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Maria Klawe Reflects on Her Career So Far, Part I

Maria Klawe

Haydee Lindo

Mark C. Wilson

Communicated by Notices Associate Editor Yvonne Lai

Background

At age 73, Maria Margaret Klawe is in the midst of a busy life and a very active career. Basic information can be found on her Wikipedia page. Most relevant to this interview, she is currently the president of Math for America, with previous appointments as president of Harvey Mudd College, dean at Princeton University, department head and dean at University of British Columbia, and manager at IBM Almaden Research Center. She is a Fellow of the AMS, ACM (of which she served as president), AAAS, and AWM, has been on the board of Microsoft, and has 21 honorary doctorates. Mark C. Wilson and Haydee Lindo interviewed her in early summer 2024. The interview has been lightly edited by all three people involved. Note: this article contains descriptions of physical abuse.

Interview

Q: When did you decide that mathematics was an essential part of your identity?

A: As I was growing up, probably just before entering my teenage years, it was pretty clear that the things I really loved were art, math, and music. I played the trumpet. I have been painting since I was 3, 4, 5 years old. Math just fit in my brain. I don’t know how else to say it. It was just really important to me. But the first time that I made a choice based on that was when I went to university. I had thought that I would do engineering as my undergraduate education, because I thought it was a good way to combine art and math.

In Canada it’s very different from the US. You almost always go to your closest home university for your undergraduate degree—there’s nothing like looking across the country and visiting places and deciding where you might want to apply. So I was going to go to the University of Alberta. I had won a province-wide engineering scholarship, and also had won a national scholarship from a mining company called Inco (now Vale Canada –Ed.).

This is around 1968. You’re walking around in a gym going from the math table to the physics table to actually manually sign up for courses. When I got to the math table, they told me that because I was an engineering major, that I couldn’t take the honors math courses, and I knew enough to know that I needed to take the honors math courses. So on the spot I changed to be an honors math major and gave up my engineering scholarship. Now it was only $500. Of course $500 was a lot more money in 1968 than it is today. But I just didn’t think twice about it. I just did it. And I just couldn’t imagine not being in the most challenging math courses that were available. I went to the first lecture of my honors calculus class, and in those days you didn’t take calculus in high school. So I’d never seen calculus, and it was just the best thing I’d ever seen. The professor (Jack Macki) decided to take the first two weeks of the yearlong course to cover the entire course, just to give a synopsis of what was going to unfold. And you couldn’t blink because you would miss something. I enjoyed those two weeks probably more than any class I’ve ever taken my life. It was just so beautiful. That’s when I realized for the first time that I wasn’t going to be able to make my life without mathematics.

It happened again about two and a half years later. I strongly believed that I should do something important with my life. By important, I mean societally important—I don’t mean like becoming a great mathematician. It was the late 60s, and I was part of the student protest movement. In my first year at university we occupied the president’s office. The president was actually a mathematician. Our request—or demand—was that he place student representatives on university-wide committees and we were only in his office for an hour because he said yes. I look at what’s going on right now. The campus protests today are much more complicated and challenging. There are very passionate supporters on both sides of the issues which makes resolution virtually impossible. Of course it was an easy thing to say yes to, but it was a big thing at that particular time. Two and a half years later I dropped out of college, not because I was not doing well, and not because I didn’t like my classes or any of those things. It was just because I felt like I had to find some way to have more impact. And the thing I learned from leaving mathematics was that I couldn’t live without mathematics in my life. So I eventually came back and finished my four-year degree a year early and went directly into the PhD Program.

Q: What are your best research experiences?

A: One that I was particularly fond of was the work on “traditional galleries require fewer watchmen”KKK83 It’s coauthored with Danny Kleitman and Jeff Kahn. I actually did all of the work myself, but it was one of those things where we had lunch together at some conference that was in—I think hosted at MIT—and we started talking. But you know the protocol. I felt very strongly that if you had talked with someone then they should be coauthors on the paper. I particularly enjoy geometric problems. And so that was one I really loved. I gave a talk about it at MoMath here in New York City a few weeks ago. It’s just surprising. Joe O’Rourke found a simpler proof O’R83. Mine depended on partitioning rectilinear polygons into convex quadrilaterals, and, so far as I know, there is no simple proof of that. Yet Joe found simply a different and easier way of showing that you could always get away with approximately $\lfloor n/4 \rfloor$ guards.

Another one that I enjoyed enormously was some work with David Kirkpatrick over the years. What’s interesting about that was we did most of the collaboration by phone. Your brains need to fit in a particular way to be able to collaborate on something by phone when you can’t see, especially because we were doing graph theory, and usually graph theory is quite visual. So that was really a lot of fun. And David, also, partly through doing our research together, got me into long-distance running because he came and spent a sabbatical at IBM Research while I was there. His idea was: we can run slowly enough that we can talk mathematics together. Up until then I had been running on the order of half an hour. We could run for an hour, an hour and 20 minutes. And of course it was David who eventually recruited Nick [Pippenger, see below –Ed.] and me to go to the University of British Columbia, and he also got me into running my first race which was a 10K. And then I ran my first marathon with David, and with another mathematician, Richard Anstee, etc, etc. It’s totally bizarre, how doing mathematical research can lead you to running a marathon.

More recently, one of the research collaborations that was just, I would say, magical, was with a student (Chai Karamchedu) at Mudd who met the dean of students (Anna Gonzalez) as he was incoming as a first year student. She liked him so much that she said “You’ve got to go meet the president and do some research with the president.” I hadn’t done mathematical research in 16 years, since I was at UBC. This was in 2019 just before the pandemic hit. So he came to my office. I had worked on a problem in Ramsey theory. That’s a joint paper with Jerry Grossman and Frank Harary GHK79. We had been able to prove that if the degrees of the 2 stars are $n$ and $m$ and $n\geq m$, if $n>3m$ we had tight upper and lower bounds. If $n<\sqrt {2}m$ we had tight bounds, and then in between $\sqrt {2}$ and $3$ it was an open problem. I think, probably in 2016, or something like that, like a few years before, I had given a talk, and at some point somebody had told me that it was maybe 37 years, or something like that, since the paper was published, and nobody had made any progress on that. So I mentioned this to Chai and gave Chai a copy of the original paper. Shortly thereafter the pandemic happened, and we started working, not on that problem, but on a related problem where the two stars are joined by a path with an odd number of vertices rather than a single edge, which, of course, has two vertices on it, and we were able to to get some some really nice results on that KK22. And of course that was primarily done over Zoom. We’ve made progress from telephones, but it’s just so interesting to me that sometimes actually doing research with someone that you’re not in the same room with can be beneficial. Because you do a lot of thinking separately, and then you share your ideas and they build off one another, and then you think separately, and you come back and forth. That was just an amazing experience with Chai who is now a graduate student, a PhD Student at the University of Maryland, working on quantum computation.

Q: You mentioned that you have a deep desire for societal impact. Could you say more about how that desire for societally important work affected the rest of your career, and whether there’s potential for that within mathematics or within academia?

A: Yes, so what I eventually realized. So I grew up with both. I thought I was male until about nine when I realized it wasn’t going to change and I continued to act like a male after that. It was completely clear I was female in terms of the gender assigned at birth, and all that kind of stuff. But I was the second of four daughters of my family. My parents had only intended to have two kids, and so when I came along, I was just “my father’s son.” I’m the first female to hold my job in all of my positions for the last 36 years or so, and I think that my father literally believed I could do anything. I mean anything intellectually, and I think that’s one of the things that enabled me to be successful in disciplines where women were not usually, because he had that belief. I think what I eventually realized was that one could make a huge difference in society if one could demonstrate that people who are under-represented in certain areas of STEM (women in math and physics and computer science and engineering, more generally people of color in all areas, people from low socioeconomic backgrounds as well) could contribute. And so I decided that the way I would actually get to still be immersed in mathematics, which eventually transformed to theoretical computer science, and feel like I was making a difference, would be to demonstrate that women and people of color and other underrepresented groups could actually thrive in very rigorous STEM careers.

That was the main reason I went to Mudd from Princeton. Princeton was horrified when I went to Harvey Mudd as president: “You’re supposed to go be president of Michigan or Yale, I mean, what is wrong with you?” And I said “I think actually, the culture of STEM is set for the most part in the undergraduate programs, because that’s really where the filter and gateways in the pipeline are.” I thought that Mudd, because of its commitment to innovation and pedagogy and curriculum, was a place that, even though it wasn’t diverse at all in the student body at the time when I arrived, it was a place that could demonstrate that if you changed curriculum and pedagogy you could attract and retain and have students thrive from all the under-represented groups. The one part I totally screwed up on was that I thought when the Mudd board was recruiting me that they knew how committed I was to diversity, and in fact they were only interested in the prestige of getting the dean of engineering from Princeton. But it was okay. We did strategic planning. We were able to make diversity something that eventually the board did support, and the faculty and students supported as well. So that’s how I found a way to combine impact and loving math and computer science. I would say those are my two favorite disciplines for sure. But I affectionately lean towards other areas of STEM as well.

Q: You started off in functional analysis, right? Were you originally interested in switching to theoretical CS just because of job prospects? Or were you already attracted to the field? And what do you think you would do today if you were in a similar situation?

A: Actually, I started off in algebraic topology. This is not a widely known thing, and it’s not something I particularly want you guys to cover. But I’m just going to tell you anyway, because it’s an important part of what shaped my life. My advisor, who has passed away a few years ago, had started a romantic relationship with me. He was married. I was married. At the time I didn’t realize that this was really an abuse of power. It broke up his marriage. It broke up my marriage. But what was more important was that he became physically extremely abusive, and almost killed me a couple of times. I had hair down to my waist, and he just cut off large chunks of it in one of the times when he was beating me up. I was 22 when this started. He grew up in Syracuse. His mother was in jail. He was raised by an aunt who had multiple boyfriends that beat him up, and almost all of his friends ended up in prison. I, of course, thought that I could get him to be sane and not to beat me up, and all these kinds of things. And we went to counseling together for a while and all that kind of stuff. But the bottom line was that he was subject to these—I don’t know whether I would say they were schizophrenic attacks or something else—but he would just go absolutely nuts. And at some point I realized that I could not have him as my supervisor, no matter what, because it was just too unstable and crazy.

So I then interviewed all the graduate students at the University of Alberta at the time about their advisors to pick the one who seemed to be the best advisor. The person I was most impressed by had only one other graduate student, Keith Taylor, who later became the vice-president of research of Dalhousie University, and a good friend. His advisor was Tony Lau. Now Tony worked in functional analysis. I had no particular interest or disinterest in any area of mathematics. I had enjoyed every single course I had taken but probably the one where I had shown the most unusual ability was a course in discrete mathematics taught by John Moon. So, Tony was very reluctant to take me on. It turns out he was only six years older than me and he only had one other graduate student, who hadn’t finished at that point, a year or two ahead of me. He decided that he would see if he could find some problems in functional analysis that a discrete mathematics problem-solving ability might be useful for. And so he found three 20-year-old problems. I solved two of them within two months, and a month or two later I showed the third one was equivalent to one of the other two. So that was actually my thesis. When I solved the first two problems, Tony thought it was a fluke. Somebody from Temple University, who was in this field, wrote to me and said, Tony should have let you have your PhD already. This is amazing. And then, when I did the third one, Tony said OK.

Tony was particularly worried that I wouldn’t get a job. There were about 100 PhDs in pure mathematics looking for jobs at the time, and maybe 20 tenure-track jobs across all of Canada and the US. And so both Keith and I, who were looking at the same time, got one of those jobs. Keith got a job at the University of Saskatchewan, and I got a job at Oakland University, in Oakland County, about 25 miles north of Detroit. I also got an NSERC postdoc which I was planning on taking to Jerusalem. But Tony really thought I should take the tenure-track job. By then I had broken up with my first advisor and was divorced from my husband. So when I went to Oakland I was single, and it was just miserable. I had always loved teaching but I was teaching students who literally couldn’t add fractions. And I was teaching intermediate calculus and multivariable calculus. It was just crazy and I was extremely lonely. Oakland was in the middle of nowhere: if you went four miles in one direction you hit Pontiac, a car-making town. If you went four miles in the other direction you hit Rochester, which was a Detroit suburb. There were no ethnic restaurants, there were no bookstores. There was nothing that you would think of in a college town, and so I coped with the loneliness by going to conferences. And I went to a math conference once a month, essentially just in order to meet and talk with people.

At one of those conferences I met Václav (Vašek) Chvátal. Vašek, a Czech mathematician, was actually the person who told me about the art gallery problem for polygons. He was on sabbatical at McGill, and on leave from Stanford, where he had a joint appointment between computer science and operations research. He was getting phone calls from his graduate students in computer science at Stanford, who were getting offers from MIT and Harvard and Bell Labs, and so on. I thought “I solved three 20-year-old problems and I’m at Oakland University—this is just totally unfair!” He told me about this guy named Andy Yao [Turing award winner 2000]. Andy had done his PhD in theoretical physics, I believe, at Harvard, and then a postdoc at Stanford, and I believe one or both of his advisors were Nobel laureates in physics. He had read the writing on the wall and went back and got a PhD in computer science in two years at UIUC. Vašek said I should just do that, and that in computer science life is easy for people with PhDs in computer science. He said that the best three places for theoretical computer science in the world were Stanford, MIT and the University of Toronto. He gave me names of people to call at all three places, so I called them all on March 15. The guy at Stanford said “Well, unfortunately, our applications for the PhD Program closed on January 15th, and you’d have to wait a year.” The guy at MIT—who happened to be Albert Meyer—said “Oh, you sound fantastic. We’d love to have you. But we can’t actually guarantee that you’d have funding as a graduate student because we have funding for 5.5 theory students, and we’ve got 11 right now.” So I called the guy in Toronto (Derek Corneil) and the province of Ontario had just changed the rules for who was eligible to get a graduate fellowship at the University of Toronto. Most of their PhD students were Americans and they had restricted it to permanent residents and Canadian citizens. Derek said, “You’re Canadian, of course we’ll take you!”

And so I showed up. I had heard that Andy took all of the courses he needed for his PhD in one year, and he did his research in the second year. So of course, that’s what I decided to do at the University of Toronto. So there I am taking five graduate courses each semester. I’ve never written a line of code or taken a CS course. I worked really hard. For the first three weeks I had no idea what was going on but but I got A’s in all of my classes and maybe I got an A- in programming languages. By the time I was in my second semester at Toronto I was getting invitations to apply for faculty jobs at Canadian Universities. I went on my first interview, which was at the University of Calgary and when I got back there was a message that I should call the head of the Computer Science Department at Toronto immediately, so I did. And he said, “We heard you were interviewing at the University of Calgary.” This guy, the head of the department, had been very reluctant to allow me into the PhD program because, he said “You already have a PhD, and I don’t think people who already have a PhD should be allowed to enroll in the PhD program.” But Derek had managed to make it happen. The head said “We have faculty positions here at the University of Toronto. There’d better be an application on my desk by first thing on Monday morning.” They hired me as a tenure-track faculty member, after nine months as a graduate student.

Not only did they do that (which was very nice, and I was very happy to have made that transition) they decided that I was going to do so well in computer science that they should introduce me to some famous computer scientists. So they put me in charge of a seminar series, and the first person who spoke in the seminar series was John Backus [1977 Turing Award winner] who was at IBM Research, but based in San Francisco, and the second person was Nick Pippenger. Now Nick had visited Toronto the year before I showed up as a graduate student for six months on sabbatical from IBM Research in Yorktown Heights. It’s a longer story than this, but the bottom line is that we were engaged to be married six weeks later. I would never have believed that I would marry somebody like Nick in the sense that he was very shy, extraordinarily bright, extraordinarily nice, but didn’t enjoy traveling, outdoor activities. He didn’t enjoy many of the things that I thought were sort of a fundamental part of my life. And the truth is, if I hadn’t been through this terrible situation in this abusive relationship while I was at the University of Alberta, I probably wouldn’t have been willing to consider Nick. But I was so—I think shattered is probably the right word—and Nick is just such a wonderful person that he was able to convince me that we should be in a relationship. So we met September 26th, and we got married May 12th or something like that.

Toronto was just thrilled. They had been trying to hire Nick for years. The MIT math department reached out to both of us to see if we’d be interested in going there. And IBM, eventually, when they realized that Nick might be serious about leaving, made me an offer. Eventually I decided that I should go to IBM and that we’d both go be part of a new group at IBM research in California in San Jose, mostly because Nick was so shy, and we wanted to have children, and I really felt like starting a family was going to be such a big change for him that actually putting him in a university and having him need to do teaching and all those kinds of things was probably not the right thing to do. And of course, going to IBM Research turned out to be a huge plus for me, mostly because I became a manager after four years, and then a second-level manager the year after that, and got really fantastic professional development in management. It’s less common in academia to get that kind of professional development.

So making the transition to computer science was definitely because of job opportunities but it also meant that I met the love of my life and we now have two children. We have three grandchildren here in New York City. Nick and I’ve been married for 44 years. The most important part about, I think, making the transition to computer science for me is I ended up meeting someone that I probably never would have met, and who definitely turned out to be the right partner for me—and vice versa.

Q: Your relationship with your first advisor will be shocking news to many. What other consequences did it have?

A: I did talk about it. I was in an interview with the Canadian Math Society a couple of years ago, and I did mention it there, and they asked me whether I wanted them to pursue it somehow. That’s when I actually checked and found out that my advisor is no longer alive. It’s all very complicated, because one of the things I have learned by talking with a lot of strong women in my career is that being in an abusive relationship is not that unusual. I almost feel like if you’re a strong woman you believe that you can solve these problems and you probably persist in a relationship much longer when you should have walked away in the first place after the first thing happened. And so maybe it is important to share that. I’ve shared it with my kids. Nick, of course, has known about it forever.

At one point somebody at the University of Alberta math department asked why I didn’t come back and visit more often. And I said because I basically had panic attacks being in the building. And my impression is that other faculty in the math department honestly didn’t know what was going on. Maybe they didn’t want to know what was going on. It was a different time. If it were happening now, I think it would be completely different. But I remember showing up one day with my face completely swollen and this was after the time that my advisor had cut off my hair, and so I had trimmed my hair so it didn’t look like somebody’s cut it off in a fight. And people said, “Wow, it’s really amazing how short hair makes your face look a completely different shape,” and I’m going “Oh, Jeez.”

In order to get away from my advisor I literally had to flee Edmonton. I had to hide for two months because he promised if I ever left him he would kill me. And so I actually spent two months in a basement never going above ground, and then I fled to Vancouver, and he did come after me there. I was staying in this mathematician’s [Roy Douglas] house, and he actually had a gun, and he went out and threatened my first advisor with a gun if he ever came back, and he didn’t come back. He and his wife were very good to me. I was pretty broken when I moved to Vancouver, and they were renting a room in their house, and that’s where I went.

Q. I don’t know if there’s ever been a time when any romantic relationship between faculty member and graduate student has ever really been acceptable, right?

A: Romantic relationships between faculty and students and between graduate teaching assistants and undergraduate students were quite common in the past. In recent years there’s much more recognition about the different levels of power involved and hence about the inappropriateness of such relationships.

Q: Can you tell us about your connection with the AMS?

A: Ron Graham noticed me when I was still a PhD student in mathematics, at a conference at UBC, and basically stayed in touch. At some point he encouraged me to run for the Board of Trustees of the AMS. I think it was around 1991, and I got elected for a five-year term. So that was really my first engagement with the AMS. I really enjoyed serving on the Board of Trustees, and, in fact, I think I was chair of the board when we selected John Ewing as the executive director of the AMS. He, of course, is my predecessor as president of Math for America. So it’s somehow a very small world.

I thought it was a really good experience. I felt like I learned a lot about governance by being on the board, and that I met a variety of interesting people.

A number of times Ron was influential in suggesting me for various roles and doing various kinds of things. I’m still very good friends with [Graham’s widow] Fan Chung. You know how they talk about mentors and sponsors? Well, Ron was definitely in the sponsor category, because I wouldn’t say he ever mentored me in terms of giving me advice, but he provided opportunities by telling people that they should consider me for different kinds of things.

I think we’re still members of the AMS and also of ACM and I think I’m still a member of the MAA and AWM.

Q: Anecdotes say that mathematicians are less likely, maybe, than other disciplines on average to take on a high-level administrative role compared to, say, chemists. Do you think that mathematical researchers are better, worse, or about average when it comes to the skills needed for organizational leadership?

A: That’s a great question. I guess I feel pretty strongly that to be an organizational leader, you actually have to really enjoy working with people, otherwise there’s just no way to be effective. I mean, you’re leading an organization that’s full of people. There a whole range of roles that are really important for leaders, but one of them is to listen to their people, mentor their people, help their people grow, help them grow into careers, all of those kinds of things.

There certainly are mathematicians who have no interest in interacting with people and maybe mathematics is a career where it’s possible to excel and thrive without being interested in interacting with people. It’s harder if you’re say a chemist, somebody who has to run a large research lab, because then you’re going to have to have those skills. But I think there are also a fair number of mathematicians who do have those skills. So Robert Zimmer, who was the president at the University of Chicago, is a great example. Obviously the president of the University of Alberta was a great example when I first started there, and John Ewing. He was chair of the math department at Ohio State, I think, and then executive director of the AMS, where I think he did a pretty good job. And then president of Math for America for 15 years, and I think he also did a good job. I do think you’re right in the sense that it is an area where you can thrive without having a lot of graduate students or a lot of interpersonal relationships. And so maybe it attracts some subset of people who don’t want to have relationships. There is lots of room for people in mathematics who are not interested in leading organizations. But then I certainly know Ralph Gomory who led IBM Research and did a fantastic job, and then went to Sloan, and, as far as I can tell did really well there.

The final part of the interview will appear in the next issue –Ed.

References

[GHK79]: Jerrold W. Grossman, Frank Harary, and Maria Klawe, Generalized Ramsey theory for graphs. X. Double stars, Discrete Math. 28 (1979), no. 3, 247–254, DOI 10.1016/0012-365X(79)90132-8. MR548624,

Show rawAMSref
\bib{GHK1979}{article}{ author={Grossman, Jerrold W.}, author={Harary, Frank}, author={Klawe, Maria}, title={Generalized Ramsey theory for graphs. X. Double stars}, journal={Discrete Math.}, volume={28}, date={1979}, number={3}, pages={247--254}, issn={0012-365X}, review={\MR {548624}}, doi={10.1016/0012-365X(79)90132-8}, }
[KK22]: Chaitanya D. Karamchedu and Maria M. Klawe, On the Ramsey numbers of odd-linked double stars, Discrete Math. 345 (2022), no. 10, Paper No. 113001, 12, DOI 10.1016/j.disc.2022.113001. MR4432156,

Show rawAMSref
\bib{KaKl2022}{article}{ author={Karamchedu, Chaitanya D.}, author={Klawe, Maria M.}, title={On the Ramsey numbers of odd-linked double stars}, journal={Discrete Math.}, volume={345}, date={2022}, number={10}, pages={Paper No. 113001, 12}, issn={0012-365X}, review={\MR {4432156}}, doi={10.1016/j.disc.2022.113001}, }
[KKK83]: J. Kahn, M. Klawe, and D. Kleitman, Traditional galleries require fewer watchmen, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 194–206, DOI 10.1137/0604020. MR699771,

Show rawAMSref
\bib{KKK1983}{article}{ author={Kahn, J.}, author={Klawe, M.}, author={Kleitman, D.}, title={Traditional galleries require fewer watchmen}, journal={SIAM J. Algebraic Discrete Methods}, volume={4}, date={1983}, number={2}, pages={194--206}, issn={0196-5212}, review={\MR {699771}}, doi={10.1137/0604020}, }
[O’R83]: Joseph O’Rourke, An alternate proof of the rectilinear art gallery theorem, J. Geom. 21 (1983), no. 2, 118–130, DOI 10.1007/BF01918136. MR745204,

Show rawAMSref
\bib{ORou1983}{article}{ author={O'Rourke, Joseph}, title={An alternate proof of the rectilinear art gallery theorem}, journal={J. Geom.}, volume={21}, date={1983}, number={2}, pages={118--130}, issn={0047-2468}, review={\MR {745204}}, doi={10.1007/BF01918136}, }