Women In Science
Neena Gupta: Shaping the Future of Algebraic Geometry
She was awarded the Infosys Prize for her groundbreaking work on the Zariski Cancellation Problem, a fundamental question in algebraic geometry first posed in 1949 by Oscar Zariski, one of the pioneers of the field
EdPublica has the privilege of speaking with Professor Neena Gupta, the recipient of the prestigious Infosys Prize 2024 in Mathematical Sciences. Professor Gupta is a faculty member in the Theoretical Statistics and Mathematics Unit at the Indian Statistical Institute, Kolkata. She was awarded the Infosys Prize for her groundbreaking work on the Zariski Cancellation Problem, a fundamental question in algebraic geometry first posed in 1949 by Oscar Zariski, one of the pioneers of the field. In 2014, she made a striking contribution by proving that Asanuma’s 3-dimensional affine variety provides a counterexample to Zariski’s original Cancellation Problem in positive characteristic. Her solution to this long-standing problem, which challenges a key assumption about the structure of affine varieties, has had a profound impact on both algebraic geometry and commutative algebra.

In this interview, we discuss the inspiration behind her research, the broader implications of her work, and the challenges she has faced as a woman in a historically male-dominated field. Professor Gupta also shares valuable insights for young aspiring mathematicians, offering advice on how to navigate the complexities of both academic life and career development.
Dear Madam, congratulations on winning the Infosys Prize 2024 in Mathematical Sciences! How does it feel to receive this prestigious recognition for your work on the
Zariski Cancellation Problem?
I am very happy to receive this recognition. It gives me a sense of fulfillment that the broader mathematical community (not just experts in my area) and society are recognizing the importance of my work.

Your work has had a significant impact on affine algebraic geometry. What was the initial inspiration or motivation behind pursuing this area of research, and what makes this problem so fundamental in algebraic geometry?
I first became aware of this area of research through lectures in algebra seminars delivered by Professor Amartya Kumar Dutta, long before he became my official supervisor. Some of the fundamental problems in this area are simple to state, and even an MSc student can understand and appreciate their importance. My curiosity to learn more about them motivated me to study the literature in this area and eventually pursue research under the supervision of Professor Dutta.

Can you briefly explain the Zariski Cancellation Problem to our readers and describe the significance of your solution in resolving this long-standing question?
The problem asks: if the affine cylinder over an affine variety is isomorphic to an affine space, does it mean that the affine variety is necessarily isomorphic to an affine space? I was the first to show that an affine 3-dimensional variety, constructed by T. Asanuma, is a counterexample to the Zariski Cancellation Problem in positive characteristic.
Your result answers the Zariski Cancellation Problem in the negative for positive characteristic. What are the broader implications of this breakthrough in algebraic geometry and commutative algebra?
The affirmative solution to the Zariski Cancellation Problem by Fujita, Miyanishi, Sugie, and Russell for two-dimensional space has been applied in several problems, leading to new theories. Therefore, it was desirable to know whether cancellation could occur in higher dimensions. My solution to the problem is negative, providing a crucial check for mathematicians to avoid the mistake of assuming cancellation in higher dimensions.
Your work on this problem revealed unexpected connections between various mathematical concepts. Can you give us an example of one such connection, and how it may influence future research in these fields?
I developed a theory that revealed surprising connections between the Zariski Cancellation Problem and other fundamental problems such as the Characterisation Problem, the Epimorphism Problem, and the Affine Fibration Problem. The theory simplified the technical arguments in my earlier papers, provided deeper insights into recent breakthroughs (including my own results), and may have paved the way for new discoveries. I used ideas from this theory to construct higher-dimensional counterexamples to the Zariski Cancellation Problem in positive characteristic.

You have achieved significant milestones in your career, including being one of the youngest recipients of the Shanti Swarup Bhatnagar Prize and the Nari Shakti Puraskar. As a woman in a field that has historically seen fewer women, what challenges have you faced, and what advice do you have for young women aspiring to build careers in mathematics and science?
I have faced the challenges that most women face, such as balancing family responsibilities, especially raising children. Fortunately, I have not faced any discrimination in the workplace, and I have a supportive family that has always shared my responsibilities, allowing me to focus on my research.
Do you think the landscape for women in mathematics and science has evolved over the years? What steps can be taken to further encourage young girls and women to pursue careers in these fields?
Certainly, there are now more women in mathematics than there were earlier, and this number is only going to increase. Having role models in this area always helps. We need to continue supporting these role models and ensure that young girls see these women as proof that they too can succeed in mathematics and science.
As a role model, how important is it for women to be represented in the mathematical sciences, and how can institutions and mentors better support women in advancing their careers?
Women constitute half of our strength, and they are equally capable of contributing to basic science and mathematics—in fact, in almost all areas of life. However, they often take on additional responsibilities within the family. With the support of family, government, and institutional measures, women can also contribute freely to the development of science and technology.

The field of algebraic geometry continues to evolve rapidly. What are some of the emerging areas within this field or in related fields that excite you, and what questions are you most eager to explore in your future work?
I find the embedding problem of Abhyankar-Sathaye very exciting. It presents an intriguing challenge, and I am eager to explore the deeper connections it may have with other areas in algebraic geometry.
As a winner of the Infosys Prize, you will undoubtedly inspire the next generation of mathematicians. What message would you like to share with young researchers who are just starting their journeys in mathematics and science?
It may initially seem difficult, but hard work and perseverance always pay off. I would urge young researchers to start early, focus on concepts, pursue research in areas they are passionate about, and not be intimidated by the size or complexity of problems. Keep pushing forward, and you will make breakthroughs in time.
Women In Science
Protecting Life on the Mountainsides: A Conversation with Prof. Le Roux
In this conversation, she discusses what’s driving rising roadkill risks in Africa’s mountains, how vulnerable species are being affected, and why conservation planning must rapidly evolve to protect these fragile ecosystems. Women in Science is a recurring Education Publica column profiling women scientists from around the world — their work, journeys, and impact
In this edition of Women in Science, Education Publica introduces Prof. Le Roux, a leading behavioural ecologist and Assistant Dean in the Faculty of Natural and Agricultural Sciences, and Associate Professor in the Department of Zoology and Entomology at the University of the Free State. Her work spans biodiversity, mountain ecosystems, and the escalating threat of wildlife mortality on roads. In this conversation, she discusses what’s driving rising roadkill risks in Africa’s mountains, how vulnerable species are being affected, and why conservation planning must rapidly evolve to protect these fragile ecosystems. Women in Science is a recurring Education Publica column profiling women scientists from around the world — their work, journeys, and impact.
You’ve dedicated your career to behavioural ecology and zoological sciences. What inspired you to pursue this path, and how has your journey shaped the way you approach issues like wildlife conservation and mountain biodiversity?
I’ve always loved being out in nature, ever since the first time my father took me for a hike up Table Mountain. Growing up, I experienced first-hand how wild animals and wilderness can be good for the soul (not just for the planet and for our physical health) – and then, as an adult, I saw in Europe and North America how very little wildness remains over there. This has really driven it home to me that we, on this continent, have very precious, living resources that we need to protect – and these resources are particularly unique in mountains. Disregarding this in favour of mining and other capitalistic ventures is really just speeding us along to a dystopian future.
Your research highlights the growing risk of roadkill in mountainous regions, particularly for endangered and vulnerable species. How is the expansion of road networks affecting wildlife in these areas?
Quite simply, these areas were previously less accessible to humans and vehicles, and the expanding road networks are changing that equation. Species at high altitudes now become more exposed to potential invasive species (which humans transport deliberately or accidentally) and collisions with vehicles. Our vehicles move far faster than natural predators do, so escaping the risk of oncoming traffic is not something any species is particularly adapted to. Populations will need to learn to avoid traffic and/or roads, if at all possible. This is not usually possible.

You mentioned that certain species, such as African wild dogs, lions, and elephants, are particularly vulnerable to roadkill. How do IUCN categories help frame the urgency of this problem?
The IUCN sets the global standard for us to understand which species to focus on in terms of conservation efforts. Knowing that nearly 8% of the mammals killed in mountains were of conservation concern, we must realise that we cannot simply ignore the risk. We are not just killing common species—we are killing species already at risk because of hunting pressure, climate change, and other threats.
Your findings show that amphibians are killed at the highest rate in mountainous regions, while mammals face greater risk in low-lying areas. What explains this difference?
It is difficult to answer because there is very limited data on population sizes of amphibians and mammals at different altitudes. Mountains provide more variation in microhabitats, so there may be pockets of ideal amphibian habitats with more freshwater and cooler microclimates. When a road cuts through such a pocket, a single car could kill dozens of amphibians at the “right” time. This should be studied further. These microclimates do not affect large mammals in the same way. It is also unclear whether mammals are killed more in low-lying areas because of more vehicles or more mammals.
Many small species are killed simply because they are less visible. Is there a broader societal or policy bias that undervalues smaller species?
Humans have an affinity for larger, charismatic species. However, the patterns are not only due to our personal biases—it is also practical. Drivers see larger animals more readily and avoid collisions because of potential damage to vehicles. Small animals are easier to disregard. Some drivers even deliberately kill snakes, but this did not create a large spike in the dataset. With effective communication, we could make drivers pay more attention to small but “special” species. We can change our behaviour.

Unpredictable weather patterns and the topography of mountain roads contribute to wildlife-vehicle collisions. How can infrastructure or road design help?
Mitigation often involves wildlife crossing structures—overpasses or underpasses—and warning signs in high-risk zones. For this to work in mountains, planners need to identify these high-risk zones and determine which structures or traffic-calming interventions are feasible. This will be a unique challenge in mountain environments.
Your study, covering 10 countries and spanning more than five decades of data, reveals major gaps in data collection. What are the most pressing gaps?
There are vast gaps in our information on population sizes and densities of vertebrate species in most African countries. If you look at the Map of Life, you’ll see how little biodiversity data we have from central and west Africa. We also found no roadkill studies in these large regions. We need to support scientists in those countries to investigate the challenges and potential solutions.
Mountain regions host unique biodiversity. How does roadkill threaten these rare or endemic species?
Because of the topography and history of mountains, they frequently host critical, unique biodiversity. Many are biodiversity hotspots. These endemic species cannot easily escape climate or anthropogenic change because physical barriers limit movement. There is also only so far “up” they can move. This is different in lowlands. Roads bring a new threat to species already vulnerable due to climate change.

Data collection on roadkill is often inconsistent. What needs to change to get a more accurate picture of the crisis?
It would be helpful if we had an international body to coordinate monitoring of roadkill risk, but I am not aware of such a body. It is not a methodological issue.
How can governments and conservation groups balance infrastructure development with protection of vulnerable species?
City planners, municipalities, and ecologists need to collaborate. Rather than relying solely on Environmental Impact Assessments, ideas for green spaces, wildlife corridors, and ecological connectivity should be included at the design stage of new developments. Such planning benefits environmental health and human wellbeing. Architects and engineers should also be encouraged to “think green” from the start.
What urgent actions are needed from both the scientific community and the public?
Identifying roadkill hotspots is essential as a first step. There are many areas where roadkill risk is lower, so we need to know where to focus mitigation measures.
Women In Science
Women in STEM Need Systemic Change
Stay committed, stay curious, and never underestimate the impact your work can have on the world
Despite notable gains in women’s participation in science careers in South Africa, women remain underrepresented across STEM fields. While more women are graduating from universities, studies continue to show that men dominate science, technology, engineering, and mathematics careers — a gap that is even more pronounced among Black women. Although women form the majority of young university graduates nationally, only about 13% of STEM graduates are women, and Black women remain significantly underrepresented in senior academic and research leadership positions.
These disparities stem from systemic barriers including gender bias, limited access to mentorship, and inconsistent availability of resources. Such obstacles continue to hinder the full and equitable participation of women in scientific careers.
At the University of the Free State (UFS), where I work, there is a growing institutional commitment to support emerging researchers — particularly women — through mentorship and research development initiatives. This aligns with Vision 130, which aims to foster research excellence and increase societal impact. I am fortunate to be part of the university’s Transformation of the Professoriate Mentoring Programme, designed to build a strong cohort of emerging scholars. The programme provides academic and research mentorship, supports access to networking and funding opportunities, and nurtures candidates toward assuming senior academic and research roles. It also helps lay the groundwork for future centres of research excellence.
Those of us who benefit from such opportunities carry a responsibility to extend mentorship to more women researchers, especially from underrepresented groups. Expanding women’s participation in science requires addressing the barriers that continue to limit progress. Key interventions include expanding mentorship and networking opportunities, increasing financial support and scholarships for women in STEM, and promoting national policies that support work–life balance and the needs of working mothers.
There is also an urgent need to raise awareness about women’s contributions to science and challenge persistent stereotypes that discourage girls from pursuing scientific careers. Building inclusive, diverse work environments where women feel valued and supported is essential to increasing both participation and retention. Progressive policies that promote the employment of Black women academics in STEM leadership roles are also critical. A diverse cohort of women in authority can provide gender-sensitive mentorship and create pathways for future scholars.
Pursuing a career in science demands hard work, resilience, and a commitment to continuous learning. It is a challenging journey, but deeply rewarding for those passionate about contributing to the advancement of humanity through research. It requires uncovering new insights, developing innovative solutions, and sharing knowledge that can transform lives. Marie Curie captured this spirit beautifully when she said, “I am among those who think that science has great beauty… like a fairy tale.” This sense of wonder should fuel every aspiring researcher.
Science is also fundamentally collaborative. Seek mentors, build networks, remain humble, and embrace learning from others. Your contributions — even those that seem small — form part of a larger scientific story that future generations will build on. If you are driven by curiosity, purpose, and a desire to contribute to the greater good, a career in science may be the path for you…
Interviews
Geometry, Curiosity and Finding ‘Her’ Place
Dr Laura Monk has quickly become one of the field’s most exciting young geometers
In modern mathematics, where imagination meets deep abstraction, Dr Laura Monk has quickly become one of the field’s most exciting young geometers. In 2024, she was awarded the Maryam Mirzakhani New Frontiers Prize, an honour regarded as one of the most prestigious recognitions for early-career women mathematicians and presented at the Breakthrough Prize ceremony—often called the “Oscars of Science.” A mathematician whose work explores the geometry of negatively curved spaces, Monk’s path into the field was shaped not only by intellectual fascination but also by uncertainty, self-doubt, and the search for belonging—a journey familiar to many women in STEM. Growing up in France, she found early encouragement from teachers who pushed her to think harder and explore deeper. Later, mentors like Nalini Anantharaman and the pioneering legacy of Iranian math genius Maryam Mirzakhani helped her see that mathematics could be a creative, expansive world—not an exclusive club.
A Royal Society Dorothy Hodgkin Fellow and Lecturer at the University of Bristol, Monk works on the geometry of negatively curved spaces and the behaviour of objects moving within them. In this conversation with Dipin Damodharan, she speaks candidly about intuition, representation, hyperbolic geometry, and the courage required to stay in mathematics when you’re not sure you fit.
‘Go for it! Math is super cool and useful’
To start with, could you tell us how your journey in mathematics began? Was there a defining moment when you realised this would become your life’s work?
I always enjoyed mathematics at school and thought it would be a good idea to study it, as I was interested in it and it opens the door to many jobs. After my first two years of study, I realized I loved the subject itself more than the idea of finding a job using it, and decided I wanted to work in mathematics (probably as a teacher).
I faced many challenges and doubts—I somehow never felt sure mathematics was “for me,” even though I loved it. But I’m very happy I stuck with it and made a few leaps of faith at the right times. At the end of my master’s, I decided to start a PhD because it is required for certain higher education teaching positions in France. I thought: three years is a lot of time, better get excited and really go for it! Luckily, I met my PhD advisor, Nalini Anantharaman, who introduced me to a fascinating research project.
The way she ventured into different areas of mathematics, tackling ambitious new projects with no apparent fear, was an incredible inspiration. She was very different from the image I had of “the mathematician.” Her mentorship made me feel confident I could do it if I wanted to. And then I did!
Growing up in France, were there specific teachers, mentors, or institutions that played a pivotal role in shaping your mathematical thinking?
Mathematics is taught and shared, and I have many teachers to thank for my mathematical upbringing. My high-school teacher had extremely high standards and told me off a few times for doing the minimum instead of pushing myself. My second-year teacher gave me a first glimpse of how exciting venturing into the unknown can be during a research project.
One of the ways maths is taught in France is through a two-year intensive preparatory school followed by further studies at university. I found this structure gave me a strong basis to build on, as well as methods to organize myself and work well.

What were some of the challenges you faced as a young woman entering a field often dominated by men? How did you navigate them?
Mathematics is, indeed, a very masculine field, and one could imagine sexist behaviours to be common. I have to say, luckily perhaps, that this has not been my experience. I have always felt extremely welcomed into this community, whether as a student or a researcher.
However, I did still struggle very much as a student with finding a sense of place and purpose in what I was doing. Though these difficulties are quite universal, I think they were amplified by being one of the only girls in my cohort. Identifying this was very helpful in overcoming these feelings, because it led me to build strong connections with my peers, to find female mentors and role models, and to invest myself in events for young women, all of which helped tremendously.
Much of your work lies at the intersection of geometry and dynamics. Could you explain your research focus in simple terms?
I study certain types of surfaces called “hyperbolic surfaces.” Unlike a piece of paper (which is flat) or a sphere (which is positively curved), hyperbolic surfaces have negative curvature: they look like Pringles. There exist many, many hyperbolic surfaces, and they appear in very different fields of mathematics: number theory, mathematical physics, dynamics…
I am trying to understand what these surfaces “look like” a bit better. In order to do so, I put all of them in a (big) bag, take one at random, and try to describe it.

Mathematics often requires deep abstraction. How do you stay connected to the beauty or “reality” behind these abstractions?
I relate more to the beauty than the reality! To me, mathematics is a gigantic world that we are building or exploring together. I find a lot of joy in how different parts of this world interact and how bridges can be built; simple ideas can come together from far apart and create something new.
What role does intuition play in your mathematical process?
A big role! One of the reasons why I have been drawn to mathematics is that, once you understand a formula or a theorem, you don’t really need to memorize it by heart anymore: it just makes sense. When I learn something new, I go through a lengthy process of unravelling everything and I often feel very confused (or sometimes even a bit desperate!).
But, one day, all of a sudden, everything becomes clear, to the extent that it is even hard to remember why I was so lost initially. I think this is one of the reasons why it is so hard for us to share and convey what we do to one another, or to the general public.

Maryam Mirzakhani’s groundbreaking work in geometry and moduli spaces continues to inspire mathematicians globally. In what ways has her work influenced your own research? You have worked on topics that build upon or are inspired by Mirzakhani’s legacy. Could you speak about this continuity—how do you see her influence evolving in your field?
Maryam Mirzakhani created my research field, and I have studied a certain part of her work in great detail. My research consists in picking a hyperbolic surface at random and looking at it. She was one of the first people to have had this amazing idea. At the time, there existed a probability model allowing one to pick hyperbolic surfaces at random, but it was completely abstract and unusable.
Through several beautiful breakthroughs, she created a method that made this possible. We are still at the beginning of the wide variety of applications following from these advances.
If you could give a message to a young girl fascinated by numbers but unsure about pursuing math, what would you say?
Go for it! Math is super cool and useful, so you will have loads of fun and learn a lot. It is ok if you don’t identify with the image of the “math guy”; there are a lot of ways to enjoy math. It is not just about proving theorems or solving exercises, it is about creativity and sharing.

Outside of mathematics, what brings you joy or fuels your curiosity?
I quite like jigsaw puzzles and knitting, both of which relax me and make me appreciate how a lot of little steps can come together to create something big. Right now, my main source of joy is my two-year-old daughter, and seeing her discover the world. If only we could stay this curious and observant about every single little thing!
Do you think artificial intelligence and computers are changing the way we do mathematics?
Computers definitely have! We used to pay people to perform long lists of computations for researchers, and to publish entire books of randomly generated numbers in order to study probabilities. Now both of these activities seem very silly. Mathematicians use computers all the time, whether to perform experiments, find the answer to a simple question, or write and share their work.
I personally choose to be optimistic about the future of AI. You would have a very hard time conveying to someone in 1980 the role that computers play in everyone’s lives, but for mathematics, they have greatly enlarged our experience and allowed us to go faster, further. Things are scary now because we do not know what is ahead of us.
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