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.

She has drawn recent attention for her ground-breaking research initiative related to neurodegenerative diseases. Her work explores the potential benefits of medicinal plants as supplementary treatments for neurodegenerative diseases such as Alzheimer’s, Parkinson’s, and Huntington’s. In this edition of ‘EdPublica’s Women in Science’ column, we introduce Dr Claudia Ntsapi, a researcher at the University of the Free State (UFS) in South Africa. Addressing the significant underrepresentation of Black women in senior academic and research leadership roles in the country, she discusses her latest research, the challenges faced by women in science, and more in an exclusive interview with EdPublica.

Dr Ntsapi, PhD, is a registered Natural Scientist (Pri. Sci. Nat) with the South African Council for Natural Scientific Professions (SACNASP). She joined the University of the Free State in late 2019 as a lecturer in the Department of Basic Medical Sciences. In addition to her teaching responsibilities, Dr Ntsapi leads the NeuroCancer Research Group, overseeing a multidisciplinary team specialising in cell biology, cell physiology, microscopy, biochemistry, and pharmaceutical methodologies.

Could you share details about your educational journey and current professional role?

I acquired my undergraduate and postgraduate qualifications at Stellenbosch University, completing a Master of Medical Science in Human Genetics in 2015 and a PhD in Physiological Sciences with a specialization in Neurophysiology in 2018. My current job profile is that of a Senior Lecturer at the University of the Free State’s Faculty of Health Sciences, within the School of Biomedical Sciences, Department of Basic Medical Sciences. In this role, I occupy administrative, academic, research, and leadership positions at both faculty and institutional levels. 

“I admired professionals in lab coats and their selfless passion for finding answers and solutions to health-related conditions that remain clinical challenges using scientific methods and evidence

What sparked your interest in pursuing the Sciences, and what were your career aspirations?

As a high school learner, my academic strengths and interests were in chemistry, math, and biological sciences. While I was initially unsure about the exact career field I wanted to pursue, I was inherently curious and fascinated by professionals working in laboratories. I was a huge fan of TV series such as CSI: Crime Scene Investigation, which follows a team of forensic investigators solving crimes using scientific methods and evidence, and Numbers, which combined crime-solving with mathematics. These shows inspired me to aspire to a field reminiscent of what I witnessed in these series. I admired professionals in lab coats and their selfless passion for finding answers and solutions to health-related conditions that remain clinical challenges using scientific methods and evidence. True to my nature as an introvert, I continue to find myself most “at home” when working in a laboratory setting. While I could not have imagined the trajectory that my academic career would take, I am without a doubt in the right profession given my innate curiosity, passion for teaching, skills transfer, and biomedical research.

What do you think about the current status of women in science careers in your country?

Despite the gains in women’s participation in science careers in South Africa, women remain underrepresented in these fields. While there has been significant progress in increasing the participation of women in science-related disciplines, studies have confirmed that men continue to dominate science, technology, engineering, and mathematics (STEM) careers. This gender disparity is further heightened among Black women. Although women represent the majority of young university graduates in South Africa, only 13% of STEM graduates are women, with Black women being significantly underrepresented in higher academic and research leadership positions. This can be attributed to systemic barriers such as gender bias, lack of mentorship, and limited access to resources, which continue to hinder true equality in science careers. 

At our institution, the University of the Free State (UFS), there is an increasing commitment to support emerging researchers, especially women, through mentorship and research development opportunities. This is part of our institution’s Vision 130, which aspires to foster excellence in research and increase the impact of our scholars on the broader societal context. I am privileged to be one of the selected candidates in our institution’s Transformation of the Professoriate Mentoring Programme, which aims to grow a critical mass of excellent emerging scholars at the UFS. This programme equips all its candidates with both academic and research mentorship to advance their development towards assuming senior academic and research positions. More importantly, this programme supports candidates in accessing networking and funding opportunities, contributing to their establishment as researchers with the potential to create centres of research excellence in the future. My hope is that those of us who have access to such opportunities can also use our privilege and positions to mentor more women researchers from underrepresented groups in the various fields of science.

“Although women represent the majority of young university graduates in South Africa, only 13% of STEM graduates are women, with Black women being significantly underrepresented in higher academic and research leadership positions

What are your suggestions to improve the participation of more women in science-related careers?

 To improve the participation of more women in science-related careers, it is crucial to address the systemic barriers that hinder their progress. This includes creating more mentorship and networking opportunities for women, providing financial support and scholarships for female students in science career fields, and implementing national policies that promote work-life balance and support for working mothers. Additionally, efforts should be made to raise awareness about the contributions of women in science and to challenge stereotypes that discourage girls from pursuing science careers. Encouraging more inclusive and diverse work environments where women feel valued and supported is essential for increasing their participation and retention in science careers. There is also a need for progressive policies that promote the employment of Black women academics in positions of authority in STEM fields. This will ensure the availability of a diversity of women mentors and academics to offer gender-sensitive support to students.

 Please tell us about your current research and its impact in the sector?

Our research group is assessing both pharmaceutically uncharacterized and the repurposing of well-known medicinal plants that have been previously reported to improve brain function in aging individuals. While these medicinal plants have shown promise in enhancing brain function in various brain-related conditions, their neuroprotective efficacy against neurodegenerative diseases remains unclear, especially as the disease progresses in severity. This is one of the focus areas of our ongoing research. I am involved in several multidisciplinary projects, collaborating with both national and international research experts from countries such as Denmark, the UK, and various national institutions, as well as colleagues from the University of the Free State. One of the primary goals of our ongoing research projects is to explore the therapeutic potential of underexplored nutraceuticals and indigenous medicinal plants in preserving vulnerable neuronal cell populations using 3D based neuronal cell models.

These models will be developed in collaboration with researchers in the University of the Free State’s School of Clinical Medicine, utilizing the CelVivo ClinoStar 2 System. This cutting-edge technology, mimics ‘animal model-like’, allowing scientists to generate cell-based models that closely resemble in-vivo like conditions. We will specifically focus on the technology’s applications in studying age-related neurodegenerative disorders, such as Alzheimer’s disease. The potential impact of this research is immense, as it may contribute to the development of novel therapeutic strategies for combating the debilitating progression of neurodegenerative diseases, ultimately improving the quality of life for affected individuals and their families. 

What is your message to aspiring students who wish to take a career in the sciences? 

Pursuing a career in the sciences requires dedication, hard work, relentless effort, and an unwavering commitment to learning and growth. It is a path filled with challenges, but the rewards are immense for those who are passionate about contributing to the betterment of humanity through medical science research. This means working tirelessly to uncover new insights, develop innovative solutions, and share your findings with the world. It means staying committed to your goals, even when faced with setbacks, and always striving to push the boundaries of what is known. Marie Curie once said, “I am among those who think that science has great beauty. A scientist in his laboratory is not only a technician: he is also a child placed before natural phenomena which impress him like a fairy tale.” This sense of wonder and curiosity should be at the heart of your scientific endeavours as an aspirant biomedical researcher. You must be driven by a deep curiosity and a desire to understand the world around you. The journey is not just about personal success but about making a meaningful impact on society. The hard work and perseverance you invest in your studies and research will not only advance your knowledge but also contribute to solving real-world problems and improving the quality of life for others. Lastly, remember that science is a collaborative field.

“Marie Curie once said, “I am among those who think that science has great beauty. A scientist in his laboratory is not only a technician: he is also a child placed before natural phenomena which impress him like a fairy tale.”

Seek out mentors, build networks, stay humble, and be open to learning from others. Your contributions, no matter how small they may seem, are part of a larger puzzle that future generations of researchers will continue to build upon. If you are passionate about making a difference, if you are committed to the relentless pursuit of knowledge, and if you are driven by a desire to contribute to the greater good, then a career in the sciences may be the right path for you. Embrace the journey, stay curious, and never lose sight of the profound impact your work can have on the world.

For Priyamvada Natarajan, her earliest exposure to scientific research arose from her childhood passion making star maps. Her love for maps never abated, and shaped her career as a theoretical astrophysicist. In the media, she’s the famous ‘cosmic cartographer’, who featured in the TIME magazine’s list of 100 most influential personalities this year.

“I realise what an honour and privilege this is,” said Natarajan to The Hindu. “It sends a message that people working in science can be seen as influential, and that is very gratifying.”

The Indian-American’s claim to fame arises from her pathbreaking research into dark matter and supermassive black holes.

She devised a mathematical technique to chart out dark matter clumps across the universe. Despite dark matter being invisible and elusive to astronomers, they’re thought to dominate some 75% of the universe’s matter. Dark matter clumps act as ‘scaffolding’, in the words of Natarajan, over which galaxies form. When light from background galaxies gets caught under the gravitational influence of dark matter clumps, they bend like they would when passed through a lens. Natarajan exploited this effect, called gravitational lensing, to map dark matter clumps across the universe.

Simulation of dark matter clumps and gas forming galaxies. Credit: Illustris Collaboration

Natarajan reflected her passion for mapping in a TEDx talk at Yale University, where she’s professor of physics and astronomy. Though she’s an ‘armchair’ cartographer, in her own description, she has resolved another major headwind in astronomy – nailing down the origins of supermassive black holes.

Black holes generally form from dying stars, after they collapse under their weight due to gravity. These black holes would swallow gas from their environment to grow in weight. However, there also exists supermassive black holes in the universe, millions of times heavier than any star or stellar-sized black hole, whose formation can’t be explained by the dying star collapse theory. One example is Sagittarius A* at the center of the Milky Way, which is a whopping four million times massive than our sun.

First direct image of Sagittarius A* at the Milky Way center. Credit: EHT

The origins of these behemoths remained in the dark until Natarajan and her collaborators shed some light to it. In their theory, massive clumps of gas in the early universe would collapse under its own weight to directly form a ‘seed’ supermassive black hole. This would grow similar to its stellar-massed counterparts by swallowing gas from its environment. In 2023, astronomers found compelling evidence to validate her theory. They reported a supermassive black hole powering the ancient quasar, UHZ1, at an epoch when no black hole could possibly have grown to attain such a massive size.

These observations came nearly two decades following Natarajan’s first paper on this in 2005. In a 2018 interview to Quanta, she expressed how content she would be with her contributions to astrophysics without having her theory requiring experimental verification done within her lifetime. For, she would be simply content at having succeeded at having her ideas resonate among astronomers for them to go search for her black holes. “I’m trying to tell myself that even that would be a supercool outcome,” she said in that interview. “But finding [the supermassive black hole ‘seed’] would be just so awesome.”

Beyond science, Natarajan’s a well-sought public speaker as well, with pursuits in the humanities as well. In fact, at Yale University, she’s the director of the Franke Program in Science and the Humanities, which fosters links between the two disciplines. Her humanities connect comes at MIT, where she did degrees in physics and mathematics before taking a three-year hiatus from science to explore her interest in the philosophy of science. However, she returned to astronomy soon thereafter, enrolling as a PhD student at Cambridge, where she worked under noted astronomer Martin Rees on black holes in the early universe which seeded her success in later years.