a hard-nosed per­son, but if someone is not do­ing what they are sup­posed to do, and you are their boss, I think you should have some power over them, to try to get them to do the right thing. At Bell Labs, I could fire people. That makes a dif­fer­ence — even if I didn’t fire them, they knew I had that power. But a ten­ured fac­ulty mem­ber ba­sic­ally can­not be fired. The de­part­ment chair can say, “I want you to do this,” and the fac­ulty mem­ber can just reply, “I don’t want to do that.”

Soon after I went to NYU, there was a re­cep­tion for new fac­ulty in arts and sci­ences, and the pres­id­ent of NYU spoke. Every­one just stood there. No one was dis­respect­ful, no one in­ter­rup­ted. At Bell Labs, if a top ex­ec­ut­ive had a meet­ing, people would go, and they would listen and join in. Here, people just were not pay­ing any at­ten­tion. And I thought: This is a dif­fer­ent place.

Jack­son: An­oth­er dif­fer­ence is that you teach at NYU.

Wright: Right. I had prom­ised to stay at least three years as chair. I ne­go­ti­ated that I would not have to teach at first. I tend to throw my­self in­to teach­ing and spend a lot of time on it, and I figured I needed time to learn how to be chair.

Stu­dents make a big dif­fer­ence. In my first week as chair, I was sit­ting in my of­fice and a stu­dent came and said, “I’m in a class, and the pro­fess­or is be­ing totally un­fair to me.” She star­ted cry­ing. I was stunned. I had just met the fac­ulty mem­ber whom she was talk­ing about. When I con­tac­ted him, he said, “Oh, please. She’s fail­ing the class and try­ing every trick in the book to get her grade changed.” She had lied to me! And her lie was of course im­me­di­ately go­ing to be de­tec­ted. That shocked me. I real­ized then I would need to deal with a more com­plex en­vir­on­ment and a dif­fer­ent group of people.

Jack­son: Less ma­ture, many of them a lot young­er.

Wright: Right. And now I al­ways keep a box of Kleenex on my desk! There was an­oth­er fe­male stu­dent who was des­per­ately try­ing to get her grade changed to an A. The pro­fess­or told me she didn’t really de­serve an A, but he might do it be­cause he could not stand it when wo­men cried. So I said, “Send her to me.” I don’t care if you are a wo­man cry­ing, I’m not go­ing to change your grade. I thought it was in­ter­est­ing to learn how people re­act to cer­tain pres­sures.

Service to the profession: It’s fun

Jack­son: You have done an enorm­ous amount of ser­vice work. You re­ceived the Dis­tin­guished Pub­lic Ser­vice Award from the Amer­ic­an Math­em­at­ic­al So­ci­ety in 2002, and after that kept do­ing even more! In par­tic­u­lar, you served on two in­ter­na­tion­al pan­els to as­sess the math­em­at­ic­al sci­ences in the United King­dom. I am in­ter­ested to hear your ob­ser­va­tions about serving on those pan­els.

Wright: I was a mem­ber of the first pan­el, which was in 2006. Jean-Pierre Bour­guignon, the greatest chair in the world, was the chair of it. The United King­dom has what they call re­search coun­cils to fund sci­ence. The one that handles math­em­at­ics is called EPSRC, En­gin­eer­ing and Phys­ic­al Sci­ences Re­search Coun­cil. The EPSRC called for the in­ter­na­tion­al as­sess­ment. That was very in­ter­est­ing, and I learned a lot.

Four years later, an­oth­er in­ter­na­tion­al as­sess­ment was held, and the EPSRC asked me to be the chair. Peter Hall from Aus­tralia was the vice-chair. We had both been on the first as­sess­ment, so we put in­to ef­fect things that would make the new as­sess­ment more ef­fi­cient.

One of the things that al­ways hap­pens in such re­views is that the people be­ing re­viewed pre­pare ahead of time, and they fill the time telling you what they’ve done. The pan­el mem­bers of­ten end up be­ing frus­trated, be­cause they can’t ask the ques­tions they want to ask. So when I was chair of the pan­el, we tried as hard as we could to be ab­so­lutely ruth­less about hav­ing time for the pan­el’s ques­tions. Also, the pan­el felt it was es­sen­tial that we have a fairly long ses­sion without any­one there from EPSRC. That was not wel­comed by the EPSRC people, but they agreed.

Margaret Wright at the White House in 2006 to celebrate the awarding of National Medals of Science to Hy Bass (left) and Brad Efron (second to left). Wright served on the nominating committee. At right is Tony Chan, at the time serving as Assistant Director of Mathematical and Physical Sciences at the National Science Foundation.
Photo courtesy of Margaret Wright.

I was very happy with the re­view, and I think the com­mit­tee was too. The EPSRC was not happy with the re­view. I won’t go in­to de­tails, but the EPSRC was plan­ning to do things a cer­tain way, and the pan­el was pretty much un­an­im­ous in say­ing that we didn’t think what they were go­ing to do was a good idea.

The over­all point that the pan­el made was the unity of math­em­at­ics. You can’t plan the good re­search that will hap­pen, so it’s im­port­ant that all the people in math­em­at­ics re­spect and sup­port each oth­er, and the EPSRC should do the same. The EPSRC would have liked it much more if we’d di­vided math­em­at­ics up in­to little cat­egor­ies.

Jack­son: The EPSRC was hop­ing for some kind of pri­or­it­ized list of areas that would be good to sup­port?

Wright: Yes, of course they were.

Jack­son: What was the most fun you had in your pub­lic ser­vice?

Wright: Prob­ably the UK re­view I was the chair of, be­cause it was such a ter­rif­ic com­mit­tee. We had many en­joy­able times and good dis­cus­sions. We shared a sim­il­ar, very pos­it­ive view about math­em­at­ics and what should be done. So that was fun. It might seem weird to say it’s “fun”!

I would also say serving as pres­id­ent of SIAM was a lot of fun. It’s a great or­gan­iz­a­tion. We dis­cussed a lot of in­ter­est­ing is­sues, we star­ted the Com­munity Lec­ture for the gen­er­al pub­lic and Di­versity Day. I really en­joyed that.

I have en­joyed my com­mit­tee work be­cause I’ve met so many great people whom I would not have known oth­er­wise, be­cause they work in dif­fer­ent fields.

Visibility in the community key for women

Jack­son: I want to ask about your cur­rent thoughts on the status of wo­men in math­em­at­ics and com­puter sci­ence. How have things changed since you first entered these fields?

Wright: They have ob­vi­ously changed a lot. De­part­ment chairs used to say ex­pli­citly to wo­men, “We are not go­ing to pro­mote you be­cause you have a hus­band who will sup­port you, you don’t need the money, and we have this man who needs to get a big­ger raise than you do.” They would be very clear about it. It’s more subtle now, but I don’t think the prob­lem is fully solved. By “prob­lem” I mean that not every­one is treated fairly based on abil­ity and that there are some­times dif­fer­ent stand­ards. But it’s much bet­ter.

Cer­tain things have con­trib­uted to that, like hav­ing more wo­men on com­mit­tees. There is evid­ence that if you have a com­mit­tee to pick in­vited speak­ers that con­tains no wo­men, there are much less likely to be wo­men in­vited speak­ers, than if you have a wo­man on the com­mit­tee. Does this mat­ter? Yes, be­cause be­ing vis­ible in the com­munity as an in­vited speak­er makes a big dif­fer­ence. Sim­il­arly, be­ing vis­ible as the ed­it­or of a journ­al makes a dif­fer­ence. Gen­er­ally, put­ting wo­men in po­s­i­tions where they are vis­ible and which are signs of re­spect is very im­port­ant, and it hap­pens much more now. The more wo­men are in po­s­i­tions of power, I think the fairer it will get. Things are bet­ter but not ideal, and it will take a while be­fore they are ideal.

Jack­son: Do you have thoughts about why there are few­er wo­men in com­puter sci­ence than in math?

Wright: A huge amount of re­search, some con­tro­ver­sial, has been done about this. I don’t have any the­or­ies that are based on real data. One is­sue that was dis­cussed a lot in the com­puter sci­ence pro­gram at Carne­gie Mel­lon Uni­versity was that the in­com­ing male un­der­gradu­ates of­ten had been pro­gram­ming since high school or even ju­ni­or high school. The fe­males had not done any­thing like that. Is that be­cause the girls were not en­cour­aged? We don’t know.

Cer­tainly the tech fields have been dom­in­ated by men. People have asked me and oth­er wo­men com­puter sci­ent­ists, “What dif­fer­ence does it make if all the top people are men? If wo­men are de­term­ined and com­pet­it­ive, they should want to get in­to a field where there is no one like them.” I’m sorry, but most people would not do that. I’m pretty com­pet­it­ive, but I want a ca­reer that I en­joy and where I will be wel­come. I don’t think most people want to go in­to a field where no one would like them and they would be ig­nored or in­sul­ted.

Look at pic­tures in the news­pa­per of top ex­ec­ut­ives in tech­no­logy. It’s get­ting bet­ter, but for a long time it was 100 per­cent men. The press also loves the im­age of the re­bel­li­ous young pro­gram­mer wear­ing a T-shirt. They don’t think it’s very im­press­ive if you’re just a reg­u­lar per­son.

Jack­son: There is the ste­reo­type of a math­em­atician as some­body who’s ab­sorbed in his work to the point of be­ing isol­ated, with­drawn, even a bit crazy. That kind of be­ha­vi­or is not ac­cept­able in wo­men.

Wright: Right, and it’s sim­il­ar in com­puter sci­ence — the ste­reo­typ­ic­al com­puter sci­ent­ist is a little crazy. By the way, I feel com­fort­able in both fields!

I’m not very out­go­ing. I would be a ter­rible per­son in a job that re­quired a lot of so­cial­iz­ing. “You don’t want to come to the party, you just want to stay home and work?” someone might ask. “Yes,” I would say. In high school I was in the sci­ence club and the math club. These were not the “cool” people, the so­cial people — no, it was a bunch of nerds, be­fore be­ing a nerd be­came something great. Now people look up to nerds. Well, good, it’s about time!