May 21, 2020
This article is part of STEMinism in the Spotlight, a monthly interview series.
Lenore Blum is an extraordinary mathematician and computer scientist. Her research has spanned many fields from model theory and differential fields to developing a theory of computation and complexity over the real numbers. She is currently an Emeritus Distinguished Career Professor of Computer Science at Carnegie Mellon University. After earning her PhD in 1968 from MIT, she moved to Berkeley to become a postdoctoral fellow and lecturer in mathematics. She later returned to Berkeley in 1988 to join the Theory Group of the International Computer Science Institute (ICSI). Lenore has also worked tirelessly to increase the number of girls and women in STEM. She formed the Bay Area chapter of the Association for Women in Mathematics (AWM) and later became the third president of AWM. In part 1 of 2, Lenore tells us about growing up and finding her passion for math in Caracas, earning her PhD from MIT, and moving to Berkeley and becoming an accidental activist.
Amanda Glazer: Can you start by telling us about when you first became interested in math?
Lenore Blum: I was born in New York City (NYC) and lived there until I was nine, then my family moved to Caracas, Venezuela. When we arrived, my parents decided to put me and my seven-year-old sister in a Venezuelan school. We had gone to a very progressive school in NYC where you didn’t know your grades. In those years, public schools in NY were very progressive.
This school in Caracas was small and very disciplined. They put me back two grades because the system was very different. That did not sit too well with me. Also, it was very rigid. The profesora would write something on the board, which we had to copy many times into our cuadernos (notebooks) and then draw beautiful pictures.
One day the principal decided to teach these two little girls [me and my sister] Spanish. The lesson was about the subjunctive case. We had had no grammar in NYC so starting with the subjunctive case was difficult.
The other part that was difficult for me was that the boys had learned a little English from movies, American movies, that was a big thing. So, they’d circle around me and my sister and say all the English words they knew like “I love you.” It was very embarrassing. So, one day I told my mom, who had been a science teacher in NYC (at the Bronx High School of Science), I didn’t want to go back. For some reason she said fine, you don’t have to go back to school and took me and my sister out.
I had a great year. We spent every day exploring the city. My mom discovered that if you take the bus down to the center of town, which is called El Silencio (due to a plague in the 1600s that had wiped out the neighborhood), you could then take other buses that would take you distant places in the city and then bring you back.
At the time, there was a large Jewish community, and also a large American community, in Caracas. My dad had gotten us a place to live in the Jewish community (San Bernardino) where there were many European immigrants. There was a cafe in the hospital that was near our house where you could get ice cream sodas and European pastries. At the end of the day after our bus trips we would end up there with all these ladies, sitting and having coffee. I was nine and a half by then. It was just so much fun. I loved it.
Even though my mom was a teacher, she didn’t home-school us. In retrospect, that surprises me, but I think she assumed we would pick things up easily. In a way she demystified me about school. I was never worried about school because I could see her grading papers. I saw that it was not the most precise kind of scary thing.
At the end of the year my parents had to decide where to send us back to school. There was an American School (Campo Alegre) in Caracas which was run by the oil companies. In those years (the 50s) the country’s natural resources were controlled by foreign companies (that’s one root of the problems that Venezuela faces today, but by no means the only one). Oil was the main resource that supported the country and the oil companies were mostly run by Americans, but also by the British and Dutch, like Shell. There were about 70,000 Americans in Venezuela at the time.
The American School was very expensive if you weren’t employed by the oil companies, which my family was not. My mother got a job teaching junior high science at the school, and because of that, my sister and I were able to attend.1 And that’s how I became an American – in Caracas. In NYC we had lived in a very Jewish community, a kind of intellectual, academic enclave. I hardly knew anyone who wasn’t Jewish. And now my classmates were from Texas, Oklahoma, California, Montana, with parents in the oil companies and access to all sorts of American fashions. I learned about pop music and Elvis Presley, which my cousins in NYC knew little about.
I was really excited to go back to school after being out for a year. The first day, they were doing some mathematics, not just long division, but something more like the Euclidean algorithm. I thought this was fantastically interesting. I caught on immediately and from that day on I loved mathematics. I was one of the best students, but in math especially. Maybe I was a good student before but because they never gave us grades in NYC, you never knew where you stood.
Recently I looked at Julia Robinson’s biography for a talk that I was preparing for (what would have been) her 100th birthday. As a youngster, due to illness, she missed a couple of years of school. I know of other mathematicians who also missed a year or more of elementary school for one reason or other. After missing school for one year, I came back with such enthusiasm that it changed my life. I think that elementary schools in the United States tend to repeat things year after year. I didn’t experience that, and so I wasn’t bored to tears. (I wonder what the effect will be now on all the students out of school due to “sheltering in place.” Probably mixed, but surely someone is studying this.)
I had a lot of friends and I was never put down for being good at math. I think that being “other” gives one a lot of freedom, and also can serve as buffer. I was “other” in lots of ways, which I saw as an advantage then, and later on.
AG: You graduated from high school in Venezuela?
LB: I did. Campo Alegre didn’t have a high school at the time, and many of the American kids went back to boarding schools in the States. That was typical, but I did not. There was an international high school (called Colegio Americano) that was run by Presbyterian missionaries. That’s where I went for high school. I was still really good in math and skipped so many classes that I was able to graduate from high school when I was barely 16.2
I remember being in a trig class and seeing the proof of a theorem and thinking to myself how beautiful it was. Very early on I felt that math was beautiful. And that proofs were beautiful and, of course, that they were independent of anybody’s interpretation or feelings. I think that’s another attraction for people who go into math. Later on, you find out that there’s a lot of faddism. You know, areas of math become fashionable, and then not—and vice versa. But at the time, it just seemed so pure and independent of people’s personal views—I loved that and the beauty of it.
So, when I was going to apply to college, I asked my high school math teacher if I should major in mathematics. He told me, “you shouldn’t do that.” But not because I was a girl. He said all the best mathematics had been done 2,000 years ago. Later on, I realized that my teacher was a missionary teaching geometry, that he probably didn’t know more math than that. So, for him, Euclid was the best mathematician. Since I didn’t want to go into a dead field, I decided to study architecture. I still loved math, but I was also a pretty good artist. I’d done many sets for school plays. As a child, art was my biggest hobby, making all sorts of things out of construction paper and such. I made my own toys and I always drew.
Caracas is a beautiful tropical city, high in the valley between two mountain ranges, one to the north and one to the south. At the time, it had some of the most beautiful modern architecture in the world. There were concrete cantilever houses overlooking the city and huge Calder mobiles in the Aula Magna of the Universidad Central. Many Italian and Spanish people had come to Venezuela to work in the booming building industry. They then became these fantastic construction architects. A lot of interesting modern Italian architecture started in Venezuela.
I applied to MIT, that’s where I wanted to go. But then I got a letter back saying all freshmen (!) had to live on campus and they only had 20 beds for women. That was 1959. That story is interesting because four years later, Katharine McCormick, a feminist and philanthropist who had graduated from MIT very early (in 1904), gave MIT a million dollars, which was a lot of money then, to build a women’s dorm. When she died, she left funds in her will to build an annex. So, they did. Then the rules changed, entering women no longer had to live on campus. This is an example of a woman who changed things—lack of dormitory space had been one of the excuses given to exclude women.
So where did you go to college?
I went to Carnegie Tech (now Carnegie Mellon), which is in Pittsburgh. I started in architecture. During my first year, I was an intern at an architectural firm, and I saw all the young people just drafting away on someone else’s plans. All we were doing, the art we were doing, was drafting, which was not very appealing to me. And the math was math for architects, mainly formulas for stress and strain – not the math I was looking for. So, I tried to switch to the Math Department. Architecture was in the School of Fine Arts and Math was in the Engineering School. To switch from Fine Arts to Engineering was not an easy thing to do. This was my second year, so I was just 17 then. I started asking professors and deans, “can I transfer?” And everyone said, “No, no, no.” But then I finally got lucky: one day I knocked on a math professor’s door and said, “I want to switch to math, can you help me?” To my surprise he responded, “Oh, fantastic! I’m giving this experimental class in computers with the computer in the basement of the business school (it was an IBM 650). The class has been going on for a while, but never mind. The computer will grade all your homework.” This was Alan Perlis who became the first head of computer science (CS) at Carnegie Mellon, the first head of CS at Yale and the first Turing award winner. He was the first in many things. I’ve always found that people who are really good at what they do are much more open.
So, that’s how I switched to mathematics, by taking this computer course, which was mainly a problem-solving course. I have lots of computer stories about that. You know decks of IBM cards, original hackers. and all that. I learned how to program in machine language, really, down to the 0s and 1s, the bits. But still I wanted to study real mathematics.
That summer, I got married and moved to Boston. There’s a parallel story about my husband, Manuel, who was at MIT.
How did you meet him?
He’s Venezuelan. I met him in Caracas when I was 10 or 11. That’s part of my Caracas story. During that first year in Venezuela, we met many Jewish families. My mother was a friend of his mother’s and we met at his house. He always tells the story of our meeting in some glamorous romantic way which always embarrasses me. He was four years older than me. He was my idol because he was interested in so many of the things that I was interested in, and he was very different from my classmates at school. We corresponded over the years, mainly during my last year of high school. He graduated from college when I graduated from high school and came back to Caracas for my graduation. We spent that summer together going to bookstores and buying philosophy and math books. His first gift to me was Thomas’ Calculus.
When I moved to Boston, I didn’t even try to apply to MIT. I transferred to Simmons College, a women’s college. There was this wonderful math teacher there. She said, “you don’t have anything to do here, let’s get you into MIT.” So, Simmons paid for me to be a special student at MIT. I took the course I had been looking for my whole life. I had always been looking for a real math course with a mathematician who was doing research and really knew their stuff. I didn’t know that at the time, but I knew what I was looking for and I knew I didn’t get it in any of my other classes. The teacher was Isadore (Is) Singer. He’s in his 90s now. He’s one of the most famous people at MIT in math. His course was just so beautiful. The first semester it was algebra, but the most abstract. The second semester it was linear algebra, but really abstract linear algebra. We never saw any equations. It was the beautiful underlying theory and pretty advanced.
When it was time for me to apply to graduate school, I finally got the nerve to apply to MIT again.
Had you known for a while that you were going to apply to graduate school?
I always wanted to. So, I tried again to apply to MIT. I remember going for an interview with the head of the Math Department in his office. As I walked in, he handed me a list of schools and said, “if I had a daughter who was going to graduate school, these are the places I’d tell her to go. MIT is not a place for women.” They clearly did not want me there. That was devastating. (Many years later when I was teaching at Berkeley, I got a brochure from MIT announcing, “MIT is a place for women.”3)
But then, I got a “lucky” break. The next Saturday the MIT Math Department had a faculty party. Somehow, at the party they were joking about this girl who was applying to the PhD program in mathematics. Can you imagine? Why would they even bring it up? Is Singer was there and he asked, “who are you talking about?” They gave my name and he said, “Oh! She’s the best student in my class.” I got accepted the next day.
Some of these “lucky” breaks come with their own troubles. The trouble with this one was I felt so grateful that I “needed” to show them that, of course, they had made the right decision. But also, I was excited that finally, I was given the opportunity to take substantive math courses. So, I started graduate school with a bang, taking eight really high-level courses. Of course, there’s no way to take eight courses (my husband, who was also a graduate student at MIT never took more than one or two courses a semester) so I started dropping them one by one. A real downer. Not a great way to start my graduate career.
Actually, MIT was a pretty good place to be. Once you're in, the faculty more or less treated you as equal, perhaps because they assumed you’d be a future colleague. MIT’s an especially great place for undergraduates, better than Harvard in that way. For example, many years later Is called me up to tell me excitedly, “Guess what, I’ve been asked to TA for calculus.” MIT has top people teaching undergraduates – and their top people are excited to do that.
I liked algebra from Is’s course, so I started taking more algebra classes including Algebraic Geometry and Number Theory. My graduate advisor was a pretty famous Number Theorist named Kenkichi Iwasawa. He was one of my PhD oral examiners. But as soon as I finished my exams and started working on my thesis with him, he took a position at Princeton. In those years women weren’t allowed at Princeton, so if I even wanted to, I couldn’t follow him there.4 Of course, his male students could. There was no internet at the time. Talking to him on the phone was very difficult, and expensive.
Iwasawa’s leaving was pretty hard on me, but another really lucky thing happened. I became the main TA for a new course that a logic professor, Hartley Rogers, was teaching. It was on model theory and it was on some very new research that was happening in model theory then, taking logic in a very sophisticated way and applying it to mathematics—to algebra, number theory and other areas of mathematics I knew about. So, I was able to see the connection between the two. There were some really great results coming from people at Cornell – Jim Ax, Simon Kochen, Michael Morley. Because I had the algebra and model theory, I was the main person at MIT to study these results and became the go-to person for anyone who wanted to find out what was going on, including Gian-Carlo Rota and a new faculty member who had just come to MIT, Gerald Sacks. Sacks asked me to be his student, so that was a big change. Using some of the sophisticated model theory I was able to get new results in differential algebra, including some that others said were not possible. I became well known for the work I did in my thesis. Some of the Cornell and Harvard folks came to MIT for my thesis defense. I had gotten into the groove by then. It was really, very good.
What did you do after you got your PhD?
When I got my PhD in 1968, I had a fellowship, a postdoc, and I could go anywhere in the country. With the enthusiasm at MIT for my thesis, and my postdoc fellowship, I thought, “Ok I can go anywhere, and people will surely appreciate my work.” I did not know that one needs mentors and support structures. It did not even dawn on me that that was something that I should be looking for. That I should go to a place where they already liked my research.
I decided to go to Berkeley. One of the reasons was that Berkeley is in California, and it reminded me a lot of Caracas. For one the weather, for another, the politics. In high school I was kind of a revolutionary. We had a dictator who was overthrown along with the military police. High school and college students took on the role of patrolling the streets. So, Berkeley sounded like coming home. But even more, Julia Robinson was there. Her research bridged logic and algebra and her paper, “The Decision Problem for Fields”, had been a mainstay on my desk while I was working on my thesis. I was looking forward to working with her.
When I arrived in Berkeley in 1968, I was shocked that Julia5 was not on the math faculty—never had a regular faculty position there. Every so often when they needed help, she was asked to teach. Since Julia signed her papers Berkeley, California, and because of her prominence, I, and everyone else I knew, thought she was on the faculty. I also found out that the Math Department hadn’t hired a woman in a regular position in 20 or 30 years. I was totally unprepared for this and underestimated its implications for me.
In 1968, a little after I came to Berkeley, I was offered an assistant professorship at Yale, by Abraham Robinson, one of the mathematicians who liked my research. It had helped position his work on model theory and algebra in a more modern direction. That would have been (one of) the first tenure-track appointments for a woman in a major math department in the country. I did not take it. My husband was already tenured in Electrical Engineering and Computer Sciences (EECS) at Berkeley and I did not want to leave him. And we had a two-year-old. The chair and the vice-chair of the Berkeley Math Department offered me a lectureship. They told me the position was comparable with the assistant professorship at Yale. Still totally naïve and optimistic I accepted.
As I said earlier, with my postdoc fellowship I had thought I could go anywhere, and people would surely appreciate my work. But I soon found out that the Berkeley logic folks did not. People were like, “Uh, what is she doing here?” At the time, they valued the theory of large cardinals, set theory, pure logic. Applied logic was viewed in the same way as applied math was at the time, not as deep as pure logic or pure math. For similar reasons I believe they didn’t take Julia Robinson’s work seriously – she was combining logic with mathematics.
A similar prejudice was brewing towards the new field of theoretical computer science. Steve Cook, the founder of the theory of NP-completeness in the West, was on the logic faculty when I arrived. The year I came he was not given tenure. They didn’t see any future to his work, so he went to Toronto. The P/NP question is now recognized as one of the deepest questions in logic.
The kinds of things I was interested in, this combo of math and logic, number theory, complexity, computer science and logic – the logicians did not see that as real stuff. (An irony for me is coming back to Berkeley this year and attending logic seminars and colloquia, I find that the area I worked in over 50 years ago, applying sophisticated model theory to mathematics, is now central to logic there.)
I taught at Berkeley for two years. The first year I taught the undergraduate logic course and the second, I taught this fantastic three-quarter graduate course in logic (Berkeley was on the trimester system then). It was a wonderful class, lots of fun, the students were great, and many became quite famous. But also, that was the year it became very clear I wasn’t going to be rehired.
And that was the year I became an accidental activist.
Click here for Part 2.
1 My mom was a popular teacher, more than I realized at the time. A recent Facebook photo post by one of the school’s alumni, elicited comments including: Mrs. Epstein’s class was something to look forward to so hands-on. She encouraged exploration, journaling and observation, all the important things in STEM education I value. She was my science teacher 1963-1966; I remember her ... she was wonderful; I never again had a better teacher than Mrs. Epstein! I still have my science notebook from her class!
2 I was co-valedictorian of my high school class with Vivette Caspi (now Girault). She was the other person who excelled in math and we became friends and study partners. We lost touch for many years until several years ago she wrote me that she was a math professor in Paris (I had no idea) and would be on sabbatical at Carnegie Mellon. Over the years, we had been at many places and conferences together, but never knew it!
3 The photo on the brochure cover was of Norwegian mathematician Ragni Piene, a graduate student in algebraic geometry at the time. Later we became friends.
4 Princeton opened up to women the year I got my PhD from MIT, which was 1968, the year of many revolutions. During that period MIT was open to women, but reluctantly.
5 Eight years later in 1976, after being (the first woman mathematician) elected to the National Academy of Sciences, Julia Robinson was offered a professorship in the Berkeley Math Department. She accepted on her terms, teaching ¼ time. Julia was 57 years old the time. One of the reasons the university gave for not hiring Julia (and other women) in regular positions was the nepotism (or more precisely, anti-nepotism) rule. As far as I know, only women were affected by such rules at the university – and many were. In effect, nepotism was an official mechanism to discriminate against women since many were married to men in similar fields. The stipulation was that it could be overridden on recommendation of the department head. I don’t know if it ever was. At Berkeley, the rule was rescinded in 1971.
Featured image: Dr. Lenore Blum in her office in Evans Hall, UC Berkeley.
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