Science

This Mathematician Doesn’t Need to See the Board to Solve Problems

Sushama Agarwal, who was born with a visual impairment didn’t let it stop her from achieving her academic dream of becoming a mathematician.

Sushama Agarwal. Credit: The Life of Science/Nandita Jayaraj

Sushama Agarwal. Credit: The Life of Science/Nandita Jayaraj

Who? Sushama Agarwal

What? Mathematician

Where? Ramanujan Institute for Advanced Study in Mathematics, Chennai

Squeezing past police vans, barricades and scattered groups of demonstrators on the wide roads of Chepauk, I made my way to Madras University’s math department. A large peaceful protest was underway. This area in Chennai is no stranger to such demonstrations as many of government institutions are located here, including one of the main campuses of the 159-year-old University of Madras.

The University’s alumni include two Nobel Laureates, a former President of India, as well as world famous mathematician Srinivasa Ramanujan after whom its math department – where I was headed – is named. The small and somewhat dilapidated building of the Ramanujan Institute for Advanced Study in Mathematics (RIASM) is separate from the majestic main campus. On the outside, its walls are filled with the remains of political posters and graffiti. I walked in, past two students and a few policemen and women who seemed to be taking a break from patrolling duty.

When I entered her office, Sushama Agarwal greeted me with a cautious smile. Born and brought up in Bhusawal, a town in Maharashtra, Agarwal moved to Chennai for a Ph.D. in 1988. She has been a faculty member at RIASM for almost two decades now. Her expertise is an abstract area of mathematics called ‘functional analysis’.

An abstract idea with a lot of applications

“Functional analysis involves describing any process in the form of mathematical functions”, said Sushama. “By doing this, it is possible to model any experiment or system to predict its behaviour. Functional analysis enables better decisions in a multitude of different domains – economics, engineering and electronics.” Agarwal, however, is focused on the mathematical theory of this applied science.

The excerpt below nicely illustrates how the need of functional analysis arose:

“Mathematicians observed that different problems from varied fields often have related features and properties. This fact was used for an effective unifying approach towards such problems, the unification being obtained by the omission of unessential details. Hence the advantage of an abstract approach is that it concentrates on the essential facts, so that these facts become clearly visible and one’s attention is not disturbed by unimportant details. Moreover, by developing a box of tools in the abstract framework, one is equipped to solve many different problems (that are really the same problem in disguise!).

For example, while fishing for various different species of fish (bass, sardines, perch, and so on), one notices that in each of these different algorithms, the basic steps are the same: all one needs is a fishing rod and some bait. Of course, what bait one uses, where and when one fishes, depends on the particular species one wants to catch, but underlying these minor details, the basic technique is the same. So one can come up with an abstract algorithm for fishing, and applying this general algorithm to the particular species at hand, one gets an algorithm for catching that particular species. Such an abstract approach also has the advantage that it helps us to tackle unseen problems. For instance, if we are faced with a hitherto unknown species of fish, all that one has to do in order to catch it is to find out what it eats, and then by applying the general fishing algorithm, one would also be able to catch this new species.

Early life and dealing with loss of vision

Managing an academic career is no walk in the park and it was even less so for Agarwal who was born with an eye disorder that left her blind by the time she was in college. I had forgotten to ask her the name of the condition but I found from a profile online that it was retinitis pigmentosa, a genetic disease where the rod and cone cells of the retina die. As this happened, her eyes lost the ability to convert light rays into nerve impulses that can be translated into images by the brain. Reports say that retinitis pigmentosa is up to ten times more prevalent in India than in the west; up to two lakh Indians are affected by it. Agarwal’s vision began deteriorating while at school. “I could read from books but not from the blackboard. By the time I was doing my M.Sc., that also went,” she said.

Agarwal was always inclined towards subjects requiring logical thinking. Maths was her favourite. It was the subject she could understand most clearly, as physics and chemistry involved experiments that were difficult to do with her visual impairment. “That’s why I went on to study math.” She continued after a pause, “Even if I was sighted I think I would have been interested in math only…”

She was completed her B.Sc. in Bhusawal, but beyond that the future looked hazy. Her father had passed away just a few years before and as her siblings were away, Agarwal was the only one to give her mother company at home. There were not many options for higher studies and for her to leave her hometown she would need someone to support her. Due to these circumstances, Agarwal spent two years at home – “I was bored doing nothing.”

A turning point and a supporter for life

Agarwal’s turning point came when a friend agreed to accompany her to a different town to do her Masters. There, she met one of her teachers, soon-to-be husband, P. Veeramani. “He came to know that I had a problem when teachers wrote some things on the board without speaking it out. At these times, continuity is broken and I wasn’t able to understand.” Veeramani was mindful of this and began to take good care to say all the lessons out loud so that Agarwal could keep up with her classmates.

As a result, she found herself more interested in his classes. Her dedication did not go unnoticed by Veeramani, who encouraged her. For the first time, Agarwal began to believe that she could pursue a doctorate in the subject that she was so fond of. Agarwal and Veeramani decided to get married and in 1988 they moved to Chennai where the latter had secured a faculty position at IIT. This worked out really well for Agarwal too as she found her Ph.D. guide S.H. Kulkarni at IIT-Madras.

In 1996, she completed her Ph.D., making her, according to one newspaper, one of the first two blind students in IIT-M to do so. But Agarwal is wary of special attention. “It’s not like I had some aim or ambition. I just took one step at a time. At each step, I made a full effort.

There are difficulties

Seldom does she accept invitations by associations to talk to other blind students – “Firstly I’m shy,” she admits with a soft laugh. There’s more to her reluctance than this, though. “It should not be the case that they do math when they are not interested. Then it will be problematic. I want the blind students to know there are difficulties.”

“Often it happens that when I want to study, no one is around to read to me. When I want to refer something, I may not be able to [on my own]. But those things we have to overcome.” Clearly, having to depend on others is not very enjoyable. “If I have to take a class, I have to first prep. I need to ask a student to write on the board for me. Some of them are not comfortable with this and it’s troublesome if the writing is not coordinated with my speaking… It’s better to not be so dependent, no?”

“Sometimes I feel that they [the blind students] can instead pursue other things that require less dependence.”

One of Agarwal’s most difficult periods was after her Ph.D. when it proved tough to get a job. “I applied to some colleges but didn’t get called for interviews. Those days, it was difficult for everyone, but it was clear that I wasn’t being considered because of my difficulty.” But she got her break with University of Madras. “The then-Vice Chancellor was a professor in Tamil literature and had a student who was visually challenged. So he had the idea of how it can be managed.” Agarwal was invited for an interview and her responses their queries about manage correction, teaching, etc. were found to be satisfactory.

Were you not anxious at all, I asked her? She smiled, “There was a bit of fear. But not about teaching – that is no problem – only about the times I may be asked to evaluate other college papers. Those tasks are not mandatory but I was afraid I’d have to do all that.” Agarwal stresses that while visually challenged persons in academia like her may require better accessibility, technology and a bit of extra care, they learn quickly. “My concentration is more. Some say my memory is good. Anything you teach me, I’ll listen very carefully and learn.”

Sushama uses her recorder so that she can listen to certain concepts, theorems and their proofs over and over again. But besides that, she is not overly reliant on technology, although she admits that technological advancements are helpful for the visually impaired in general. Though there is a Braille system for mathematics, Agarwal does not use it. She didn’t find the need to as she was not born blind and can recognise the regular mathematical symbols if someone feels it out on her palm.

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An example of Nemeth Braille used to depict a math expression. Credit: The Life of Science

A helping hand

Throughout the interview, there was another person in the room witnessing our conversation. I’d presumed that she was another faculty member until Agarwal finally introduced her to me as her assistant Kamali Natarajan. Natarajan has worked with her for nearly four years now. “I go and pick her up in the morning, sit with her here and then go back with her to her home before returning to mine,” Natarajan said, in a mixture of Tamil and English. “Till I joined Ma’am, I was a housewife.”

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Sushama’s assistant Kamali

Agarwal told me that Natarajan did not continue her education after passing tenth standard and getting married early. After her children both married, she found herself with a lot of free time. So when Natarajan saw a job notice in the neighbourhood newsletter for a visually impaired maths professor’s assistant, she contacted Agarwal. “Today, Madam is like a friend. We share everything and if I don’t see her for two days I miss her,” Natarajan said, making Agarwal smile widely. “And of course, the salary I get is very helpful!”

So what is it like for a non-academic person to spend her days in a building full of mathematicians? Natarajan’s eyes widened in mock horror. “Math is very difficult, very difficult. If you look at the research scholars, you’ll see they are always serious. In other colleges, students talk about films, politics. But these students, nothing, only math math math.” I noticed Agarwal trying her best to restrain her amusement. “I feel like taking them to the waterfalls – you know – to cool their head. So serious they are always… anyway, they are great,” Natarajan added, dramatically. By this time Agarwal was chuckling at her assistant’s comments.

As I finished my tea and got ready to leave, Agarwal was thoughtful. “If I had been part of some association [of the visually impaired] right from the beginning, I would have also participated in all these activities – they go for trekking and walk very normally on the road, you know? I don’t go walking alone. I always take someone with me. But I just need a touch. Then I’ll follow her or walk side-by-side.”

Teaching at RIASM

The Ramanujan Institute teaches math in a way very few other colleges do, according to Agarwal. “We emphasise on the concepts rather than giving notes to study. In other places, they don’t do this because they want 100% results in their class. Because of this students may find it difficult, but only in their first semester.”

When she was a student herself, there were very few women taking up math. Today, 3/4th of her M.Sc. class comprises ladies. “Maybe this is because boys have more pressure to take up jobs [after graduation]. At least five or six of each batch of around 30 students go on to do their Ph.Ds,” said Agarwal.

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