ICTP’s Postgraduate Diploma Programme was founded to help students from a broad range of countries in the developing world consolidate their knowledge with a view to continuing in international higher education. Over a thousand students have graduated from the Diploma Programme since its inception in 1991, many going on to academic careers in physics and mathematics. Over a quarter of past diploma students chose to specialise in mathematics.
One of the Postgraduate Diploma Programme’s latest graduates, Indonesian student Rubio Gunawan The, talks about his studies and the challenges faced by mathematicians in Indonesia.
Tell us a little about yourself.
My name is Rubio Gunawan The, and I'm from Indonesia. Here at ICTP, I studied mathematics, and I have a Bachelor's degree in mathematics from Indonesia.
How did you discover your interest in mathematics?
My father is a mathematician. He works at Institut Teknologi Bandung (ITB) in Indonesia, and this is the University I studied at for my Bachelor’s degree. So, from a young age, I was already exposed to the fact that there are many different ways to engage in mathematics. There's research, which is so much more than what we see and learn at school, and it's actually very diverse. At school, math tends to be a bit too formulaic, so it's very hard to see how this feels, but once you do research for yourself, you realize that there are so many ways to creatively solve a problem. I was also exposed to and participated in the Math Olympiad competitions when I was at school and university.
What challenges have you faced in pursuing your studies?
I think the two biggest challenges for me were, firstly, simply the logistics of living abroad. This is the first time I have lived outside my hometown. My university in Indonesia is in my hometown because my father works there. So, that's a huge difference. The second challenge for me was that mathematics research is very different from the mathematics you do in class or olympiads, and that can be difficult sometimes. In those settings, every problem you are given has already been well studied, even though it might be very challenging. It's something that's already known to have a solution. With research, sometimes you just have to be more original, and solving a problem will take more time. And sometimes, there isn't a clear solution.
How did you come to be in the diploma program?
I first heard of it from a diploma student who attended ICTP last year. He told me that this program exists, and I thought that this is a good opportunity to expand my background and try to join some kind of a network of researchers and professors. Also, I wanted to find somewhere to prepare for a Master's or PhD.
What is your diploma thesis about?
I'm working on dynamical systems, more specifically ergodic theory, with Stefano Luzzatto in the MATH section. We are basically looking for systems that have a nice dynamical property in terms of measure. There's this concept called measure theory, which is usually used for probability theory. When it's applied to dynamical systems, if a system has something that we call an ergodic measure, we know that it will have several nice dynamical properties. And one such class of systems that is known to us, regarding measure theory, is an Anosov diffeomorphism. I’m basically reviewing how to prove that this diffeomorphism is ergodic. And we're trying to do something a bit original at the end of it, trying to do something that we find more intuitive than what’s in the available literature.
Were you exposed to these theories before you came here?
In the case of dynamical systems, these theories were completely new to me. I did not study these at all in my Bachelor's degree.
How did doing the diploma affect you?
I've learned a lot in one year, I think. My Bachelor’s degree was four years long, and I think in this one year, I've probably learned more than I did in all those four years. Also, I feel more confident in my ability to learn higher mathematics and to do research because doing my thesis taught me a lot. It's been challenging but I think I've made good progress.
What's the next step for you?
I’m going to start a joint PhD with SISSA and ICTP now. I don't know if I will be continuing with the dynamical systems I’m studying currently. I like this field very much. I think it's very likely that I'll be continuing in this direction, but who knows, maybe in the first year at SISSA, I’ll find something even more interesting.
What's your opinion of the postgraduate diploma program?
It exposed us as students to a lot of currently active researchers in many different fields. It’s also very well crafted. It gave me a better idea of what being a mathematician is like, compared to my first degree, in which I wasn’t exposed to much state-of-the-art research.
One thing is that the timing of the programme makes it a bit awkward to apply for Master’s or PhD places, in terms of the application deadlines. This is a struggle for a lot of us, as we start the diploma just before a big season for applying to a lot of universities, particularly in the US and Canada.
What are the challenges faced by mathematicians in Indonesia?
I think the main challenge is that Indonesia has a very big population, so it should have a massive pool of talent. But it's not something we've really tapped into. There’s an access issue, and a lot of untapped potential away from the bigger cities. Many people who come from more rural areas aren’t exposed to the benefits of good quality mathematics education.
Also, I don't really think mathematics is a very popular field in Indonesia, and there’s not so much interest. This problem starts earlier in the schooling system. We score pretty low in the PISA international numeracy exams [Programme for International Student Assessment (PISA); a worldwide study by the Organisation for Economic Co-operation and Development (OECD)]. In my opinion, a lot of people would enjoy mathematics, but they don't because of how their school teaches it.
Mathematics can be pure or applied. Interest in applied mathematics in Indonesia is growing. For example, for those who do statistics or maybe data science. The demand for that type of mathematics is growing, such as for actuarial science, but the pure side of the field is still underappreciated.