Award-winning maths guru makes a difference where his roots are

On 28 August 2024, the Royal Society, the world’s oldest scientific academy, awarded the prominent Tunisian mathematics professor, Ali Baklouti, the Africa Prize for his contribution to science. As part of his groundbreaking works, Baklouti developed new mathematical approaches to solve two long-standing mathematical problems.

These problems are referred to as conjectures in his field. A conjecture is a mathematical statement, hypothesis or proposition that has not been proven. Once proven, a conjecture becomes a theorem or a mathematical statement with a definitive conclusion based on proven facts.

Baklouti’s work on the Corwin-Greenleaf conjecture and the polynomial conjecture for nilpotent restrictions helps push scientific frontiers by opening the way for them to be applied in various scientific and technological domains.

University World News spoke to the award-winning professor about his work, his fears about the significant challenges of teaching maths in Africa that he says could affect the future of scientific and technological progress on the continent, and his commitment to his community.

UWN: When and how did your interest in mathematics start?

AB: My interest in mathematics began at a very young age. I was always fascinated by numbers and logical puzzles, and I would spend hours solving maths problems just for fun. While I wasn’t considered a prodigy, I had a natural affinity for mathematics and enjoyed tackling complex challenges.

Although there were no mathematicians in my family, my parents always encouraged my curiosity and supported my academic pursuits. This support, combined with my passion, naturally led me to a career in mathematics.

UWN: Where did you study and what impact did it have on you?

AB: I graduated from the University of Metz [now part of the University of Lorraine] in France in 1995. My time there had a profound impact on my academic and professional development. The rigorous training and exposure to advanced mathematical concepts during my studies laid a strong foundation for my future work.

After completing my degree, I quickly joined the Tunisian university system, where I rapidly advanced through the academic and scientific ranks. This early integration into the academic community allowed me to contribute significantly to both research and teaching in Tunisia.

UWN: Apart from harmonic analysis, what other branches of mathematics are you grounded in and why do they appeal to you?

AB: I am also well-versed in Lie groups and Fourier analysis. These areas of mathematics appeal to me because they offer powerful tools for understanding symmetries and transformations, which are fundamental concepts in many areas of mathematics and physics.

The rich structures in Lie groups and the versatility of Fourier analysis in breaking down complex functions into simpler components have always fascinated me. The deformation theory comes also as a very important related subject and has many meaningful aftermaths. These fields not only complement my work in harmonic analysis but also provide a broader perspective on how different mathematical concepts interconnect.

UWN: What does it take to be a good mathematician?

AB: It takes a combination of curiosity, persistence and creativity. Curiosity drives the desire to explore new problems and understand the underlying principles of mathematics. Persistence is crucial because solving complex problems often requires sustainable effort and the willingness to embrace challenges and setbacks. Creativity is needed to think outside the existing methods and ideas and to develop innovative solutions or new approaches.

Additionally, a good mathematician must have a solid foundation in mathematical theory, the ability to communicate ideas clearly, and a passion for continuous learning and discovery.

UWN: What do you consider your major mathematical breakthroughs?

AB: One of my major mathematical breakthroughs was proving two long-standing conjectures, the Corwin-Greenleaf and the polynomial conjecture for nilpotent restrictions. These achievements were the result of years of dedicated research and collaboration with other mathematicians. By solving these problems, we were able to unlock new insights and open further avenues of exploration in the field.

My work has contributed to humanity by advancing our understanding of complex mathematical concepts, which can have applications in various scientific and technological domains. Although my contributions may seem abstract, they play a crucial role in the broader progress of knowledge and innovation.

UWN: What do you think of mathematics teaching at African universities?

AB: The teaching of mathematics at African universities faces significant challenges, one of which is the decreasing interest in mathematics-related fields among students. This trend is alarming, as it could affect the future of scientific and technological progress in the region.

To address this issue, it is essential to cultivate a love for mathematics in children from a young age. Creating a positive and engaging experience with mathematics early on can help prevent later reluctance or avoidance of the subject. Strategic solutions and innovative teaching methods are needed to make mathematics more appealing and relevant. This can include incorporating hands-on activities, real-world applications and interactive learning experiences that highlight the importance of mathematics in everyday life.

Additionally, improving the overall quality of mathematics education, investing in resources, and supporting teachers are crucial steps in reversing this trend and ensuring that more students recognise the value and potential of pursuing mathematics.

UWN: You championed your university collaboration with a Japanese institution. Are there any other collaborations? What is the importance of university collaborations?

AB: I have been deeply involved in fostering collaboration between my university and Japanese institutions. We organise a Tunisian Japanese conference every two years, with the most recent one held in 2023 in Monastir, where nearly 30 Japanese participants joined us to exchange ideas. This ongoing partnership has been highly productive and has greatly enriched our academic environment.

In addition to our work with Japan, we have also established collaborations with institutions in France, Germany, India, Morocco, Saudi Arabia and Indonesia. These partnerships are crucial for several reasons. They facilitate the exchange of knowledge and ideas, enhance research opportunities, and provide valuable international perspectives that can drive innovation and academic excellence. Such collaborations help broaden the scope of our research, improve educational outcomes and strengthen our global academic network.

UWN: During the 25th Annual Congress of the Tunisian Mathematical Society that you helped organise, there was an exhibition of women in mathematics in the world. Why do we have so few female mathematicians and what needs to be done to usher more women into this field?

AB: Acting as president, I had the privilege of helping to organise the conference. We featured an exhibition highlighting women in mathematics from around the world. This exhibition aimed to shed light on the achievements of female mathematicians and inspire more women to enter the field. The underrepresentation of women in mathematics is a multifaceted issue.

Historically, societal stereotypes and biases have discouraged women from pursuing careers in mathematics. These biases can manifest in various ways, from subtle discouragements to a lack of female role models and mentors. To increase the number of women in mathematics, several key actions are necessary. Encourage girls to pursue mathematics from an early age by providing positive reinforcement and challenging them to engage. Highlight the achievements of female mathematicians and provide mentorship programmes to support young women. Seeing successful women in the field can inspire and motivate others to follow in their footsteps.

UWN: Is there a relationship between maths and the empirical world; any examples from your work?

AB: Yes, there is a significant relationship between mathematics and the empirical world. Mathematics provides a framework for understanding and solving real-world problems, and its applications are found in numerous fields. For example, in artificial intelligence (AI), mathematical concepts such as algorithms, probability, and linear algebra are fundamental. These mathematical principles are used to develop models that can recognise patterns, make predictions, and improve decision-making processes.

Distortion of geometric shapes in nature can occur due to various external factors. Many naturally occurring geometric shapes exhibit significant beauty but can be altered by factors. To organise and understand these distortions, we can take several approaches, like use mathematics to describe and explain how environmental factors affect geometric shapes. For example, differential equations can be employed to model erosion or weathering processes and how they alter shapes over time.

UWN: The job of mathematicians is to help solve problems, but some mathematical problems have been unsolvable. Why?

AB: This deeply depends on the nature and the complexity of the problems. The resolution of difficult problems depends also upon the human capacities interested in the related subjects.

UWN: Which books have you written and how are they used?

AB: I have authored several important books that are used at advanced levels in mathematics:

• Representation theory of solvable Lie groups and related topics [part of the Springer Monographs in Mathematics series and co-authored by Hidenori Fujiwara and Jean Ludwig, published in 2021]. This book is aimed at researchers and advanced graduate students, focusing on the representation theory of solvable Lie groups. It offers an in-depth exploration of theoretical aspects, making it a key resource in this field.

• Deformation theory of discontinuous groups [De Gruyter Expositions in Mathematics series, published in 2022] targets graduate students and researchers with an interest in group theory, particularly in the deformation theory of discontinuous groups. It provides comprehensive coverage of the topic, both theoretically and practically.

These books are essential resources for those involved in advanced mathematical research and study.

UWN: You were born in Sfax, Tunisia, and you still live and work there. The brain drain has cost Africa some of its most brilliant minds. What has kept you at home?

AB: Indeed, I was born in Sfax and served as the vice president of the University of Sfax from 2020-24. Currently, I am a professor in the faculty of sciences.

What has kept me at home is a deep sense of responsibility and commitment to my community. I believe in the potential of our institutions and the importance of contributing to their growth. My goal has always been to make a difference here, where my roots are, and to inspire others to do the same.