Yvon Maday, new holder of the Chair in Computer Science and Digital Sciences at the Collège de France

How did your interest in mathematics and computer science begin?

Yvon Maday: I have always been very curious. As a child, I asked a lot of questions about technology. Even in nursery school, for example, I remember staying behind during break time to make a 24-hour clock, instead of a 12-hour one, so that I could explain the concept of 12-hour and 24-hour time to my classmates. This desire to investigate and then find an educational way to explain the things I understand has never left me. It was a passion, so when my teachers encouraged me to pursue scientific studies, I felt right at home. Later, I realised that there were several types of mathematics, some fundamental, others more applied. I was obviously attracted to the rigorous aspect of fundamental mathematics, but from the beginning of my thesis, I quickly turned to its applied counterpart, particularly in biology. During my PhD, I also studied medicine in parallel until my third year. I wanted to understand, on the one hand, the discipline itself and, on the other, those who practise it, their issues and their approaches. This enabled me to collaborate with doctors, knowing their language and their logic, since I had seen how they had been introduced to the various concepts in their field of study, such as cardiac mechanics and pulmonary functions, which interested me. In short, I don't think I'm an applied mathematician, but rather an interdisciplinary mathematician: I love and aspire to develop useful mathematics to answer questions posed by other disciplines.

What are you doing to build this bridge between mathematics and the various fields of application that require it?

This connection is something that has always been close to my heart. If, for example, we want industries in France to progress, we must help them to be drivers of innovation. Industrial research centres need to have rapid access to inventions in mathematics, and advances in research must be able to lead to industrial innovations. Conversely, we need to understand industrial problems in order to develop and apply mathematical theories that will enable us to answer these questions. In the 1990s, I had already spent a lot of time in the United States, particularly during the summers when research activity in France slows down a little. I wanted to offer a summer research programme in France, and I set my sights on the International Centre for Mathematical Meetings (CIRM), which was available at that time of year and located in the Calanques, offering an ideal setting! Together with the director at the time, we transformed the place by installing air conditioning and computing machines, and so, in 1996, the Centre for Advanced Mathematical Studies in Scientific Computing (CEMRACS) was born. Together with Frédéric Coquel, I organised this event for the first three years to show what could be done, and little by little, industrialists got on board. They proposed specific, well-defined topics that could be addressed and resolved during the summer period by working in this exceptional setting, morning, noon and night. That's the whole point of this centre: we have researchers of all generations living together, giving presentations and exchanging ideas all day long for weeks on end. This helps to break the ice – young and old get to know each other, learn to collaborate and trust each other – and explore the topics in depth. CEMRACS is now well accepted in the French research landscape and by industrialists, who eagerly await the new theme each year. It is also a wonderful experience for young people, as it opens them up to topics that are generally different from those they explore in their theses. And the projects continue beyond the summer, sometimes through international collaborations. It is an intense period, where the brain cells work hard, and so enriching that the organisers are very happy to participate in this activity. We look forward to celebrating the thirtieth edition of this event next year.

Among other things, you are a specialist in numerical analysis. What does that involve?

In science, technology and industry, we seek to understand phenomena in order to master, anticipate or control them. This understanding leads to simplified models, where the essential principles are identified and the quantities of interest are represented. These models mathematically translate reality and allow us to simulate, on a computer, experiments that are costly or impossible to carry out in a laboratory. The quality of a simulation depends on the relevance of the model and the accuracy of the numerical methods, which is the domain of the numerical analysis specialist. For a new phenomenon, we often start with simplified models in order to develop algorithmic strategies before moving on to more complete versions. The aim is to simplify without betraying the essentials, to evaluate the methods on a reduced model, and then to progress towards the final model. This work includes designing algorithms adapted to computer architectures – from parallel computing to quantum computers – as well as creating methods for reducing complexity, intended to speed up heavy simulations while maintaining their accuracy. These approaches are attracting keen interest in industrial, societal and medical fields. In recent years, I have applied them to computational chemistry.

How do you communicate with your colleagues from other disciplines when you need to create such models?

First, you need to understand the model you want to build. Then you step back for an hour, a week, a month or a year – this is a necessary step to test the initial methods and find the ones that will work. Once you have a simplified model with reliable and robust numerical methods, you go back to your colleagues. In an industrial setting, it is sometimes necessary to respond quickly to partners' needs. In such cases, it is acceptable to propose an approach that is not fully finalised, provided that it remains reasonable and justified. We have to juggle the realities of industry and those of fundamental research – industry wants an answer in six months, while research can provide a very good one in ten years. Some people understand this, others do not. However, this means that we now have research projects that can be funded and that will enable us, in the long term, to develop infinitely better methods and much better understood models.

Mathematical research makes sense when it connects theory to action, and the key is knowing how to apply these mathematical objectives to industrial, economic and societal challenges. I tried to find the right people to talk to in each of the disciplines I studied in order to understand the root of the problem, rather than just scratching the surface. I wanted to ask the right questions and find the mathematical and simulation tools to try to answer them. Much of my work is related to modelling and is based on discussions with colleagues from other disciplines. For example, during the global Covid pandemic, I organised videoconference seminars to review the mathematics of epidemiology. This was not my area of expertise at all, as I was working on my ERC grant in computational chemistry at the time, and my previous work in biology had focused more on organ modelling. But in this time of health crisis, epidemiological models seemed to be either non-existent or little known. One of our initiatives led us to research and quantify the presence of the virus in wastewater, which gave rise to the ‘Obépine’ research initiative. From April 2020 onwards, this enabled us to show that measurements of viral particles in wastewater reflected the dynamics of infections observed in the population. This was quite innovative, and we had to be convincing. We were supported by various academies, and the Ministry of Research backed us up and enabled us to monitor more than 200 stations from 2021 onwards. The connected municipalities received a weekly update on the pandemic based on measurements taken in their wastewater. It is important to understand that this is a very turbid environment, which causes a lot of errors in the measurements, and biologists were used to dealing with data that sometimes did not make sense. Mathematical modelling made it possible to correct them and produce a clean and meaningful signal.

This year, you will be taking up the annual Chair in Computer Science and Digital Sciences at the Collège de France. What does this mean to you and what are your expectations?

It's a surprise and an exceptional event in my career. Ending my professional career with a chair at the Collège de France is unexpected and somewhat intimidating, I must admit, but I derive a great deal of pleasure and pride from it. As for the topics I will be addressing this year, there were several possibilities. I could have talked about computational chemistry, my most recent field of work, but that would not have had the impact I hope to achieve by talking about model reduction. It is a method that lends itself to a wide variety of disciplines and is currently well established in industry. What I expect from this chair is that people will increase their use of this tool throughout the application environment. For this reason, after each lecture, I will invite industrialists to speak at seminars. This is a good way to address the use of numerical methods, but also to present the problems that remain unresolved to date and to stimulate research activity to solve them. In June, there will be a conference where I will bring together academic and non-academic experts on the subject to discuss recent results that I will not have been able to cover during my lectures, and to go further than what I will have been able to present in the lessons. For me, it's an opportunity to revitalise this research, which has certainly been well received in industry, but deserves to be taken further.