Manjul Bhargava is the first person of Indian origin to have won the coveted Fields Medal in Mathematics for his path-breaking work in Number Theory.
The 44-year-old professor of mathematics at Princeton University, who was in Bengaluru last week, enthralled the audience at the tenth Infosys Science Foundation Awards by explaining why all mathematics is a search for patterns and the reason why such patterns exist.
Earlier, in an exclusive conversation — anchored by ET — Bhargava discussed a plethora of issues ranging from the importance of early childhood education to the need for a borderless world of ideas with Infosys founder NR Narayana Murthy. Edited Excerpts:
Murthy: Is it true that both Harvard and Princeton fought hard to attract you as a faculty and, in the process, you became the youngest professor appointed by Princeton?
Bhargava: There is something in the US that does not happen in India. Seniority is not a concern. They were interested in hiring me for the work that I have done … Princeton was the first to give me a tenured full professor’s role, within one-and-a-half years of my PhD.
Murthy: You became the first person of Indian origin to win the Fields Medal, the equivalent of Nobel Prize in mathematics. Tell us a little bit about how you have got Fields…
Bhargava: One aspect of my work was studying cubic equations in two variables Quadratic Formula … even at cubic equation, nobody knows how to solve it. Part of the work I did shows that there is an algorithm that will solve at least 80% of the cubic equations. Prior to that it was not even known.
Murthy: Most youngsters are scared of mathematics. I have met a few undergraduates at Princeton who raved about your course on mathematics of card tricks…
Bhargava: I feel all of mathematics is recreational. You have to see the fun of what you are doing to really become passionate about it. For me, mathematics is always fun. Unfortunately, usual mathematics curriculum doesn’t do too much of that and that is the reason youngsters are scared of that. Teaching mathematics in puzzle, in magic, in music — that helps you see the fun side.
Murthy: Why has Indian education not kept pace with global leaders in science and mathematics?
Bhargava: One thing missing in Indian education is (freedom) for teachers to innovate, to learn the latest and to update their curriculum. Often teachers are just given a book and (told to) teach page by page. Such autonomy is there in other countries … for teachers to innovate, be creative and learn the latest. Unfortunately, it is not there in the system in India, which requires cultural change.
Murthy: You took a year off from Princeton to work on a committee in designing a modern education system for Indian schools and colleges. Tell us the major suggestions:
Bhargava: One of the things I have already mentioned is changing the culture of promotions, salary increase and merit-based hiring. Institutional architecture has to be designed to enable that cultural shift. Kids get interested in science, or whatever their passion is, very early.
The Indian education system at the moment does not give too much attention until Grade 1. But the fact is that 85% of a child’s brain development happens before the age of six. One really has to stimulate children’s mind even before the age of six.
For families that are well-to-do, that kind of stimulation happens automatically. That kind of cognitive stimulation does not happen in poorer families and where both parents are working. So, when they enter Grade 1, they are already behind the rest of the class. Provision for early childhood education is very important.
(There is a need for) more multidisciplinary education. Why are we putting people in silos in 8th, 9th grade? Even for their board exams they have to go for either arts or science. In college, if they are doing engineering, they are only doing engineering. They don’t get any stimulation on the other side of the brain. I think this is something that really has to change.
This actually was the ancient Indian tradition of holistic education and studying science through arts and arts through science. Breaking silos is going to be very important in coming years.
Murthy: Do you see world-class work being done in India in mathematics?
Bhargava: Oh, absolutely. There is a lot of world-class work happening at certain institutions: ISI, TIFR, ICTS, CMI and also at IITs. But compared to the population of India, it is not nearly where it should be.
We have these islands of excellence in mathematics. But India is huge, we have so much mathematics talent and so much has to be happening. I would say we’re not there at all. So many young people are discouraged to go into mathematics even if they’re good at mathematics, in part because there are such few islands of excellence.
Murthy: One of the best writers to explain complex things simply is Jayant Narlikar. Seven Wonders of the Cosmos — the way he explains it is so simple. Who are the Indian authors who explain mathematics in a simple way today?
Bhargava: It’s very rare for scientists and mathematicians in India, and even around the world, to be able to explain the work they do in lay terms. Even the PhD programmes in India and abroad have very little emphasis on the communication aspect.
It’s not just important to have scientific breakthroughs, but it’s also important to explain them to the public, so they can understand how it’s relevant to them. This is not emphasised enough in India.
A lot of these books we’re talking about, they’re available only in English and these really need to reach the masses. Where students learn in their native tongue, and if you want to really get young people in those areas interested in mathematics and science, it’s very important to have learning resources, popular science books, videos available in the languages they think in and think best in.
One of the big problems for science PhDs in India is that they learn science in English and then they go back to their hometown as heroes and they aren’t able to explain it in their own native language.
That’s a big problem. One of the recommendations I’d give is that science PhDs should also take a course in communication to be able to communicate what they do with the general public and also with each other.
Murthy: Are you a traditional existence kind of mathematician or an algorithmic mathematician? And what is the future of algorithmic mathematics or computational mathematics?
Bhargava: It’s a mix of existence and algorithmic mathematics. I like to know that things exist, but I also want to be able to find them. Not just to know something is there, but to locate it and play with it.
As far as computers are concerned, they’ve definitely helped a lot in science and mathematical research. Obviously, computers have been very important in conducting experiments.
So, for example, in number theory, seeing this pattern of five numbers adding up to square numbers. But, of course, there are much more complicated problems that computers can do. Often doing experiments allows you to generate data much more quickly than you can look at and search for patterns, and use those patterns to make conjectures. But from there, to get from the conjecture to the theorem, the creativity that’s required is just not there in computers.
We talk about AI (artificial intelligence) to help us at some point, but we’re nowhere there yet. The beautiful theorems that humans prove, no computer is even close to doing that. The human mind with its combination of creativity and analytical thinking — it’s not there in machines yet.
ET: You lead efforts to bring global teachers to India for short-term courses. What’s your world view?
Bhargava: There are many areas of research in India that are currently not being pursued. This has been an opportunity for faculty here to learn about research that’s being done there (abroad) that we need.
It’s also converse, where research being done here, (foreign) faculty members get to come and learn it here. So, this initiative has allowed for some of that interaction, but we need more of that. That’s been the goal of it.
You’ll learn the benefits only in the long term, but we should be able to have more collaboration on an international level to bring the best of the world and the best of the research here.
ET: One of the grouses of academicians here is that India has not been able to attract world-class faculty to spend longer time here…
Bhargava: With more faculty coming here and seeing the ecosystem and building relationships with researchers, they will be motivated to spend more time here, even outside the programme.
Lots of faculty have started to come back, more to private places at the moment because the kind of autonomy that faculty have abroad is not yet there in public institutions like IITs.
Places like Ashoka University, Azim Premji University, these kinds of multidisciplinary institutions where faculty have that autonomy to teach how they like, are getting a lot of people to come back.
ET: As a country, we face massive unemployment and there’s a concern that artificial intelligence and machine learning technologies will exacerbate the problem…
Murthy: I don’t think so. As long as the human brain is utilised to bring in innovation and frees more people from drudgery, I believe these technologies will add value. I remember in the 70s in the UK, there used to be huge argument against computerisation.
Later on, in the 80s against ATMs, but what both computerised systems and ATMs did was to improve human productivity, improve comfort and convenience for customers. Today, online transactions have helped you sit at home and select the groceries you want to buy.
The key is to use these technologies in areas that are assistive, that improve human productivity, and at the same time focus more on the human touch. We need to make human beings do more important tasks and, as long as we do that, I don’t see a problem.
ET: We see walls being erected at borders, but also imaginary walls by governments restricting people and ideas. Do you think this will stop exchange of ideas at the academic level?
Bhargava: Free exchange of ideas is very important for progress and research in any area. I very much hope that academics will remain free to work with academicians across countries.
It is very important for all countries to ensure that. The same with artists, the same with all kinds of ideas. Free exchange of ideas is what allows humanity to progress and science to progress and, hopefully, despite any walls that are being built, it’ll remain free for academics, researchers and artists.
ET: What about trade barriers?
Murthy: I think a peaceful, harmonious, pleasant world requires that we all make efforts towards the betterment of every country. We need to work on balance of trade, ensure that if I’m exporting something to a country, then I’m also buying from that country, so that there is opportunity for people of both countries to become better.
We should not even allow this to become a situation of a trade war. I think the leaders of nations need to work together to create a world where there is harmony and peace and goodwill among various nations.
ET: France and Germany have produced some of the best mathematicians than any other countries…
Bhargava: Given their populations compared to India, China and the US, they still produce an amazing amount of mathematics and science. It’s a cultural thing.
Their culture really supports mathematics and science and they’ve set up amazing institutions. And the media and public celebrate mathematicians and scientists. There you’ll find roads named after them.
In the US, most of the roads are named after politicians, maybe actors and actresses, singers… But mathematics and science isn’t at the top of the list when naming icons.