Live Mint | Saturday, Dec 05 2015 | Leslie D’Monte |
The math scholar on his love for the subject, renouncing worldly life and applications of geometric topology
Prof. Mahan Mj, also known as Mahan Maharaj or Swami Vidyanathananda, is not your typical math scholar. Born Mahan Mitra in 1968, he has a PhD from the University of California, Berkeley, in mathematics. He renounced worldly life to become a monk by joining the Ramakrishna Mission in 1998, but continues to teach and research in mathematics. After St Xavier’s Collegiate School in Kolkata, he graduated from IIT Kanpur. He initially wanted to major in electrical engineering, but his love for mathematics got the better of him. A recipient of the Shanti Swarup Bhatnagar Prize for science and technology in 2011 and Infosys Prize in mathematics in November 2015, Mahan explains why he sees no contradiction in being a monk and simultaneously doing research in a subject like complex geometry at the Tata Institute of Fundamental Research (TIFR). Edited excerpts from an interview:
When did you fall in love with math? Given that you had opted to graduate in electrical engineering, how did your parents react when you changed courses mid-stream?
I got introduced to Euclid’s geometry in Class VI. That sort of really sparked off an interest in maths. But then, I think, it was peer pressure and social conditioning in Class XII that made me opt for IIT. When I joined IIT Kanpur, I had opted for electrical engineering, but I soon realized it was not my cup of tea. However, the institution allowed you to apply for a change in course at the end of the first year. I had decided to switch to maths towards the middle of the third semester, so I was asked to write an application to effect the change. I hadn’t told my parents till then (laughs). I wrote them a longish letter because at that point (in 1989), they had some apprehensions about a purely academic career. I don’t think my parents were fully convinced, but they let me go ahead. Within six months, they reconciled to the fact. We had some outstanding teachers. I recall, in particular, one teacher—Shobha Madan—who taught us two or three courses in topology and that really sort of fuelled my love for that subject.
When did you first feel drawn to spirituality and becoming a monk?
I just wanted to do math. But when I was at Berkeley, I sort of decided during my third year that this (becoming a monk) may be a good idea. It was around 1995. It was not very sudden. It was a slow process. I wanted to be of some service to others in the larger sense. For that, being part of the Ramakrishna Mission made sense. I finished my PhD in 1997 and came back to India. It took another six months to convince my parents, who were concerned, among other things, that I would not have a bank balance or family. During this period, I patiently worked at the Chennai Mathematical Institute. I joined the Chennai Math (branch of the Ramakrishna Mission) in March 1998. It took my parents a while to get accustomed to my being a monk.
How do you reconcile dealing with spirituality on the one hand and subjects like geometry and topology on the other?
Spirituality is an extremely loaded term. In the context of the Ramakrishna Mission, it is pretty simple. There is a personal quest. So, when we are doing our research, it’s the quest for knowledge. It’s a personal thing. The other part is service—to be of relevance to a larger group of people. So when one teaches maths, it is the service part to a larger community; when one does research, it’s the personal part. There are some stereotypes associated with this word called monk, which is what perhaps contributes to this perceived contradiction. Hence, for me, being a mathematician is not that far removed from being a monk.
What is your current role at TIFR?
I joined the School of Mathematics at the institution in November, and it has been lucky for me (referring to him getting the Infosys award in the same month). There isn’t too much teaching. It’s primarily research. But I visit IIT Bombay once a week to teach some students there. India has a strong and old tradition in pure mathematics like Bhaskara and Aryabhata. But geometry, per se, is not that old. It is picking up. The area that I work in, which is geometric topology, has just about 10-15 mathematicians in the country.
Can you simplify the term geometric topology?
The area of geometry that I work on is called hyberbolic geometry (non-Euclidean geometry). Geometry deals with properties of lines, circles, planes, points, etc. Imagine two branches from the trunk of a tree—they will form a ‘Y’ shape along with the trunk of the tree. If a squirrel wants to move from one branch to another (assuming it does not jump), it will have to travel down from one branch to the point where it meets the trunk and then climb up the other branch. Let’s name the base of the tree as 0, the tip of one branch as 1 and let’s call the tip of the second branch 2. Let’s name the point at which these branches meet as X. Thus, the squirrel will have three paths—1-X-2; 0-X-1; and 0-X-2. These are the analogues of the three sides of a triangle in the plain geometry that we studied in school. In plane Euclidean geometry, you can imagine squeezing out whatever is inside a triangle till it becomes a Y (of the tree). You can play the same game with a tree with more branches. So what’s the difference between a Euclidean triangle and this Y? If you scale the Y by making the tips longer, they still have a meeting point. But if you continue to make the sides of a Euclidean (Euclid, the Greek mathematician from Alexandria is often referred to as the “Father of Geometry”) triangle longer, the inside fat area will become fatter and fatter. Spaces which have triangles that are uniformly thin are called hyberbolic spaces.
What we have described above is one side of the story: hyperbolic geometry. Next, when you observe a tree a little closely, you will notice that the initial branches are not as long as the trunk. And the branches continue to grow shorter and shorter till you get very small, slender branches. The question that a hyberbolic geometer would ask is: Why do the branches become smaller as you go further away from the trunk? Is it an accident? Why, for instance, are leaves not as long as stems? The answer is that had they been so, you would have not been able to fit them in 3D space. What’s happening here is that the hyberbolic geometry of the tree is conflicting with the flat Euclidean geometry of the three-dimensional space in which we live. If you look closely at the foliage of the tree, you will notice that the large structure of the tree is being replicated at the tip of the branches. This kind of geometry at the surface of the tree is self-replicating. Thus, it has a property that may be described as “self similarity at all scales”. The foliage is an example of a fractal. In effect, there is a constant interplay between the two-dimensional fractal geometry on the surface of the tree and the 3D hyberbolic geometry of the tree itself. This is a kind of naive visual representation of most of the work I do.
What are the applications of your work? For instance, according to a May 2010 paper by Bell Laboratories, hyperbolic metric spaces seem to be a good model to study traffic behaviour in large complex networks…
Let’s consider the transmission of signals in the brain. The connection of neurons inside the brain is analogous to hyberbolic geometry, while the brain’s surface can be said to be fractal in nature. I don’t think too much work has been done to really use this particular example, but some kind of hypothesis has been structured for neural connections. A similar thing takes place on the Internet, with the large number of pipes connected to each other. It will be completely untrue to say that this is an application of my work. Rather, it’s an application of the broad area which covers my work.
Do you think enough is being done to popularize mathematics in India?
A lot of work has been done in the last couple of decades. We have the Math Olympiad (the Mathematical Olympiad Programme in India leads to participation of Indian students in the International Mathematical Olympiad) and Board of Mathematics (National Board for Higher Mathematics) that have really sparked off a lot of interest in maths. States like Maharashtra and Bengal have benefitted greatly from these moves.- Courtesy / Read More … cyclopaedia / Ramakrishna Mission Vivekananda University