How would you describe your award-winning work to school students?
My work is about counting discrete things (things you can count), like the grains of sand or the grains of rice, but by using continuous objects like waves. So, they might seem like very different things initially, but they have one thing in common — waves, which are periodic objects (have a regular pattern).
Similarly, the kind of things that my work is interested in counting are periodic (like points which form a lattice — numbers in a line which are distributed periodically). I use a type of mathematics called harmonic analysis, which studies waves and helps me count in three or more dimensions. Harmonic comes from the fact, again, that you’re studying waves, so these are harmonies. Sometimes, you can use these tools to count things which are also periodic. You don’t want to count just numbers in a line, but actually in three dimensions or even in n dimensions, general dimensions, you can’t imagine them, but you can study them using math.
What I want to look at is how these fractions (which are numbers that you can really describe well in a calculator or a computer) distribute around nice shapes like a sphere, a cone or a cylinder.
Since you’ve been part of universities both in India and abroad, how is academia different in these places?
There are different kinds of educational institutions. Wisconsin, where I went to get a PhD, was huge. It had like 50,000 students, whereas the institution I was previously at was tiny. So, one good thing about universities abroad in the US and Germany is the exposure which you get as a student.
Outside universities are also very well funded by the government, by private government grants and by private entities, which means that there’s a lot of funding available for students to attend conferences, leading to great exposure to modern research at a younger age. That’s something that Indian students get less of, and that’s not just about the universities; it’s also about how much funding is available.
Also, at least in Bonn and Madison, some of the students start reading research papers at a much younger age, and they have the confidence to try to tackle problems. Not everyone does it, but I wish that I had seen more of that when I was a student. My institution, NISER Bhubaneswar, was very small when I started, but what I liked there was the opportunities we got to engage with our instructors.
What are a few things that you think Indian universities can improve?
Again, I don’t think that’s so much on the university, so much as we definitely, as a country, should encourage more schemes to have more funding for basic sciences. The achievements of things like ISRO or experimental sciences are very great, and they’re also achievements that you can immediately appreciate. I guess that’s why it’s more glamorised as well. Things in the basic sciences, on the other hand, might not see immediate returns; you might not be able to immediately justify why it’s interesting what you’re doing. I admit, what I am doing is very abstract, and on the face of it, it has nothing to do with real life, but you never know.
But there’s one thing, I think India has the largest number of universities in the world, and we have a lot of very good research institutions, but what would be good is to get these places to be well-funded, to have more infrastructure. Our researchers in India should also interact with those abroad and vice versa. For the same reason, making things easier bureaucratically, making it easier for foreign researchers to visit India, which is actually right now very tricky, is important.
Another thing is hierarchy. Our faculty members, I thought, were not very hierarchical, but again, from second-hand accounts that I’ve heard, sometimes professors in universities can be a bit more distant or hierarchical in terms of interactions between teachers and students. And I think, especially if you are learning science, it happens best when people can express themselves freely and ask a lot of questions, and there’s a lot of back and forth. And that’s definitely a skill you need later on if you want to become a researcher. And I definitely found that to be much more in the US. Respecting people does not necessarily mean you don’t question them. Having questions and curiosity is very important in any field of education, any branch in the university. To exchange ideas and learn new things is very important in any area.
A lot of students in India tend to find maths boring, why do you think that is, and what can be done differently?
I should just say that I feel like this is a problem like everywhere, not just in India. In India, at least in my experience, I’ve seen more fear than like, even finding it boring or not. And I think one reason is the way things are structured. Things tend to be very competitive, which means that to even get access to good institutions, you really have to write an exam and score certain marks. I feel like some of the fear already comes from there, because you are not really learning something. The main objective often tends not to be to understand something.
It’s mostly how if I can solve this problem very fast, then that means I can crack this exam or get this percentage. And we are often taught to think that way in school, because we have these exams. Then the way things are taught — sometimes teachers expect you to just learn things very fast, like memorise a method, and you get the answer. And if the students can’t do that, then they face consequences like bad marks or scolding. I don’t think that’s the way to encourage anything, and I feel it’s more prominent in mathematics since one can’t just rely on memorisation. At the end of the day, you need to understand things, and you need to be able to learn to apply your skills to new kinds of problems, which is something that students are not able to do. So I feel that’s one of the reasons why people might find it boring in India or abroad.
I think it would be really great if there were some sections of the syllabus where students could play around with the problems. It’s okay to make mistakes and then learn with it. I think that most students will find it interesting. I don’t think that we can make everybody like it because you do need a lot of effort or practice to be good at it. Not everybody might enjoy that. But I definitely think more people would be surprised that when they are taught math the right way, how well they can do, and how many more people have more mathematical ability than they themselves give credit for.
What made you pursue mathematics as a subject?
So when I was in school, I used to like math because it involved the least amount of memorisation once you start to solve something. It might initially take a bit of time to get the hang of things, but once you understand the logic behind it, you can use it for a particular problem and also extend it to other kinds of problems. So I used to like that aspect that I didn’t have to be nervous about remembering things.
Another aspect that I liked was that it was totally independent of other subjects. Like in physics, if you want to study it, you need mathematics. But you can study mathematics in and of itself, although it’s not true that it’s completely independent. Now there are a lot of connections. But back then, I used to like that independence and that you could just focus on one thing. And how a lot of times, it’s not true for research questions in general, but a lot of times, any question you ask has a clear answer, which was not subject to interpretation.
In physics or other areas in experimental sciences, you have a hypothesis, and then you might have an experiment to support it or a theory, but then something new might come up, and then you realise that that theory was wrong, or you have to change the hypothesis. But in math, once you prove something, it’s just true always. So that’s what attracted me towards math.
What are the challenges that young women face when they pursue STEM, and what would your advice be to them?
I think there are different experiences you have on a practical level and some on an existential level. Like, when I did my schooling, throughout my life I was in only girls’ institutions, and I didn’t realise it at that time, but it really takes this weight off your mind, because if you are just surrounded by women all the time, you don’t think of yourself as a woman. You are just existing freely.
And then if I’m good in my school, if I’m good at math, I’m not a woman who’s good at math. I’m just a student who’s good at math. In my family, there wasn’t an aspect of, ‘wow, you are a girl who’s good at math’. They were just happy that I was good at it. So I never thought that it was something different that I was doing.
But I didn’t realise at that time how special that feeling was, because when I came to my undergrad, then the percentage of women suddenly dropped, and when I took math, it dropped even further, like in our entire undergrad program, it was just two of us.
Then, as you go further into research, you start collaborating with people, or even when you’re finding the correct advisor for your PhD, there is this human interaction element to this, like, who are you comfortable with? Who do you think you can freely talk to? And that is definitely something which women in STEM find less of.
There are a lot of informal networks, for example, in research, where you attend a conference and you go for dinner with someone and just start talking about some things, which I feel women are less exposed to because that’s the human tendency, right? We find it more comfortable to talk to people who are of a similar background, like the same country or the same gender. That would not have been so much of an issue if math was 50% men and 50% women, but it’s not like that, which means that you end up sometimes falling behind those kinds of informal connections, which might lead to collaborations.
Also, in conferences, before asking questions, I would just be like, ‘Oh, this is a good question to ask.’ People shouldn’t feel that if I’m the only woman in the room, I’m asking a wrong question or something, and thinking of how it reflects on me being an Indian or me being a woman comes up.
At the end of my PhD, I actually attended a women’s-only conference, and I could just subconsciously see how free I felt about asking questions and being wrong or right. And that is when I realised, ‘Oh, this is how men feel all the time’.
But definitely, I think things are changing, and there are already a lot of really good women who are doing really good work. So, I hope that more young girls see this and also feel that there’s no reason I can’t be good at it if I put enough time and enough effort into it.
For young students aspiring to pursue mathematics, what streams of studies would you suggest and from which university?
It really depends on people’s interests. If one is very sure that they want to pursue math, we have some very good institutions like Chennai Math Institute and the Indian Statistical Institute, which offer very good undergrad education just in math. But it is hard since they also have specialised exams. So students should look at their websites and then prepare accordingly. If one is interested in theoretical or computational mathematics, I think IITs might offer better courses.
Then there’s the Indian Institute of Science. I think that it has one of the best places to do science, and the course is a four-year course. So first year, you can study everything and then decide which area you want to go to. I think there are some of the best mathematicians in India working at IISc.
And then there are also IISERs and NISER, which was my home institution. They also have the advantage of the first couple of years. First two years in IISER and the first year in NISER, you study all subjects like physics, chemistry, math, biology, computer science, and then you have to make a decision. So I think if one knows that they want to do research, but they’re not sure what they want to do, I think these institutions are very good.
I have been more involved with research institutions. So I don’t know so much about the other Indian universities, but the University of Hyderabad used to have a very good integrated master’s program. Also, one always has the option of doing a three-year bachelor’s from any university, like Delhi University, and then preparing for these master’s exams and then going to another institution and doing it.
I’ve also seen that nowadays, when I’m teaching, I see more and more Indian students doing their undergrad from abroad as well, like at our institution in Madison. But of course, the fee is a bit of a challenge. In Germany, the universities are free. So if one can somehow sustain themselves, then I think the University of Bonn has master’s programs in English.
‘It’s like writing a poem’: prize winner Rajula Srivastava on doing maths
