When I studied at the University of Bilbao, it was the first years of the 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 political climate of the time did not allow for peace and quiet, and yet María Jesús had an excellent career and stood out among the students of the time.

In the 1970s, having Basque everywhere was a desire and a dream. There was no one to ask, the only way was to take action. Maria Jesus was willing to do mathematics in Basque, as we have seen with her thesis. She participated in seminars organised by the Faculty of Science and in 1977, while still a student, she gave her first lectures at the UEU.

... the UEU published the first university-level Basque mathematics book, Espazio topologikoak, written by María Jesús Esteban and five other students, all women. Basque was making its way in pre-university education and was gradually appearing in universities. The need to agree on scientific terminology and to standardise it as much as possible was clear. Thus, the project to create a mathematics dictionary was launched in 1978, under the leadership of Karlos Santamaria. The dictionary was published four years later and contained definitions of terms, long articles and a glossary in four languages. Maria Jesus stood out in the team that worked on it, as they acknowledge in the preface: "in a final phase, by mutual agreement, María Jesús Esteban has been responsible for correcting the content of all the articles at the three levels, establishing reference symbols and standardising the entire body." It was no small task!

As was customary, doctoral students found their first collaborators among recent PhD graduates, who acted as intermediaries with the supervisors. This is how Maria Jesus began her research with Pierre-Louis Lions, who would become her closest collaborator for the next ten years.

We prove that, under general conditions, there exist one positive solution and infinitely many non-trivial and radial solutions, which decay exponentially at infinity, of the problem

          $-\Delta u = g(u)$ in $\mathbb{R}^{2}$

where g(0) = 0.

The proof relies on some critical-points results.

It was Pierre-Louis Lions 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 had never thought about that possibility. ... 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.

... 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. ... 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 this paper we study the existence of positive nontrivial periodic solutions of semilinear parabolic problems. Most of the nonlinearities considered are of the superlinear type. Some bifurcation results are proved as well.

The solutions of Skyrme's variational problem describe the structure of mesons in a field of weak energy. The problem consists in minimising the corresponding energy among the functions from $\mathbb{R}^{3}$ to $S^{3}$ which have a fixed "degree" without making any symmetry assumptions. We prove the existence of minima and study their properties.

Fuelled by close interaction with the worlds of business and industry, our work covers a wide range of fields, including economics, finance, actuarial science, astronomy, mathematical physics, mechanics, quantum chemistry, imaging, data science, statistical learning, biology, epidemiology and linguistics.

The purpose of this note is to derive compactness properties for both incompressible and compressible viscous flows in a bounded domain interacting with a finite number of rigid bodies. We prove the global existence of weak solutions away from collisions.

Over the past 25 years, the curriculum vitae of María Jesús Esteban clearly exemplifies the busy life of a prestigious scientific researcher: constant travel, as many of her collaborations take place during invited visits to universities around the world, not to mention the more than one hundred invited lectures at conferences and the teaching of specialised courses. She has also directed research projects and participated in international scientific committees, whether for the selection of important awards - notably the Abel Prizes, those of the European Mathematical Society, and the joint awards of the Association for Women in Mathematics and the Society for Industrial and Applied Mathematics in the United States - or for the evaluation of mathematical research in Germany, Austria, Denmark, Italy, Norway, and also in Spain, specifically in the Severo Ochoa Centres call for proposals. Particularly noteworthy is the trust placed in her by the European Research Council to chair the panel of experts in Mathematics (PE1) for the Advanced Scientists Grants in the 2014-2015 biennium. She has always been available to collaborate on countless occasions in various activities of the Royal Spanish Mathematical Society and the Spanish Society of Applied Mathematics.

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 programmes 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.

What I most like doing when I am not working is going to the movies and visiting museums and art exhibitions. Hiking has always been a favourite of mine, too. I had almost stopped doing it, but the COVID period has pushed me to walk a lot again.

Some of Maria's most influential mathematical work concerns the description of the behaviour of elastic bodies immersed in fluids. In another strand of her research she has studied critical points for an energy functional associated with various nonlinear Dirac equations in relativistic quantum chemistry, and minimisers for the Skyrme's model in chromodynamics. These are very challenging problems involving nonlinear partial differential equations. Unlike in life, in which inequalities are to be avoided, for such equations inequalities, expressing that one quantity is less than another, turn out to be fundamental. Maria is responsible for many important developments concerning such inequalities ...

Speaking of surprising, it seems surprising to me how much my life has changed since I started working. I started my research calmly, happily. But, as the years have passed, my work has grown and diversified, and life has gradually become much more complicated, and the boundary between personal and professional life has almost completely disappeared. Forever? I don't think so: I am getting older, and now, perhaps, I will regain my personal life. But, to be honest, I did not expect this when I started working.