“The path of analysis, abstraction, and the elaboration of the formal structures of logic and mathematics initiated by the Greeks is what has given us the framework and the sophisticated tools that underpin the empirical sciences and social practice,” said the BBVA Foundation’s Director Rafael Pardo in his address to the ceremony. “At a time when goverment science policies predominantly focus on the applied side of knowledge, we need to uphold the importance of maintaining support for the pursuit of knowledge for knowledge’s sake, that is, basic or fundamental science, as well as knowledge that directly pursues the solution of practical problems. The history of science and innovation testifies to the irreplaceable and hard-to-improvise role of frontier basic research. This diversity of modes and orientations of scientific work, both fundamental and applied, is magnificently represented by the contributions of tonight’s laureates.”

The gala, held in the Madrid headquarters of the BBVA Foundation, celebrated the achievements of a total of 10 mathematicians: the winners of the Vicent Caselles Awards, bestowed by the RSME and the BBVA Foundation, which each year distinguish the excellence of six young researchers aged under 30, either Spanish or pursuing their careers in Spain; the RSME’s José Luis Rubio de Francia Prize for researchers under 32 years of age, whom the BBVA Foundation provides with 35,000 euros funding for a three-year research project; and the RSME Medals awarded to outstanding professionals for their exceptional and continuing contributions to the field of mathematics.

The Director of the BBVA Foundation stressed the importance of awards granted by organizations like the RSME, that are an expression of civil society: “In a country like ours, with a marked deficit in associationism, and a lack of independent organizations and institutions, the importance of having scientific societies committed to using knowledge for the improvement of the public realm cannot be emphasized enough.”

“The re-emergence of irrational and divisive voices in our society and its institutions is one of the major challenges of the present day,” Rafael Pardo continued. “The problem, and it is a grave one, lies not only in the denial of validated knowledge in areas like health and the environment displayed by certain social segments, but also in the growing polarization of elites in the public realm, fuelled by the exaltation of the emotional, the activation of stereotypes, the counterpositioning not just of values but of incommensurable maps of reality, and the erosion of rational dialogue, which lend themselves to the stigmatizing of the other.”

In this context, the Foundation’s Director talked of “the importance of broadening and strengthening the public’s scientific culture, which, as well as benefiting each individual in diverse facets of their lives, can serve as an aggregate counterweight or immunization against the discourse and behavior of certain elites. The life stories and contributions of the winners here tonight are a window for rationality and reason-based consensus which it is important for society to know of and recognize.”

Eva Gallardo, President of the RSME, referred in her speech to the mathematical society’s duty to “face up to the growing challenge of disinformation and denialist currents that threaten the wellbeing, security and progress of society, and even the stability of our democracies.” At a time of worldwide challenges like the “global climate emergency” and “the search for new sustainable energy sources,” the RSME President was adamant that “only a firm commitment to science can offer solutions” and that mathematics “has much contribute in areas like the reliability of algorithms, modeling or cybersecurity.”

“The society we live in has to understand the importance of science and rigorous scientific knowledge, available to all, in helping us confront an increasingly uncertain and fast-moving future with confidence and rigor,” Professor Gallardo concluded.

Ten researchers recognized for their brilliant scientific careers

The BBVA Foundation and RSME’s Vicent Caselles Awards were launched in 2015 to recognize and encourage the talent of young researchers in mathematics and, through them, to give the science of mathematics greater public visibility. Six awards are given annually, each endowed with 2,000 euros, to researchers aged under 30 who are either Spanish nationals or have carried out their research work in a university or scientific center within Spain.

The awardees in the 2023 edition are: Robert Cardona Aguilar, lecturer at the University of Barcelona; Claudia García López, lecturer at the University of Granada; Roberto Giménez Conejero, postdoctoral researcher at the Alfréd Rényi Institute of Mathematics (Hungary); Paula Gordaliza Pastor, lecturer at the Public University of Navarra and a researcher in the Basque Center for Applied Mathematics; Óscar Rivero Salgado, a lecturer at the University of Santiago de Compostela; and María Soria Carro, Hill Assistant Professor at Rutgers University (New Jersey, United States).

Xavier Fernández-Real, a postdoctoral researcher in the Institute of Mathematics at the École Polytechnique Federale de Lausanne (Switzerland), was presented at the ceremony with the José Luis Rubio de Francia Prize. This award for young mathematicians aged up to 32 who are Spanish nationals or have conducted research in Spain comes with a start-up grant of 35,000 euros from the BBVA Foundation to fund the winner’s research over the next three years.

The RSME Medals, which recognize individuals who have made exceptional and continuing contributions in any field of mathematical activity, were also handed out at the ceremony. Recipients were Professor Francisco José Marcellán Español, Emeritus Professor at the Universidad Carlos III de Madrid (UC3M), Professor María del Carmen Romero Fuster, a retired professor formerly of the University of Valencia, and Professor Luis Vega González of the University of the Basque Country (UPV/EHU) and Scientific Director of the Severo Ochoa program at the Basque Center for Applied Mathematics.

The value and beauty of curiosity-driven mathematics

In their speeches at the ceremony, the awardees stressed the value of mathematics driven by curiosity alone, which does not seek immediate applications but is ultimately what lays the foundations for the technological revolutions of the future. “Research in pure mathematics, an area to which my discipline, number theory, belongs, does not have a direct impact on society, but it is also true that any technological application is preceded by tangible advances in the basic science on which it is based,” said Óscar Rivero. The focus of this researcher’s work is one of the Millennium Problems, worth one million dollars to whoever can solve them; in this case, the Birch and Swinnerton-Dyer conjecture, centered on elliptic curves, mathematical objects that play a key role in the cryptography field.

A similar argument was put forward by Roberto Giménez Conejero: “In the face of ignorance and the desire for immediacy, we must remember that there has always been a delay of 50 years or more between a breakthrough in pure mathematics and its application.” Giménez’s research interest lies in singularities, properties that appear in objects or mathematical functions when they change abruptly rather than smoothly, and that are key to extracting information from objects when they cannot be directly observed. In this area of inquiry, he combines techniques from algebraic geometry with others from such disparate fields of math as differential and algebraic topology, differential equations, number theory and combinatorics.”

“Mathematics is not its applications, and it shines most brightly when freed from the chains of immediate utility,” declared Xavier Fernández-Real, winner of the José Luis Rubio de Francia Prize. This researcher studies the so-called free boundary problems, which are used to model phenomena as varied as the melting of ice, the exchange of substances at the cellular level, or the evolution of the stock market. But speaking about what truly inspires and motivates his work he explained: “My main catalyst for further study and research is, plain and simple, my own curiosity. Can the essence of human achievement be confined within the narrow walls of practicality? It is in its at times perceived futility that mathematics finds its greatest utility, for it is there that the human spirit finds itself free to explore the depths of creativity and abstract thought.”

From aeronautics and biomedicine to artificial intelligence

The awardee’s speeches also reflected the immense power and transversal applicability of mathematics. María Soria Carro defined the language of mathematics as “an exciting world full of fascinating open problems,” whose solution “can have an enormous impact on the advancement of our quality of life as a society.” This promise, indeed, is exemplified by her own research. She studies the mathematical equations that describe how a physical quantity changes on either side of a surface separating two different media, for example, the speed of light as it passes from air to water. This work, she explained, may have applications in many fields, from biology to geophysics and even aeronautical engineering, “to develop composite materials of different fibers, such as those used to build airplane wings or fuselages that have to resist high loads.”

The power of mathematics to elucidate phenomena in nature – from the inside of the human body to behavior on the surface of other planets – is a source of fascination for Claudia García, whose research looks at the equations that describe the movement of fluids such as water. Not stopping at the currents of Earth’s rivers and oceans, her work has explained what happens in a region of Saturn’s surface, where a hexagon full of vortices is formed, and can even help analyze blood flow, with potential applications in biomedicine. “Although they seem like relatively distant fields, mathematically the models governing these phenomena have very similar properties. It often happens that these results, which may at first seem of purely mathematical interest, find direct application years later to explain phenomena occurring in nature.”

For Paula Gordaliza, distinguished for her research on developing methods to detect, control and correct the biases of artificial intelligence, “the dizzying pace of recent decades and the development of powerful computing methods and tools show that the usefulness of mathematical research can be both tangible and immediate.” Regarding the risk that algorithms might discriminate against certain groups on the basis of gender, ethnicity, political orientation or other traits when deciding on such vital issues as who gets a job or is accepted for a bank loan, Gordaliza pointed out that “a prime objective of mathematics is to open up the black boxes of artificial intelligence,” so people have more trust in the technology.

The limits of mathematical reasoning and the surprising universe they reveal

Finally, the limits of mathematical reasoning were addressed by Robert Cardona, whose work relates the motion of fluids like air or water to their geometrical structure. This researcher has shown that it is not always possible to predict a fluid’s behavior over time, even when all the starting conditions are known. In mathematical terms, the trajectory of the fluid is “undecidable,” so cannot be accurately predicted with mathematical tools. “Besides the theoretical and applied importance of the existence of such limitations, the philosophical consequences of these kinds of results should give us pause for thought,” said Cardona. “They are telling us that mathematical reasoning, supposedly so unquestionable and universal, is sometimes not enough, even within its own rules. The universe surprises us, and that only makes things more interesting, as well as boosting mathematical research’s value for society.”

Vicent Caselles Award jury

Appointed by the BBVA Foundation and the Spanish Royal Mathematical Society, this year’s jury was chaired by Luis Narváez Macarro, Professor of Algebra at the University of Seville, and formed by: Diego Córdoba Gazolaz, Research Professor in the Institute of Mathematical Sciences-CSIC; Joan Elías i García, Professor of Mathematics at the University of Barcelona; María Ángeles Gil Álvarez, Professor of Statistics and Operations Research at the University of Oviedo; María del Mar González Nogueras, Associate Professor at the Universidad Autónoma de Madrid; and Antonio Ros Mulero, Professor of Geometry and Topology at the University of Granada.