###### Image Credit: Harsh Kumar Khatwani.

Professor Sujatha Ramdorai is a mathematician renowned for her contributions to the Iwasawa theory. She has won several awards, notably the Shanti Swarup Bhatnagar Award in 2004, the ICTP Ramanujan Prize in 2006, the Krieger-Nelson Prize in 2020, and the Padma Shri in 2023. She currently holds the Canada Research Chair in the Department of Mathematics at the University of British Columbia in Canada. Professor Ramdorai (**SR**) recently spoke to Debdutta Paul (**DP**) and Harsh Kumar Khatwani (**HKK**) on her recent visit to the ICTS-TIFR for the Inaugural Meeting of Asian-Oceanian Women in Mathematics.

The full text of the interview is reproduced below. The answers are lightly edited for readability. The questions and initials are in bold, and **DP**’s additions are in square brackets. Scroll down for the edited audio recording.

**DP: Welcome, Professor Ramdorai. Can you tell us what inspired you to pursue a career in mathematics?**

**SR:** I think it was abstraction. From a very young age, I liked this idea that you only needed to understand in order to do well in that subject. And it was always clear that once you understood, then you did not have to fear the mathematics monthly test. And mathematics was also highly valued in society. If you did well in mathematics, then you were to be appreciated. Everybody said, “Oh, they got full marks, she got full marks in mathematics.” Once you do well and you get these positive inputs, then it continues and you do better… that’s my feeling.

**DP: Can you tell us about your field of study in mathematics?**

**SR:** Okay, I work in the broad area of what’s called algebraic number theory. And initially, I started out when I did my PhD, it was more in the algebra, and gradually I moved to number theory, and algebraic number theory. And within algebraic number theory, I work in an area which is called Iwasawa theory. This was started by the Japanese mathematician Iwasawa in the 1960s to understand what are called number fields and elliptic curves over number fields, a whole range of questions related to those.

**DP: Is there any key insight for high school students from your field of mathematics?**

**SR:** Very often high school students tend to think that mathematics is a done and dusted subject, and the truth is, it’s far from that. For instance, take this equation: *x*^{2} + *y*^{2} = *z*^{2}. Then we know that this has infinitely many integer solutions. This is just Pythagoras’ theorem. You have lots of Pythagorean triples, but then you change it to *x ^{n}* +

*y*=

^{n}*z*, where

^{n}*n*is greater than or equal to three. Then the solutions become very sparse. And it was conjectured 350 years ago that the solutions are the ‘obvious’ ones, where

*x*,

*y*,

*z*should be equal to zero. That is, one of them should be zero. And this was left unknown for 350 years. And in fact, so many subjects in algebraic number theory came out of trying to understand how to prove this or understand this phenomenon, and this is now today called Fermat’s Last Theorem, which was proved only at the end of the last century. So I think this is a key takeaway that students should remember that mathematics is exciting because it has lots of unsolved problems which later find applications not just within mathematics, but also in other areas.

**DP: Coming to your journey as a mathematician in academia, did you face any unique challenges as a woman?**

**SR:** I wouldn’t say so… not in my early years, not in my school, not in my college. I got married very young — not that my parents forced me, it was out of choice — I met somebody who I liked and my parents said, look, if you are seeing this person, then you better get married. And so I got married when I was still in undergraduate college. And it helped to have a very supportive family both before marriage and then with my husband, who has been a great supporter. In fact, he was the one during my 12th when I was debating between going to professional courses like engineering because that was the time that engineering was getting to be very fashionable, computer science was getting to be fashionable, but I also liked mathematics and I was dithering between those two, and then my husband strongly supported — my to-be husband, he was not then my husband, yet — he supported me strongly, saying, “Look, everybody does engineering. If you like mathematics, why don’t you pursue mathematics?” It’s those kinds of supportive environments that helped. Even [in] undergraduate days, the teachers were very supportive. In research, when I was at TIFR, I can’t say that it was completely supportive, except for a small subset. My advisor was Professor Parimala Raman, who is a very well-known mathematician herself; and her advisor, my grand advisor, was Professor Sridharan, who was a great believer in the capabilities and potential of women. He was one of those early pioneers under whom many women graduated in India. I think it helps to have that kind of… not patronising, but supportive [environment]... Since by then I was a mother and I was commuting 35 kilometres each way, having a group which I could be a part of was not easy because I was not staying on campus. And there it really helped that I had somebody like Professor Sridharan at the workplace, [who was] extremely supportive and encouraging also, without being patronising.

**DP: Over the years, how did you and how do you today balance your responsibilities as an academic with your personal commitments?**

**SR:** Okay, now I have almost hardly any personal commitments. Now I have a grown-up daughter and grandchildren. I don’t get to spend as much time with my grandchildren as I would like to, but otherwise, it’s not been difficult. It was more difficult in my PhD time when I was commuting 35 kilometres each way, and there wasn’t any daycare available. But again, I was lucky in the sense that I lived in an extended family. I lived with my mother-in-law and her mother-in-law. So there were challenges, but we worked out a *modus vivendi*, in some sense. So on the one hand I didn’t have to worry about who will look after my child because I knew that she was safe in a home environment, [no worrying about] what will happen if the daycare closes? But on the other hand, I think it would have been greatly beneficial if there were more daycare facilities at the place of work, things like that. And I’m glad to see those things are changing now.

**DP: But mathematics still is a male-dominated field and young women who are interested in pursuing it as a career may be intimidated by this fact. What advice do you have for them?**

**SR:** I think they should just follow their hearts and follow their passion. It helps to have a strongly supportive environment. And I think talking to the parents would help. And if a youngster is married, then talking to the… extended family. And also enabling lateral entries — somebody can decide, I still love mathematics at the age of 35 and might want to come and learn more. And those things are possible today with technology. And that’s the advantage of mathematics. You don’t need a lab. You need a book, you need a pencil, you need somebody to talk to, which today can be done remotely. Those kinds of networks and mentorships should be encouraged.

**DP: And for that, how important do you think are meetings like the Inaugural Meeting of the AOWM?**

**SR:** Very important. And in fact, I was just talking to a few others. This network should sort of be branched out. It shouldn’t remain a single network, it should become a tree… connect to other networks. And then explore the possibility of joint supervision because everybody is busy. And then joint supervision can also help a student by way of getting varied perspectives rather than being limited to one supervisor. Of course, all this calls for coordination. And also at any level, I think there should also be the individual contacts, [and] how they get along. I don’t want a student to be caught between two different advisors each of whom thinks that the other is handling the student. There should be co-mentoring and these possibilities should be looked into.

**HKK: You mentioned that when you started doing PhD, you started to face a bit of a challenge. Can you shed light on that?**

**SR:** As I said, I was commuting 35 kilometres each way. And those days I had to take a train and then if you missed the 5:37 [PM] train — I still remember the Virar local I would take from Churchgate to Andheri (*laughs*). And before that, when I was in Bombay, it was a new place. I moved from Bangalore to Bombay and access to resources was a bit of a problem. Of course, TIFR was fantastic in that way and I am sure it still is in the kind of library access that it had. And people who stayed there had some advantages because they could spend all evening, all night discussing, night seminars, those kinds of things. But in a way, I think I was also fortunate not to get caught in that because it also gave me the mental space to think of other things because it can add to its own pressure when you are within a closed echo chamber, everybody is talking about who is better, who is not better…all those kind of comparisons. Which I don’t know if things have changed now [as] I have been far removed from the Indian system for a long time. But there is a certain toxicity and judgmental behaviour which is not always beneficial.

**DP: Did you face any systemic barrier?**

**SR:** I won’t say systemic barriers, but I would say yes you had to go the extra mile to prove that things weren’t happening to you just because you were a woman. In fact, in 2004, there was an ICM in Zurich, Switzerland, and at that time, that was the first time that ‘women in mathematics’ was being talked about in Europe. And there was one afternoon — there’s a person called Eva Bayer who used to feel that there are systemic barriers for women and this should be changed in Europe — and then she organised a session on women in mathematics and what can we do about that. And I remember the few of us from India who were there wondering whether we should be seen in a place like that. Because then will our male colleagues come back and tell us, “Oh no, you’re part of that, you expect special treatment because you’re a woman.” So it’s damned if you do, damned if you don’t. That kind of systemic attitude, I would say. I won’t say systemic barriers, [but] systemic attitude. And I think that persists largely.

**DP: Even for affirmative action, do people look down?**

**SR:** For affirmative action, I mean, just look at the number of mental health issues in IIT[s]. I know of people… we read that all the time in the newspapers, right? And this, from what I read in the West, it’s the same — meaning among the Indian diaspora in the West, you face systemic challenges because they feel that you got there unfairly because of affirmative action. And I know of cases where people have got where they have without affirmative action, but they happen to be from those sections of society, and then the assumption is that they are where they are because they are from that section. It goes against the grain of affirmative action. So I think there should be this larger education in India about social justice and how that can make a better place for everybody rather, this sense of entitlement and non-entitlement.