Strength In Numbers

WHO CARES ABOUT the applause? Do I need applause to feel good about myself?” Attributed to reclusive Hol­lywood actor Marlon Brando, these words may well have been uttered by a mathemati­cian. Denizens of academia, especially those whose world revolves around numbers, tend to view it as a world sufficient unto itself and not burdened by the happenings outside it. But Neena Gupta is different. Much as she would like to hunker down in her office at the Indian Statistical Institute (ISI) in Kolkata and work on the next problem, she knows the importance of having—and being—a role model. Considered one of the most promis­ing young mathematicians working in India today, Gupta, 39, has been selected to deliver the Emmy Noether Lecture at the Joint Math­ematics Meetings to be held in Seattle, US, in January 2025. This is a big deal, not only because it is a high-profile academic event, but also because Noether was a pioneering mathematician who fled Nazi Germany in 1933 and spent the next two decades in the US advancing the field of abstract algebra and forging a path for future women mathematicians. “For In­dian women, it is very important to get recognised, because otherwise, their families may no longer support them in their pursuit of research,” Gupta says. Pure luck and a rebellious streak combined to help her pursue a Master’s programme in mathematics followed by a PhD. “ISI was just a kilometre from home. That’s the only reason my parents allowed me to study further. There was talk of marriage when I finished my undergrad but I asked for more time. I promised my parents I would finish my PhD in two-three years,” says Gupta, who now has an eight-year-old daughter.

Like a tree flourishing against all odds, Gupta won the 2021 Ramanujan Prize for young mathematicians from developing countries, for her work in affine algebraic geometry and com­mutative algebra, specifically for her solution to the Zariski can­cellation problem. “International recognition like this comes maybe once in a lifetime if one is lucky. I am very aware that this award may well inspire other young Indian women to take up mathematics,” says Gupta, who was awarded the Shanti Swarup Bhatnagar prize, the highest honour in India in the field of science and technology, in 2019. Slowly, as more women take up research in mathematics—Gupta has two women students pursuing their PhD with her guidance—she hopes it becomes a level playing field. “Academics get maternity leave but only if they have tenured positions. What if you are a postdoc?” Wom­en have to “make sure to showcase their work” and “put them­selves out there” to be recognised, she says. “When you have a young child, you tend not to travel to conferences or network with other faculty members. I have been in that position and I know how important it is to sell yourself, even as you continue to do good maths. It’s definitely harder for women. But when maths is a passion, not just a job, you don’t worry about all this, you don’t even worry that it may not be a lucrative career. You just want to keep doing maths.”

Some of Gupta’s most cherished memories from childhood are of solving problems at home after school. Successful wom­en mathematicians seem to share a love of the subject from a very young age, and a consequent dogged pursuit of it, disre­garding social norms and well-meaning advice from peers. Parental support, generous academic mentors, and husbands who made sure they did not have to sacrifice their careers to solve the ‘two-body problem’ of dual-career couples in aca­demia certainly helped, but they weren’t—and still aren’t—a given for everyone. Like her namesake, V Lakshmibai was a te­nacious and sharp mind in the area of algebraic geometry, men­tored by CS Seshadri, one of the greats of Indian mathematics, and yet, she left India following a difficult marriage to teach at Northeastern University in Boston, US. Lakshmibai died last year, aged 78. The Indian Women and Mathematics (IWM), a collective formed in 2013, and funded by the National Board for Higher Mathematics (NBHM), plans to honour her at its annu­al conference this year. IWM has been working to address the gender gap in mathematics by organising workshops, talks, and conferences, both regionally and at the national level, for undergraduate, postgraduate, and PhD students.

Anita Naolekar, a member of the executive committee of IWM since its founding, estimates that there may be about 2,000 women working in maths in India today, including PhD students, postdocs, and faculty. “The numbers are slowly in­creasing but we don’t know where the women disappear post PhD. With the new IISERs and other institutions, there are more faculty positions than ever, but we don’t yet see as many women in top jobs in mathematics,” says Naolekar. Outreach efforts by IWM include getting prominent mathematicians to tour small towns and give talks; a winter school for women students in the second year of their undergraduate course; regional conferences conducted in a different part of the coun­try every year—in Maharashtra, Kashmir, and Gujarat in the past three years—where local students and professors get to interact with leading mathematicians; building a network for women mathematicians and other interventions. “The results are beginning to show,” says Naolekar. To be sure, the All India Survey on Higher Education (AISHE) report 2021-22, released in February, indicates a heartening trend, with wom­en students enrolled in PhD courses doubling from 47,717 in 2014-15 to 98,636 in 2021-21. In mathematics, women now make up about 43.4 per cent of all PhD students and 60 per cent of MSc students. “We have a long way to go before more women start producing world-class research. At premier research institutes, even now we come across some batches without a single woman,” says Naolekar, who was the only student from her batch at IIT Kharagpur who hadn’t applied for placement after MSc. “At every stage, I kept applying for the next course, and the next, until it was clear to me that I simply wanted to do mathematics all my life,” she says.

IN THE EXCITEMENT around STEM (science, tech­nology, engineering, and mathematics) in India post Chandrayaan-3, mathematics is still the least glamour­ous subject—partly because “mathematicians don’t throw around buzzwords like physicists and bioscientists do,” says Sujatha Ramdorai, a globally recognised number theorist who was awarded the Padma Shri last year for her contribution to mathematics. “People have heard of string theory, dark mat­ter, and nanoparticles, even if most of them don’t really know what these are. In contrast, I have been asked if number theory is the same as numerology. Very few people realise that you cannot do rocket science or even build a strong bridge with­out mathematics,” says Ramdorai, who was the first Indian to receive the Ramanujan Prize in 2006. After high school, Ramdorai very nearly chose computer science before realising that the abstraction inherent in mathematics held a deep aes­thetic appeal for her. She enjoyed the institutional freedom of the Tata Institute of Fundamental Research (TIFR), Mumbai, even as her peers working in the industry were earning six times her salary. “I grew up in a society that respected teach­ers, but now, people think you end up as a teacher if you fail at everything else,” she says. “As a country, we get more bang for the buck for whatever little we invest in science and maths. The fact that we have so many mathematicians competing at the highest levels despite the lack of a concerted effort to pro­mote mathematics is proof of this,” says Ramdorai, who has served for over a decade on various advisory committees for the Government of India, including the National Knowledge Commission and the Scientific Advisory Council to the Prime Minister. Diagnosed with brain cancer in 2015, Ramdorai now splits her time between Canada, where she is a professor of mathematics and Canada Research Chair at the University of British Columbia, and Bengaluru, where her mother lives, and continues to do top-tier research.

Many of Ramdorai’s teachers, including Parimala Raman who was her PhD adviser, were women and she found herself turning to Emmy Noether, who had in fact mentored Albert Einstein, for inspiration. Ramdorai’s story, which begins with her choosing to do research at TIFR as a young mother, is one of several moving biographies of mathematicians that appear in Lilavati’s Daughters, a book of essays on 100 women scientists published in 2008 by the Indian Academy of Sciences. Daughter of the 12th-century mathematician Bhaskaracharya, for whom he wrote the eponymous treatise, Lilavati was the first woman student of mathematics in India. “She has innumerable descendants … the Indian women of sci­ence,” the book’s foreword explains. Among them is the first generation of successful women mathematicians from India, including Mangala Narlikar, Parimala Raman, Rajinder Jeet Hans-Gill, Sudesh Kaur Khanduja, Indira Narayanaswamy and Mythily Ramaswamy, who have raised an impressive cohort of younger mathematics researchers and set the stage for many Lilavatis to come. Having such role models and mentors, and stories of other successful women working in the field, has surely helped many a young mathematician reinforce her self-worth.

WHEN SIDDHI PATHAK, a 31-year-old assistant professor at the Chennai Mathematical Institute, is invited to give lectures at universities in south India, students are often taken by surprise, she says, “because they are used to older male professors”. Slowly but surely, this perception is changing, with young women like her teaching at some of the most prestigious institutions for mathematics in the country, including the IITs, the IISERs, and the IIITs. “We now have many students completing their PhDs quickly and taking up their first jobs at a very young age. I am especially impressed with the quality of women students we have been getting in recent years,” says Sanoli Gun, a number theorist from the Institute of Mathematical Sciences (IMSc), Chennai. Women students at IMSc tend to do quite well and are never at the bottom of the class, says Gun. “The challenge with female students is that we have to deal with more than mathematical problems. Even though we don’t want to, we always end up get­ting involved in their personal lives to troubleshoot problems they may face at home or in society at large.”

Gun is the first elected president of the Asian-Oceanian Women in Mathematics, the continental organisation for women mathematicians established in 2022 by the Committee for Women in Mathematics, which is a part of the International Mathematical Union, to push for women’s rep­resentation in mathematics in Asia. “There are lots of women mathematicians in South Korea, and very few in Japan. India is somewhere in the middle,” says Gun, on the sidelines of a policy meeting at the International Centre for Theoretical Sciences (ICTS) in Bengaluru to outline a vision for the future of STEM. As far as women’s representation in mathematics goes, Gun sees two main problems. “Eighty per cent of our students come from remote rural places. But the women students we get generally come from well-to-do urban back­grounds. There is a huge pool of students we are missing out on,” she says. The second problem is that women remain invisible despite doing good work. “Many women have not been acknowledged over the years simply because they work quietly, and rarely fight for recognition, and because they are overlooked by default. Very often, male organisers do not bother to look for competent women to invite to give talks or chair committees.”

Radhika Ganapathy, a number theo­rist at the Indian Institute of Science, Ben­galuru, is one of the quiet ones, working away at her office on the upper floor of the Department of Mathematics, a handsome building set in a verdant garden. “I think most mathematicians only worry about being recognised within the community, or even by a small subgroup of research­ers that they personally respect. That is the only validation we get,” she says. Increas­ingly, however, more and more women mathematicians are participating in the big dialogue of women in STEM and in­volving themselves in efforts to open up imaginative spaces for young girls so that they may be able to consider a career in pure science or mathematics. Early ex­posure to academic research, or even in­teractions with researchers conducted at the high-school level, could help draw more students to STEM, says Ganapathy, who took up academics because her brother did so before her. A supportive family is almost a prerequisite, she says, to succeed in a career that may only start yielding fruit when one is 40 or older. “There are few positions at research institutions in India, which means that most of us end up doing two postdocs and we are close to 40 by the time we have tenure. If you want to wait that long to start a family or to get married, not many parents will be okay with that.” A career in academics does give you the flexibility to raise a family while you teach and pursue research, she says. Ganapathy’s day begins early and she winds up in the afternoon to go home to her young son.

Riddhi Shah, a professor of mathematics at Jawaharlal Nehru University in Delhi and a former chair of the IWM executive committee who moved from TIFR to the national capital in 2007 so that she and her husband, a theoreti­cal physicist, could finally be together after 14 years of marriage, admits it wasn’t easy to bring up a child alone while missing out on networking opportunities. “When people went to lunch and talked over tea, I picked up my son, fed him lunch, and took him to daycare.” She has since been campaigning for support structures, opportunities, and toilets for women at academic institutions. “I was among the lucky ones,” she says, referring to her supportive family, and a charmed childhood in Ahmedabad. In her story featured in Lilavati’s Daughters, she says she enjoyed the TIFR interview so much that she didn’t care about the outcome. “I feel that our going to remote places to conduct lectures and workshops has had some im­pact. I have had girls from small towns tell me that talking to women mathematicians inspired them to do a PhD,” she says.

Girls no longer have to be rebellious prodigies to pursue a career in mathematics, says Vinay Nair, cofounder of the Rais­ing a Mathematician (RAM) Foundation, a Mumbai-based nonprofit that conducts workshops and residential camps for students with a “bigger appetite for mathematics”, bringing experts from academia to give lectures with a view to build­ing a research mentality. “There are resources and networks available to them before they set out into their adult lives and decide on a career path. More importantly, there are a lot of educators working on making maths interesting at the school level,” he says. RAM also conducts a week-long online camp for girls aged 12-15 and continues to nurture them for months, helping them prepare for Olympiads, apply for fellowships, and audit courses online. “There is nothing quite like the col­lective energy of 100-plus students passionate about math­ematics and trying to solve problems together all day and well into the night,” says Saee Patil, a precocious 17-year-old from Sangli, Maharashtra, who has attended several programmes conducted by RAM, including the residential flagship RAM Training Programme in 2018. “At the time, all I knew was some advanced algebra and geometry. The camp exposed me to some very cool maths, like topology and fractals. I have also developed an interest in theoretical computer science since then,” says Patil, who has represented India at several maths Olympiads but decided to consciously focus on “enjoying the maths” instead of being competitive. “When I was four, I figured out a nice trick to add two single-digit numbers. Then I found a pattern in the table of 99 that blew me away. Then I started wondering about divisibility tests for prime num­bers,” says Patil, who is unschooled and lives on a farm with her sister, parents, and pets. “I have always been interested in maths, but meeting and learning from mathematicians has made me want to go to CMI [Chennai Mathematical Institute] and to pursue academics.”

bioscientistseducationIndian womenmathematicsNeena GuptaphysicistsRiddhi ShahSujatha RamdoraiWomen Issue 2024