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María Jesús Esteban: Lectures and interviews

We present below three lectures by María Jesús Esteban Galarza and three interviews.

1.
The first lecture we give is María Jesús Esteban's lecture after being awarded an honorary doctorate by the University of the Basque Country on 4 March 2016. We give an English translation of the original which appears in Basque in the booklet:

María Jesús Esteban Galarza, Doctor Honoris Causa, Universidad del País Vasco (4 March 2016), 41-48.

María Jesús Esteban's lecture to the University of the Basque Country.

Rector of the University of the Basque Country,
Deputy Minister of Universities and Research,
Vice-Rectors,
Dean,
Esteemed ladies and gentlemen,
Ladies and gentlemen,
Colleagues and friends,
Good morning.

First of all, many thanks to Javi Duoandikoetxea, a friend of many years, for his presentation.

Today is a very special and moving day for me and I owe this to the University of the Basque Country. It is always a great honour to receive the title of Doctor Honoris Causa, but in this case, for me, it has much greater value, since it is happening in my country and in my first university.

As Javi Duoandikoetxea said, I studied here. Well, it was called the University of Bilbao, not the University of the Basque Country, but it was the embryo of the UPV/EHU. When I studied here, it was the first years of this university, and those who studied here in those first years will remember those heroic times: no transport to go to Leioa, assemblies and more assemblies and the police often following us, even on campus … However, I have very good memories of those years.

The current University of the Basque Country is, of course, something else, an international university. I finished my studies here and went to Paris, but I have been back many times, to the Mathematics departments, to give lectures, to see my colleagues and friends and to work with them from time to time, which has given me the opportunity to see how this university has changed, and realising that change has been very satisfying for me.

In Basque I was talking about my undergraduate years at what was then called the University of Bilbao. But before getting to that, I would have to say first that I was very lucky to grow up in a family where being girls never put us in trouble or gave us limits because we were women, and where study and work were always an aim and an example to follow. I was also lucky to study in a public institute that, despite not being considered the best in Basauri by many people, was a great place where I had very good professors and, in particular, an excellent mathematics professor, José María García, whose example helped me to make my decision to study mathematics as a career. Once I finished my degree, I got a scholarship from the French Government and I went to Paris to do my doctoral thesis, guided by two of the excellent professors I had in Leioa, Isabel Zuazo and Mikel Bilbao, whose presence here today in this event has filled me with joy, and even though I had plans to return to the Basque Country, I stayed in Paris. I did my doctoral thesis at the University of Paris VI, officially under the direction of Professor Haim Brezis, but in reality working with Professor Pierre-Louis Lions, very young even then, actually as young as I was, but already a great mathematician, who years later received the Fields Medal, one of the greatest prizes in mathematics, equivalent to the Nobel Prize, which does not exist in my discipline. It was he who one day, when I was already finishing my thesis, told me that I had to apply for a position at the CNRS (the French National Centre for Scientific Research). I never thought about that possibility. In fact I was here in spirit although living in France.

These were very important years in the Basque Country, years of transition, of the creation of scientific schools, of the formation of a teaching body at the University of Bilbao. Also years of struggle because the Basque would occupy the place that belonged to it. It was in those years that around pioneers like Professor Joserra Etxebarria, in what was then called the Faculty of Sciences, we enthusiastically worked on Basque dictionaries in various scientific areas, among them Mathematics. I saw myself returning to Bilbao and participating in all those movements. Pierre-Louis Lions, who had already understood that one of my main objectives was to contribute to the development of scientific research in the Basque Country, convinced me that by staying a few more years in Paris and continuing my training in a high-level scientific environment, in a department of the best in the world, the Laboratoire d'Analyse Numérique of the University of Paris VI, I would be better prepared to return. It seemed like a good idea, I presented myself at the CNRS, I got the position I had applied for, one of the best to which a young mathematician can aspire in France ... and I stayed there ... and I'm still at the CNRS, not the same position as then naturally.

I was warmly welcomed at the CNRS and the University of Paris VI, and a few years later, when I was promoted to the position of director of research, equivalent to a full professor, I moved to what is now my university, Paris-Dauphine.

I am very fortunate to have had an exceptional doctoral advisor who, in those days (I was his first student, in fact), still had plenty of time to chat and talk about mathematics, and also about physics, which he knew well. He introduced me to research in partial differential equations and variational methods applied to mathematical physics. He also encouraged me to take an interest in problems from other scientific fields. And so I embarked on the path of applied mathematics. Changing topics from time to time, I always maintained that what I enjoyed most was solving "real-world" problems, or conducting theoretical studies that could help solve them. And so I became interested in problems in quantum physics and chemistry, the interaction of fluids with solids, particle physics, and so on. And I'm still doing that. Naturally, when I started working on problems from other scientific fields, I had to invest a considerable amount of time in studying their terminology, concepts, challenges, and working methods. In my undergraduate studies, I had only taken one physics course, which meant that years later I had to invest a lot of time and energy studying, for example, quantum physics and chemistry.

In these thirty-six years as a researcher, I have collaborated with many colleagues from diverse countries and specialties. I really enjoy teamwork because sharing different perspectives and approaches is very enriching. Furthermore, many of my collaborators have become good friends. I've collaborated with so many people - I can't name them all here - but perhaps I'll mention a few who have played a special role in my career. First, there's Eric Séré, with whom I began an intensive research programme in the 1990s, focusing on the mathematical and, above all, variational study of linear and nonlinear problems in relativistic quantum mechanics, centred around the Dirac equation. Nothing had been done in this area from a mathematical perspective until then, and we introduced methods that have become classics today. There's also Jean Dolbeault and Michael Loss, two outstanding researchers with whom I have worked and continue to work intensively, currently in the area of ​​functional inequalities and their optimal constants. Then, alone or with other colleagues, especially with Benoit Desjardins, I have also researched fluid mechanics, and more specifically, the weak formulation of fluid-solid interaction. And I'll stop here with the description of my research work, to move on to another significant dimension of my career.

After several years of research, I realised - or rather, those around me realised - that I enjoyed working on collective and organisational projects … that I liked it and that I was capable of it. So, starting at my university as a department head and faculty member, I then moved on to the national level, becoming president of the French Society for Applied Mathematics (SMAI), helping to foster a large and important scientific community, not only in France but also internationally. From there, I became involved in European organisational initiatives in applied and industrial mathematics through the Applied Mathematics Committee of the European Mathematical Society (EMS), and also through my significant involvement in the Forward Look project "Mathematics and Industry," funded by the European Science Foundation (ESF). Little by little, with each step I took, I became involved in different communities and networks, found new colleagues and friends, with whom I continue to work for what I believe is the good of our scientific community, but also the good of our society. One of the reasons I do what I do is that I am convinced that mathematics can solve many practical, industrial, technological, and social problems, and that to increase the impact of mathematics on our society, we must raise awareness of its usefulness. Within our scientific community, we need to find colleagues willing to get involved in solving truly applied problems, but we also need to convince companies (small and large), governments, public agencies, and Brussels that investing in mathematics is investing in the future for all of us.

And now, I've recently taken the leap to the truly international level through the presidency of ICIAM (International Council for Industrial and Applied Mathematics), during which I will try to export the experience I have at the European level to other continents and situations very different from our own. ICIAM, through its activities, conferences, awards, and programmes, helps member societies develop science policies with the aim of increasing the impact of mathematics on the technological development of their countries.

Mathematics is an important science, one of the great ones. It is by no means a science that serves other sciences, as many claim. It has its own logic and structure. It is a science that is rapidly expanding. Many people think that everything in mathematics has been done for a long time. They don't realise that the volume of new results, theorems, methods, and theories continues to increase, and at an almost dizzying pace.

Not all mathematicians, far from it, work on concrete, "real-life" problems. Most of them study theoretical and internal problems in mathematics. There is an explosion of new topics, interesting problems, and fascinating methods and results. This groundwork, this fundamental research, may or may not have applications later, but it must be done and supported. On the other hand, a good part of the mathematical community is in fields that have a direct or indirect, rapid impact on other sciences or applied areas (industry, health, transportation, energy, logistics, etc.). Examples of this type of research can also be found, and we should be pleased about this, at the University of the Basque Country and in places like the Basque Research Centre BCAM.

Today at this university is a day of celebration of mathematics and its various aspects. And for this, I thank, we thank, this university and its departments of Mathematics, Applied Mathematics, and Statistics and Operations Research.

Finally, once again, my warmest thanks to the University of the Basque Country for awarding me this title today. It is a great honour for me! Thank you very much!

2.
The second lecture we give is María Jesús Esteban's lecture after being awarded an honorary doctorate by the University of Valencia on 17 May 2017. We give an English translation of the original which appears in Spanish in the booklet:

Discurso de Investidura como Doctora 'Honoris Causa' por la Universitat de València: María Jesús Esteban (València, 17 de mayo de 2017).

María Jesús Esteban's lecture to the University of Valencia.

Dear Rector,
Dear Vice-Rectors,
Dear Colleagues,
Ladies and Gentlemen,
Good morning!

It is a great honour for me to be here today at this ceremony where I will receive an honorary doctorate from the University of Valencia, a university with centuries of history and numerous outstanding academic achievements. I am very sorry that I cannot address you in Catalan; I understand it thanks to my Catalan and Valencian friends, but unfortunately, I do not speak it.

As you will see later, although I grew up and studied in the Basque Country, I am mathematically French, having completed my doctoral thesis and most of my professional career in France. Despite living abroad, since moving to France I have always maintained relationships and collaborations with Spanish mathematicians, with whom I have had, or still have, numerous thematic and cultural affinities. This is particularly true with Valencian mathematicians who work here, such as Professors Olga Gil and Rosa Donat, as well as mathematicians of Valencian origin who now work elsewhere.

But my path and that of Valencian, and Spanish, applied mathematics crossed in a remarkable way one day in May 2013 in Beijing. That day, in a close competition, I was elected the next president of ICIAM, the International Council for Industrial and Applied Mathematics. And at the same meeting, in an even closer election, Spanish applied mathematicians secured the hosting of the 2019 ICIAM congress at this university in Valencia. They achieved this in competition with two other excellent candidates, one from Brazil and the other from the Netherlands. Two victories, then, just hours apart, that bind me and my ICIAM presidency to this university in a very special and heartfelt way.

I'm now going to try to explain a little about how I got to this point. As I mentioned before, I did my university studies in Bilbao, at a new university then called the University of Bilbao, which soon became the University of the Basque Country. I studied in a complicated environment, with classes taught by teams that had been hastily assembled. Those years of study were full of everything, good and bad, and a lot of chaos, because they were also very turbulent political years, years of transition after the end of the Franco regime. During those years, I was lucky enough to have some excellent professors who encouraged me to continue working in research after finishing my degree, but who clearly explained that I had to leave the country to do so under good conditions. Accepting that was a bit difficult because at that time I was very involved in cultural and political activities, and working diligently on projects promoting Basque culture and science. Specifically, with a group of people from the University of Bilbao and several science outreach organisations, we created the first mathematical dictionary in four languages: Basque, Spanish, English, and French, which required us to invent a great deal of specialised vocabulary that didn't yet exist. Anyway, after graduating, the French government awarded me a grant to do my doctoral thesis in Paris, and off I went ... and there I stayed!

This was largely due to the fact that, upon completing my thesis, the CNRS offered me a full-time research position, a privilege I have been able to maintain throughout my career. The CNRS is a very important scientific organisation, one of the most important in the world in terms of research, covering all areas of knowledge. But it's important to know that, unlike similar organisations in other countries, almost all of us researchers at the CNRS work in university departments. In my case, I work in the CEREMADE department at Paris-Dauphine University, after spending more than a dozen years at Pierre and Marie Curie University - the very university where I completed my doctoral thesis.

I was incredibly fortunate to do my doctoral thesis at a top-tier international department of applied mathematics, now called the Jacques-Louis Lions Laboratory, named after a great mathematician, the founder and driving force behind applied and industrial mathematics in France. And I was also lucky enough to begin working in research, quite by chance, with his son, Pierre-Louis Lions, also a great mathematician, who years later won the Fields Medal, one of the highest honours a mathematician can receive in the world, often compared to the Nobel Prize. My thesis advisor encouraged me to work on mathematical problems with applications in physics and taught me to appreciate working in applied mathematics, or at least mathematics motivated by applications. That, and the twists of fate, led me to develop research programmes in mathematics applied to quantum physics and chemistry, and also to solid-fluid interactions, for example. I've been fortunate to have regular collaborators who have become friends - many, but I'll mention only the most important: Eric Séré and Mathieu Lewin in relativistic quantum mechanics; Jean Dolbeault and Michael Loss on various topics, but lately on a very interesting research program concerning functional inequalities and the symmetry of their optimal solutions. For me, collaborative work is very enjoyable and interesting, and nowadays, practically indispensable. And I've been lucky to have many excellent collaborators. My work has been primarily theoretical, but I've always been interested in practical applications, and in fact, I've also worked on constructing algorithms for calculating solutions to problems that interested me. This was to illustrate theoretical results, but also to formulate conjectures and hypotheses. My specialties are the theory of partial differential equations and mathematical physics, but I've also done some work in numerical analysis. My preferred methods are variational methods, which are my main area of ​​expertise and play a fundamental role in solving numerous problems in physics, especially quantum physics. So, I've been fascinated by the applications and interactions of mathematics almost my entire life, and I've always worked in centres where researchers had the same kind of profile, even going as far as industrial contracts. In fact, many of my colleagues worked on aeronautical, automotive, space, and financial projects. ... The whole culture around me was geared in that direction.

And this trend has only intensified. The fundamental role that mathematics can and should play in the economic development of our advanced societies is increasingly recognised. As I explained yesterday in my public lecture, mathematics has become an indispensable tool for technological development, given its ubiquitous presence in data processing, simulation, machine learning, and artificial intelligence, to name just a few of the increasingly important areas of scientific and technological advancement. To illustrate this more concretely, I will cite only recent impact studies conducted in Great Britain, the Netherlands, and France, all of which show that high-level mathematics accounts for approximately 15-16% of GDP, and in France, 10% of all jobs nationwide. Impressive figures indeed! And even more impressive considering that these figures are so consistently observed across countries, despite their vastly different economic and industrial structures.

Well, being so excited about the explanations of the importance of mathematics for society, I have strayed from my initial path, in which I was explaining what has brought me here today.

At some point in my career, whether by choice or by chance, I began to get involved in university administration. However, I always maintained my research as an activity I didn't want to give up. First, as head of my department, a position I held for several years, and then as a member of the university faculty. Later, somewhat unexpectedly - another twist of fate - I became seriously involved with the French Society of Applied and Industrial Mathematics (SMAI). Initially as secretary general and vice-president, I served as president from 2009 to 2012. It was during this period that my relationship with the Spanish applied mathematics community deepened, especially through the cordial and collaborative relationship between SMAI and the Spanish Society of Applied Mathematics (SEMA). We collaborated not only on bilateral activities and programs but also in European and international forums, such as the European Mathematical Society's council, where I chaired its applied mathematics committee for a time, and, of course, at the ICIAM council level. By engaging in some international politics together, with very similar perspectives, we forged relationships of trust and regular collaboration. And now here we are, two years away from the major ICIAM congress that will take place on this campus in July 2019. This will be an important moment from many points of view; for this university, I hope it will be a great honour to host a congress of such size and importance; it will also be, I am sure, a great boost for the Spanish applied mathematics community, for the SEMA society, which is currently chaired by Professor Rosa Donat, a professor at this university, after having been chaired by Professor Rafael Bru, also from Valencia, a professor at the Polytechnic University of Valencia. It will also be a boost and an honour for European mathematics in general, because mathematical congresses of this magnitude do not take place in Europe very often. The previous ICIAM congresses took place in Beijing in 2015 and in Vancouver in 2011. For us, for the ICIAM community, it will be a great honour and a great pleasure to be here, to celebrate this important gathering in a city of light, sea, and knowledge like Valencia. ICIAM is an international community; we have members representing many countries and every continent. Our community includes many academics, but also numerous engineers and researchers from public and industrial laboratories. Our activities are aimed at promoting and coordinating applied and industrial mathematics internationally. And the ICIAM congress is the most important event on our calendar; it is the moment when we come together to share the latest results and significant scientific achievements, the latest developments and applications of mathematics in high technology. It is also the occasion for awarding the five prizes that ICIAM presents every four years. This congress is also a very opportune moment for dialogue with society, with young people, and I am sure that Valencian and Spanish colleagues in general will be able to use this occasion to give a media and educational dimension to this event.

I would like to thank this university in advance for welcoming us here on its campus in two years' time, and I also personally express my gratitude for the great honour bestowed upon me today by the University of Valencia in awarding me the degree of Doctor Honoris Causa. Thank you very much. Moltes gràcies.

3.
The third lecture we give is María Jesús Esteban's public lecture How Mathematics Is Changing the World at the First World Meeting for Women in Mathematics (WM)2 . This meeting was held in Rio de Janeiro on 31 July 2018, as a satellite event of the International Congress of Mathematicians 2018. It was organised by the International Mathematical Union's Committee for Women in Mathematics. We give below a version of the talk which was published in the Proceeding of (WM)2 .

How Mathematics Is Changing the World

Abstract. Mathematics was always, and is now more than ever, a key technology for innovation. Not many people would understand this sentence, because there is a wide-spread belief that Mathematics is not really useful except for teaching purposes. But actually the above statement can be made without any problem, because Mathematics is playing an increasing role in the development of new technologies, and its influence is only going to increase in the future. In the talk given in the WMWM meeting I tried to "prove" the above statements with examples.

The Message Behind the Talk Given at the WM2

There are three keywords to explain why Mathematics is so important for innovation. And they are: Modelling, Simulation and Optimisation (MSO).

Modelling means that using mathematical language, mathematical functions, mathematical equations, it is possible to describe natural (physical, mechanical, chemical, biological, ... ) phenomena and their evolution. Once a phenomenon is described by a given model, this model can be studied in order to understand how it will develop in different conditions and under different influences. A large class of possible situations can be taken into consideration. In each of those, the phenomenon or process can be studied mathematically, but more often using discretisation and computational means. This is what is called Simulation. One can simulate a given process, in a given situation, with the help of a model and a computer (or many computers). Once this is done, one can also optimise over the conditions under which the process takes place. That is, one can choose a criterion, or several ones, to select the optimal result. This can consist in optimising time, cost, energy, etc. This last part of the full process is what is naturally called Optimisation.

Let us discuss Modelling in more detail. What is it? First, a given phenomenon or process is detailed in a quantitative way, in the form of equations, or functions, or mathematics objects and their relations. These equations can describe the behaviour of fluids, solids, waves, sound, heat, the deformation of a solid, the combustion of an engine, or the evolution of an epidemic of some illness in a given medium. This is what modelling can do for natural phenomena, to quantify the relations between the different aspects of what one wants to describe: force, speed, deformation, intensity, mass, energy, etc. But modelling can be also used to describe a process, like for instance how to clean a blurred image or an old movie. Or how to organise a network's functioning in an optimal way. Or how to code information on internet securely.

In the past, many physical and mechanical processes were dealt with "by hand" and by building and using prototypes. Modelling allows us to overcome that costly and lengthy process and becomes a way to accelerate the birth and development of new technologies. In some cases it is not only a case of reducing the cost, or the time needed to build a new object, a plane, a machine, a car ... but in many cases prototyping is more and more out of reach, or too dangerous, while modelling is always possible. Other possible uses of modelling can help, for instance, to describe the organisation of a large set of objects or people, like the planes and the personnel of a big transportation company. This is what is called logistics.

Modelling can be done in a deterministic way, using equations or functions relating different variables, or it can be done using probabilistic or statistical functions and concepts when there is some randomness in the underlying process. Or using other concepts coming from various fields of Mathematics. The situation will ask for one or another, and often various approaches are possible and different groups will use different approaches to address the same question. When modelling is done to describe a problem in a scientific field which is not Mathematics, like Physics, or Biology for instance, this work is often done by specialists in that field, or by them and mathematicians together. This is natural since in order to depict a phenomenon well, one has to understand the underlying processes, and for that a specialist is often needed. Also, the phenomena or processes one wants to model are frequently too complex to be treated, and so one has to choose how to simplify the modelling in a way that it still makes sense. This means that the important part of the model has to be kept in it, and some other parts, the less relevant details, those that will not play an important role in the result, at least not in a significant way, maybe be forgotten, at least for some time. This again has to be decided by specialists who know what is the most important part that has to be kept, and what can be neglected in the first stage.

Note that modelling can involve continuous or discrete mathematics, and even if in the past the natural mathematical fields most used in modelling were the so-called applied mathematics ones, like differential equations, probability and statistics, numerical analysis, etc, nowadays practically all fields of mathematics can help to deal with applications, like algebra, geometry, topology, number theory, etc.

Modelling can be used to solve problems in all kinds of societal and industrial fields, in logistics, to organise the material and personnel organisation of big transportation companies; in manufacturing, to help designing machines and parts of machines needing a sophisticated design; to help in building new efficient engines, airplanes, cars, smartphones; imagining smart cities; supervising and controlling pollution; to help in finding optimal therapies for cancer and other illnesses; or designing the optimal shape of a bypass; in decision making using so-called operations research theory, etc.

Then comes Simulation. What is this about? The models that one studies in most situations are impossible to be solved in an analytical or exact way. Mathematics can be used to prove that the problem under study has solutions or not, and if yes, what kind of properties they enjoy. But if one wants to know the solutions more concretely, and this is often of the utmost importance in applications, computers have to be used to calculate approximate solutions. This means that the model has to be discretised, approximating an infinite number of points or dimensions by a finite number of them, and then trying to solve the problem in that discrete set-up. This can be again done in many different ways, and mathematicians are endlessly improving the properties of the algorithms they use to solve a particular equation or system of equations, or model, this being done in order to obtain an ever better approximation. Once one has the discrete model, it can be implemented and solved with the help of computers. This is the meaning of simulation for a given problem, to study it in an approximate way with the help of computers and so "see" the solution, or the evolution of functions, etc, in a concrete way. The solutions of course will not be exact, but, if the discretisation and the algorithm used are good, they will give a very good idea about the exact solutions that cannot be known. And in many cases one can even measure how far from each other the exact and the approximate solutions are.

The third methodology which helps to make Mathematics so useful for innovation, industry and for the design and treatment of societal activities is Optimisation. And this goes together with the two previous ones. In the design of a model or an algorithm many choices are made, about the constraints, about the relevant parameters which characterise the situation in which the experiment or activity takes place, etc. How to make those choices in an optimal manner is not known a priori. Optimisation means that one chooses, in the models, in the discretisation, in the algorithms, the values of the parameters or of the constraints that yield the best result. Best in which sense? This will be based on some well-chosen criteria: one can want to optimise energy, time, cost, quantity of material, money, etc. And how is this achieved? The simulation can be done for different sets of values of the parameters and then the results of the different computations compared. Then, the best set of parameters is chosen in the end. But one can also use optimisation techniques that allow us to know a priori how to proceed to get optimal results.

These three aspects of how and why Mathematics is so important for applications in the real world are the basis of the whole construction. But they can be complemented with other branches of Science and computational methods involving for instance Artificial Intelligence (AI) aspects, data analysis, statistical criteria, etc.

We will conclude the paper by considering these branches. Apart from this aspect, it is good to mention that many people, and not only mathematicians, can model, simulate and optimise. Or use codes designed to do this. What a mathematician can add is to make all the above with a certainty of obtaining good results, or at least being able to measure the errors made in a simulation, or showing how to control the instabilities that can arise from tiny variations in the data. Mathematicians prove theorems, and not only of existence, stability, etc. They can also prove theorems about the discretisations and algorithms that they devise in order to find approximate solutions for a given model or problem. And those theorems can provide the users with vital information about error estimates, speed of convergence of an algorithm, stability, robustness, reliability, etc. Mathematicians can thus provide results which are robust and guaranteed. And which go together with measures of the error or the reliability. This is of course a big plus for a company, which wants to be sure that their products will be good and competitive. Or their processes optimal and efficient. Nowadays the use of Modelling, Simulation, Optimisation (MSO) together with machine learning and AI is becoming a must. And a new and very interesting concept, very much liked by advanced industry, is that of digital twins. A digital twin is a digital model for physical assets, processes and systems that can be used for various purposes. It integrates MSO with artificial intelligence, machine learning and software analytics with data to create living digital simulation models that update and change continuously. Again mathematicians can, and should, play an important role in the creation and maintenance of digital twins. And they have to do it with engineers and other scientists, experts in the fields concerned with the model. The integration of different kinds of expertise is a guarantee to enhance the success of the twin's results.

Many people use to say that Mathematics is the language of Science. And the final report of the European Forward Look for Mathematics in Industry [1] said that Mathematics is also the language of innovation. The above statements about the possibilities of Mathematics and mathematicians to help solve real problems and to help companies produce better technologies, and do it in a more competitive and efficient way, is not just blah blah: they have recently been made more precise. Indeed, there have been several independent studies proving and quantifying the economic impact of Mathematics on the economy of three European countries. The impact studies of Mathematics on the British [2], Dutch [3] and French [4] economies and societies have shown incredible numbers, thus proving that investing in Mathematics is really worth it!

4.
María Jesús Esteban Galarza, a researcher and mathematician at the French National Centre for Scientific Research (CNRS), was awarded the Elhuyar Emeritus Prize on 12 May 2016 for her work promoting science and the standardisation of the Basque language. On the day following the presentation she was interviewed by Iraitz Vázquez. In the interview she pointed out that the way mathematics is taught will help many students overcome their fear of the subject. "It should be explained practically so that students see its applications and it's not just an abstract concept." We give below an English translation of the interview which appears at Iraitz Vázquez, "Sin las matemáticas no tendríamos ni teléfonos móviles ni coches", El Diario Vasco (13 May 2017).

"Without mathematics, we wouldn't have mobile phones or cars."

Iraitz Vázquez (I.V.): What are mathematics used for?

Maria J. Esteban (M.J.E.): It's used for almost everything. Without it, we wouldn't have cars or cell phones. Virtually all products for calculating prices or insurance costs rely on them. Furthermore, algorithms are also behind new technologies. In short, they're present in many areas of our lives.

I.V.: Why do many young people struggle with mathematics?

M.J.E.: To study mathematics, you need logical reasoning skills, although in most cases it's a matter of personal preference. But I also think we need to analyse how students develop a taste for these subjects. Many find it difficult to study abstract concepts and ask us why they didn't understand what they learnt in school. In high schools, these concepts should be explained through practical exercises. If we can motivate them in this way, we'll achieve a more than acceptable goal.

I.V.: So the work of the schools isn't adequate?

M.J.E.: In France, we're running a campaign with teachers, proposing a way of teaching mathematics that uses practical examples. I think this is how we can motivate students.

I.V.: How can we get a student to actually enjoy mathematics?

M.J.E.: Some students aren't good at it, while others enjoy it. One way to improve students' attitudes is by explaining the purpose of mathematical exercises. If they only study them abstractly, what we're teaching them is ultimately rather useless.

I.V.: Is the lack of interest in this subject the fault of the education system?

M.J.E.: I'm not familiar with the Basque education system, so I'll focus on the French system. In France, the problem is motivation and the limited time dedicated to mathematics. In recent years, the type of curriculum has changed a lot, and it's noticeable that students are graduating with less knowledge than before. Now, they study more subjects, but with less depth than a few years ago.

I.V.: How can you explain to people what mathematics is?

M.J.E.: The easiest way is with examples. I often give talks to people who have nothing to do with the world of mathematics. What I tell them is that, for example, having a smartphone is impossible without mathematics. When you manage to motivate people, you make them think and see how essential mathematics is.

I.V.: Why is mathematics so poorly regarded by students?

M.J.E.: Because they don't know what it's for. Some students think it's a punishment, and that's when they struggle.

I.V.: Should a student who wants to study the humanities also study mathematics?

M.J.E.: I think so. For example, in sociology or economics, you have to use calculus and statistics, so it's essential to have a solid foundation. You shouldn't just study hypotheses, but also logical reasoning.

I.V.: Is there still room for further research in mathematics?

M.J.E.: There's more and more research being done, and there are more problems to solve. Mathematics has increasingly more applications in industry, with new uses. New technologies have given rise to new problems, and we have to solve them. Contrary to what people think, there's still a lot to be done going forward. Behind the design of new materials or medicines, there may be solved mathematical problems.

I.V.: What problem would you have liked to solve?

M.J.E.: I don't have one in particular that I'd like to solve. I mainly work on applications in Physics and Chemistry, but no problem obsesses me. I'm always working on two or three at a time. Naturally, I want to solve them, but they aren't fundamental to my career. There's always one that resists, and you can set it aside, but you come back to it later with new methods of solution.

I.V.: Why did you decide to go to France to do research?

M.J.E.: At that time, the University of the Basque Country was just starting out, and there wasn't the possibility of doing a high-level doctoral thesis. I received a grant from the French government - one of the leading countries in this field - and it was a very good opportunity. I intended to return to the Basque Country when I finished, but a very important research position came up, and I decided to stay in the world's leading city for mathematics.

I.V.: What is your view of the current situation at the University of the Basque Country?

M.J.E.: The research being done is excellent; it's very different from what I was used to. I've collaborated with some top-level researchers.

I.V.: How important was it for Basque that mathematics could be taught in this language?

M.J.E.: If you want to live in Basque, you also have to be able to study in this language. I think it's normal that a vocabulary has been developed so that people can live their lives in Basque. It's part of life and a personal choice. I, for example, don't even do all of my work in French; I do it in English because it's the international language, but that only comes with specialisation.

I.V.: How do you see the current situation of Basque?

M.J.E.: It has improved a lot. You hear it in the streets, and all children learn it in schools. Now you see advertising in Basque at train and bus stops. Fifteen or twenty years ago, this was impossible. This is a sign that there's an audience and people understand it; otherwise, brands wouldn't spend money on advertising.

I.V.: Is an award like the one from Elhuyar more exciting because it's given at home?

M.J.E.: Absolutely. Any recognition that comes from the Basque Country is very special to me. But I want to emphasise that the work we did in disseminating science in Basque was a collaborative effort. We were a group of people who wanted to create science and research in Basque, and we produced a university-level dictionary of Basque vocabulary.

5.
Anaïs Culot interviewed María Jesús Esteban on 15 July 2019. In the interview, on the occasion of the ICIAM World Congress, the international organisation she chaired, Esteban details the collaboration between her discipline and industry.

Mathematics and industry: a perfect match.

Anaïs Culot (A.C.): You are the president of the International Council for Industrial and Applied Mathematics (ICIAM), which is holding its congress in Valencia, Spain, from July 15 to 19. What is it about?

Maria J. Esteban (M.J.E.): The International Council for Mathematical Applications (ICIAM) is an international council that brings together learned societies from all continents with a strong interest in the applications of mathematics. Every four years, we organise the world's largest mathematics congress - this year, for the 2019 ICIAM Congress, approximately 4,000 people are expected in Valencia - whose objectives are to present currently important themes, review research from the past four years, and look to future directions. The congress showcases the applications of mathematics to other sciences, to societal issues, and also to industry. One day is specifically dedicated to presenting successful partnerships between mathematics and industry.

A.C.: Where do we find mathematics in industry?

M.J.E.: Today, everything is modelled. And many problems that can be modelled mathematically are common to all industries, from aeronautics to pharmaceuticals. We can describe the design processes of new objects, the organisation of large production networks, the behaviour of a material, and so on, using equations. These mathematical descriptions allow us to optimise existing systems and address problems on production lines so that they become more efficient. But mathematics also enables the creation of new products. It fosters innovation by proposing new designs, new construction materials, and new electronics. Signal processing and image analysis can be used to monitor product quality. With high-performance computing, we can perform simulations rather than conducting lengthy and expensive full-scale testing.

A.C.: Does the industry face recurring problems that mathematicians can address?

M.J.E.: The digital revolution, with the rise of digital technologies and artificial intelligence - fields in which mathematics plays a crucial role - is having a significant impact on manufacturers. The concept of the industry of the future, which must be connected, competitive, and ever more innovative, is becoming increasingly prevalent. Manufacturers also generate vast amounts of data that they struggle to manage. Big data exacerbates this phenomenon: how can this data be analysed, understood, and used to improve their organisation, production, or sales? Today, it is possible to address increasingly complex problems and use increasingly powerful algorithms, thanks to ever-improving computer performance. Among the concerns of manufacturers to which mathematics can provide solutions are reducing costs and risks, designing more competitive products with appropriate materials, and so on.

A.C.: How do mathematicians and industrialists come to collaborate?

M.J.E.: It's very diverse. Partnerships can be initiated by industry as well as researchers. They can involve taking full responsibility for a project or providing complementary skills to solve a problem encountered during the R&D phase. It's quite common for collaborations to develop through shared knowledge, because someone has heard about a colleague's project. Large companies often have mathematicians in their R&D departments or consult universities and engineering schools when needed, unlike SMEs and start-ups, which are less familiar with this type of exchange. In France, the Agency for Mathematics in Interaction with Business and Society (AMIES) reaches out to small and medium-sized enterprises to demonstrate the benefits of working with mathematicians. It then funds the initial stages of certain projects. Through AMIES, we primarily try to engage companies by example, somewhat like a showcase. Illustrating our work with success stories works well with industry professionals who might otherwise hesitate to get involved. Collaboration presentation days also highlight the wide variety of applications as well as the mathematics used (partial differential equations, probabilities, statistics, numerical analysis, scientific computing and even number theory, geometry ...).

A.C.: How do these collaborations work?

M.J.E.: The manufacturers who commit to our services quickly understand the benefits of working with us and are generally satisfied with the results. Regarding our approach to problem-solving, there are two main stages: designing an algorithm and verifying it. We must guarantee its convergence speed and stability. When doing applied mathematics, we don't just adapt existing algorithms. We often have to find new methods that require a significant amount of theoretical mathematics.

A.C.: What might be the constraints and advantages of these collaborations?

M.J.E.: The timeframes are different. Manufacturers, especially small businesses, need results quickly, sometimes within six months, whereas a research program can last four years. This is because they lack the necessary funds to invest more. The biggest challenge then becomes assessing whether we can meet their needs. Other companies, however, can invest in the long term, for example, when launching a new production line. We often use recent methods that can be adapted, provided they are slightly modified. This is the case, for example, with the numerical acceleration of an algorithm. This method, which a bank uses to calculate a stock price in a few seconds to avoid losing customers, can also be used in many other contexts. Beyond applications, companies need to know a precise margin of error for the tools we offer them because they cannot afford to have only a rough idea of ​​their products' properties. One of the advantages of working with a mathematician is that they can offer a guarantee on the maximum size of errors in the results produced by an algorithm.

A.C.: How does France compare to other countries in this type of collaboration?

M.J.E.: A study published a few years ago demonstrated the impact of mathematics on the French economy. It revealed that 15% of GDP is influenced by mathematics. Similar studies have been conducted in Great Britain, the Netherlands, and Spain. The strongest industry in Great Britain is finance, while the Netherlands is more involved in energy and electronics. Despite differing industrial structures, similar results show that approximately 15% of GDP is influenced by mathematics in all these countries.

A.C.: Throughout your career, what examples of unusual collaborations have you observed?

M.J.E.: In image processing, for example, smartphone cameras are becoming increasingly sophisticated. Some innovative companies have developed mathematical methods that can clean up images even if you move slightly during capture. Highly sophisticated algorithms that act instantly improve colours, edge sharpness, and more. Another industrial application, involving extensive research on fluids, materials, and shapes, comes from the École Polytechnique Fédérale de Lausanne (EPFL), which worked with a company specialising in racing boats. Researchers worked on a completely new sailboat design and modelled all the material properties, from the shape of the hull and sails to that of the masts, and so on. The result: the sailboat won the America's Cup several times. Among the presentations organised by AMIES, there was the example of a company developing an airbag for motorcycles. They were very pleased with the collaboration and the opportunity to work on a product that is both innovative and potentially life-saving. In general, mathematics has an undeniable impact on daily life, but we don't talk about it enough. Mathematics is everywhere, and not just there to "annoy" students at school.

6.
Thierry Horsin, the president of SMAI, interviewed Maria J Esteban in March 2020. Let us explain the abbreviations used in the text. The SMAI is the French Society for Applied and Industrial Mathematics, ICIAM is the International Council for Industrial and Applied Mathematics, SEMA is the Specialty Equipment Market Association, FEM is the Mathematics Employment Forum, SFdS is the Société Française de Statistique, CIMPA is the Centre International de Mathématiques Pures et Appliquées, and AMIES is the Agency for Mathematics-Industry Relationships.

Thierry Horsin interviews Maria J Esteban.

Thierry Horsin (T.H.): During your years as president of ICIAM, have you observed an upward shift in the perception of the usefulness of mathematics by political leaders worldwide? And in France? And if so, how has it manifested itself?

Maria J. Esteban (M.J.E.): It's clear that in recent years there has been much more talk about the usefulness of mathematics in economic life and with regard to technological development. The impact study of mathematics conducted in several European countries has awakened many people to this issue, but I'm not sure it will have concrete consequences for mathematical research. The arrival of the "Big Data" revolution and artificial intelligence further highlights the importance of mathematics. Mathematical algorithms are discussed more in the media as an important basis for technological development and also for forecasting (climate, epidemics, etc.). I don't know if this greater visibility has truly reached the "political" world, the world of decision-makers. The media, certainly, has.

There are countries where this new perception of the usefulness of mathematics has prompted policymakers to allocate more resources to mathematics. I've seen this very concretely in several Asian countries (mainly Japan and South Korea). Last year, I also noticed a significant shift in Spain surrounding the organisation of the ICIAM congress. From what I understand, the extensive media campaign highlighting the usefulness of mathematics had an almost immediate impact on politicians' perceptions and attitudes toward mathematics and mathematicians.

In France? The impact assessment and the creation of AMIES were important factors in facilitating a change in the perception of mathematics as a technology of the future. The buzz surrounding artificial intelligence is also bringing mathematics into the conversation. But I don't believe that the practical importance of mathematics has been truly grasped at the political level, or at least, not sufficiently.

T.H.: How do you explain the apparent difference you point out between France and Spain? And do you see any way that could prove effective in addition to all the actions put in place (AMIES, which you had the idea of ​​creating with Frédéric Coquel, the Maths Employment Forum, the surveys you mention, the INTERFACE program ...) in particular, what message could ICIAM convey in this regard in light of this recent awareness?

M.J.E.: I think the difference is due to two things. Firstly, the fact that the ICIAM congress took place in Spain and received a lot of media coverage (print, TV, internet, etc.). But it's also important to see that the congress organisers and the SEMA company made a huge effort to communicate with the general public, using a (private) science communication and outreach agency, 'Divulga,' which has been around for a few years and which organised the entire dissemination campaign. We don't have anything like 'Divulga' in France, and it would be very useful to have one! Once the media coverage was so extensive, decision-makers understood the significance of the congress and, indirectly, the importance of mathematics for society. Finally, the presence of the King of Spain at the congress's opening gave it even greater resonance and awakened politicians who, until then, had treated mathematicians with little attention or interest.

In France, it is true that the creation of AMIES has significantly changed the perception of the value and usefulness of mathematical applications. This impact of AMIES and other initiatives moving in the same direction has been felt not only in industry and among the general public, but also within the mathematical community itself. Regarding the perceptions of young people and students, an event like the FEM, organised by AMIES, the SFdS, and the SMAI, was a resounding success. We must continue to develop good ideas that change the perception of mathematics and its usefulness in society at large: among decision-makers, yes, but especially among families, young people, teachers ... everywhere.

T.H.: There's been an increase in the number of CIMPA schools dedicated to applied mathematics. This is certainly something to celebrate, just as we can welcome the creation of a Mathematics Day for Development. We can imagine there's a real enthusiasm for big data mathematics and artificial intelligence. In your opinion, which themes offer the most potential for contributing to development?

M.J.E.: I believe that beyond the areas of mathematics that have always contributed to solving problems arising from the real world, industry, and applications to other sciences, such as ordinary differential equations and partial differential equations, numerical analysis, scientific computing, statistics, and probability, today many other fields can contribute in this direction, such as geometry, algebra, topology, number theory, etc. Obviously, not everything done in these fields can be applied, far from it, but a wide variety of mathematics is needed when one wants to tackle the study and resolution of "real-life" problems. More and more I think that the division between pure and applied mathematics should evolve towards a distinction between theoretical and applied mathematicians, because what matters is not so much the type of mathematics one studies, but above all the will and desire to study practical, concrete problems, problems coming from outside of mathematics.

T.H.: There is strong mobilisation within the European mathematical scientific community for open science. What is the situation globally, and does applied mathematics have a specific message to convey to ensure this trend becomes widespread? I am thinking, for example, of greater recognition of the added value of mathematics for the socio-economic world in order to encourage and solicit government funding.

M.J.E.: I think the movement for open science knows no borders, and the entire mathematical community worldwide is involved. This is due to ideological reasons, our vision of the work we do, but also to economic motivations, because mathematicians cannot pay to publish, as our grant system is not designed for this, unlike in other scientific fields, such as biology. I don't believe there is a distinction between theoretical and applied mathematics in this movement, and I would say that, on the contrary, I often see a stronger awareness and mobilisation for Open Access in very theoretical communities. That said, a very important difference is that Open Science concerns not only publications, but also algorithms and computational code, which must also be freely accessible. And this concerns the applied mathematics community much more, of course.

T.H.: 44% of the key technologies cited in the Ministry of Industry's Horizon 2020 report use mathematics. Do 44% of colleagues identify as doing applied mathematics? In France? Worldwide?

M.J.E.: Yes, I would say that in France, about half of university mathematicians are registered with section 26 of the CNU (National Council of Universities). But this doesn't mean, far from it, that all mathematicians registered with section 26 of the CNU are truly ready to work on genuinely applied topics. ... Non-French mathematicians have often told me that much of what is considered applied mathematics in France, in their country, would simply be applicable mathematics ... that's an interesting distinction.

T.H.: I heard this distinction during a hearing and I didn't understand it, or perhaps I misunderstood it. Some colleagues don't see themselves as doing applied mathematics, but rather as facilitators between mathematics and other scientific fields. Among those I know, I really admire the way they take ownership of mathematics and use it. In your opinion, is that what leads to the distinction? Is there a particular message that the Maths for Development Day should convey regarding these "facilitators" or applied mathematics?

M.J.E.: I don't know. I see the distinction more as a question of attitude between mathematicians who are interested in solving problems that come from outside mathematics and those who aren't directly interested in it. It's not about the type of mathematics one uses, but what one wants to do with it.

T.H.: You have just received a prestigious award, the Jacques-Louis Lions Prize. Allow me to congratulate you again. How have you perceived the contribution of Lions as seen from the perspective of ICIAM compared to before your experience as its president?

M.J.E.: Jacques-Louis Lions was a great mathematician, but moreover, he truly launched mathematics and many mathematicians in the direction of concrete applications to real-life, even industrial, problems. He opened up new avenues of research, launched new theories, encouraged interdisciplinarity, and prepared the tools to do so. At the international level, he played a significant role in structuring the global applied mathematics community, and he was instrumental in the creation of ICIAM.

T.H.: Can you specify which tools of interdisciplinarity you are referring to?

M.J.E.: Jacques-Louis Lions proposed a comprehensive vision of mathematics applicable to solving real-world problems, encompassing modelling, mathematical analysis, numerical analysis, and scientific computing, while also emphasising concrete applications through direct interaction with industry. He founded a school that developed this vision and worked across the various components of his overall programme. The structure of the different research and development departments enabled rapid, practical, and effective progress. Among his many students, we find individuals who have developed the research programmes he proposed and who have significantly broadened the mathematics-industry interface in France. He himself set an example by maintaining a highly varied professional activity, ranging from theoretical work to direct involvement in management and industrial collaborations.

T.H.: At ICIAM 2019, you also received a SIAM award for your involvement in the global community. Congratulations again. Scientific excellence is mentioned in almost every sentence (myself included). In your opinion, can the excellence of some, which we would like to be universal, exist without the involvement of others? And if so, do you think this is well received at the political level?

M.J.E.: Yes, you're right, we talk too much about excellence, often wrongly or without real reason. We use it as an excuse for many actions and programmes. Obviously, excellence is important, but by using the word constantly, it loses all its force and meaning. And you're also right when you say that talking about the excellence of some without taking into account the collective work behind it isn't quite right. There are excellent, outstanding mathematicians whose results and role in the community are very important. But the media, decision-makers, and journalists often see them as isolated individuals who produce wonders on their own, as if they lived in a world apart, which is almost never the case. Mathematicians, like all scientists, live and work in a community that constantly produces important results, that advances science, and from time to time, an outstanding scientist produces remarkable results from this work. They deserve great credit, no doubt, but the work is often collective, and it's the whole community that carries out the projects. Geniuses are brilliant, yes, but often their discoveries are the culmination of a long and collective effort.

T.H.: I wasn't really expecting a different answer. I think that's especially true considering the difficulty in applied and industrial mathematics of understanding and modelling problems that are inherently applied or industrial; it requires a lot of time and groundwork. Regarding collaborations with companies and industries, do you think they are valued enough in a career? How could we encourage more colleagues to get involved in this type of work?

M.J.E.: Everyone agrees that collaborations with companies are not valued enough and that this type of work counts for far less than publications when recruiting or promoting a researcher or professor. Evaluation criteria should be multifaceted, including, of course, written output (articles and books), teaching, research supervision, and management activities - which are already partly well-evaluated - but also activities related to interdisciplinary and even industrial collaborations. The time required to grasp a new real-world problem, model it, study it, discretise it, perform the corresponding calculations, code it, and interact with stakeholders in the industrial or scientific sectors with whom one collaborates is enormous, and this should be given significant consideration when evaluating any mathematician. It's essential. I don't believe there's a 'legal' barrier to this; it's more a problem of mentality and a lack of interest and vision on the part of many colleagues who participate in recruitment or promotion committees.

Regarding the second part of the question, I think the work one does as a mathematician depends on personal tastes, but also on the training one has received and the perception of the surrounding community. It's by changing mindsets within the mathematical community, by valuing this type of work, by showing that one can have a successful career, academic or in the private sector, doing highly applied mathematics, that young people, and not-so-young people, will move in this direction. Much has been done in recent years, but we must continue relentlessly.

T.H.: At the doctoral level, do you have any suggestions in this regard?

M.J.E.: It is before the doctorate that we need to open young people's eyes. Once they have chosen their thesis supervisor, the choice is already pretty much made ... but perhaps within the framework of doctoral schools we could offer more introductory seminars, information on careers ... and there are of course the SEME where we can send students for modelling training ... or the new Interface program of the CIRM.

T.H.: Being a research director at the CNRS doesn't mean one isn't interested in teaching issues. I know these issues are important to you. Personally, I think the connection between teaching and research is fundamental and that it strengthens the discipline. It seems to me that this connection is very strong in France, in applied mathematics or mathematics in general, perhaps more so than in many other fields. Am I wrong? Is this the case worldwide? We talk a lot about the LPPR (Loi de Programmation Pluriannuelle de la Recherche) and not the LPPRE (Loi de Programmation Pluriannuelle de la Recherche et Enseignement), the E for teaching (enseignement) - should we have one? Speaking of the LPPR, if you had only one recommendation, based on your experience as president of ICIAM, what would it be?

M.J.E.: The link between teaching and research is fundamental, of course. I can't say if this is clearer in mathematics than in other scientific fields, but probably so. And I believe this isn't a French or European phenomenon, but a global one. Just look at the enormous investment made by countries like China and South Korea in mathematics education and also in mathematics research, both in theoretical mathematics and in highly applied, even industrial, mathematics. I don't know if a LPPRE (Loi de Programmation Pluriannuelle de la Recherche et Enseignement) is necessary, but what is clear is that the evolution of mathematics curricula in primary, middle, and high schools hasn't been heading in the right direction for quite some time, and that the training and preparation of primary and secondary school teachers should be reviewed. And again, this isn't just a French problem, unfortunately! Interesting analyses and proposals were made in the Torossian-Villani report.

T.H.: You succeeded another woman, Barbara Keyfitz, as president of ICIAM. From what you know of Barbara's experience as president and what you've learned from your own, is there anything that could improve gender parity issues in France in the field we're concerned with? Perhaps a difficult question: which country would you cite as an example regarding these gender parity issues?

M.J.E.: That's a very difficult question that many people ask in very diverse contexts. For example, there was an international study on the 'Gender Gap in Science,' largely funded by the International Council of Science, in which IMU and ICIAM participated. The final report will be released soon, and it contains very interesting information and answers to your questions. The website for this initiative is https://gender-gap-in-science.org/, and the book containing the results of this study is available at https://zenodo.org/records/3882609. [Note. We have updated (in 2025) the links to the website for the book - the link given in the original article no longer works.]

Even though the situation in France isn't great, I think we're not doing too badly on the issue of gender parity because, unfortunately, the situation is much worse almost everywhere else. There are countries with a higher proportion of female mathematicians, but in those countries, the representation of women in the workforce is generally less favourable than in France. Much remains to be done, and this is a matter of education in schools, but also of culture within families and society in general. Based on my personal experience, I would say that what is most important is for young women not to see their gender or background as an obstacle to pursuing any career path or reaching any level of the hierarchy. When you don't see limits, you can go as far as your abilities allow. There are also all the structural and organisational issues that need improvement, of course, but a change in mindset is, once again, what is needed to truly make progress on gender equality.

T.H.: To conclude this interview, for which I thank you very much, is there anything you would like to add?

M.J.E.: First of all, a huge thank you for this fascinating discussion, which could easily go on because there is so much to say about our work as mathematicians and about our community and its organisation. My experience as president of ICIAM has given me a unique opportunity to see the differences between countries, and even between continents, regarding the organisation of mathematicians, the perception of their work, and current trends. But I can't forget that this whole part of my career began at SMAI, because it was from the moment I took on responsibilities in our beloved society that I began to take a real interest in community and association issues. So, a big thank you to SMAI for everything it has given me and for what it has allowed me to understand and accomplish.

References (show)

Last Updated December 2025