Scientific Achievements, Personal Motivation, and a Constructive Community Mindset

Academy Award-winning Research Professor Károly Böröczky reflects on the lessons of his career and his guiding principles. He recently co-authored a book with Fields Medalist Alessio Figalli. 

Scientific achievements, personal motivation, and a constructive, community-oriented view of mathematics. It is difficult to decide which of these can most closely be associated with Károly Böröczky, Research Professor at Rényi Institute. Alongside his research as a member of the Geometry Research Department led by Géza Tóth, he also serves as Director of the Erdős Center. 

“In my life, both doing research and helping to organize science have always played very important roles. For the past thirty years, these two activities have gone hand in hand. We often think, and I share this view, that the average physicist or mathematician is not particularly interested in management, and that making decisions related to the organization of scientific work is rather far from their personality. Indeed, only relatively few of us are also drawn to this kind of work,” he reveals in an interview with renyi.hu. 

He adds that this dual role has greatly enriched his professional life, including his work as a mathematician. “From 2012 onwards, I chaired the Department of Mathematics at Central European University (CEU). At a university primarily focused on the social sciences, this was both an unusual and an exciting challenge, carried out within the framework of the collaboration between Rényi Institute and CEU. I was helping to build a dialogue between a purely theoretical branch of mathematics and the social sciences, and it worked remarkably well. We collaborated mainly with departments and researchers using quantitative methods. As part of this highly promising interdisciplinary effort, I myself learned a great deal about the social sciences. Unfortunately, this collaboration was brought to an end by a political decision around 2018,” he recalls, adding that the memory of this successful bridge-building effort continues to give him great satisfaction.

He brought this extensive experience in scientific leadership and research management back to Rényi Institute, which continued to rely on his expertise even while he was abroad. Following CEU’s forced departure from Hungary, he worked at the University of California, Davis, and later spent a year at ETH Zurich. During his time in Zurich, and in close consultation with the Institute’s current Director General, András Stipsicz, he had already begun organizing and shaping what would become the Erdős Center. He subsequently returned to Rényi Institute full-time, taking up the position of Director of the Erdős Center.  

Established in 2019, the Erdős Center is one of the organizational units of the Rényi Institute, but it has also increasingly become a recognized brand on its own. A $750,000 Targeted Grants for Institutes award from the Simons Foundation specifically supports the Erdős Center’s summer schools and postdoctoral researchers. The Center’s extensive experience in organizing thematic semesters, summer schools, and workshops also plays an important role in the successful Simons Collaborations grant awarded to an international consortium. The Erdős Center is receiving a growing number of requests from European colleagues (i. e. researchers from Berlin or Warsaw) to host scientific events. On several occasions, Rényi Institute’s main lecture hall, with seating for 100 participants, has even proved too small for the demand. Both the Erdős Center and Rényi Institute as a whole are characterized by the close and effective cooperation between the administration and the leadership. Everyone is committed to coordinating the often competing demands of financial management, administration, communications, and scientific excellence to ensure the success of the Institute’s activities.

"Leading the Erdős Center has surpassed even my responsibilities at CEU in terms of its international scope,” says Research Professor Károly Böröczky.

“The Erdős Center is a genuine window onto the world. Our scientific events are organized by researchers from across the globe, and it is extraordinary to see this international network come to life. A typical summer school brings together around one hundred PhD students and/or postdoctoral researchers from a dozen or more countries, i. e. the United States, China, and many others, to learn from leading professors who themselves come from all over the world.”

Each year, the Rényi Institute hosts eight to ten major international events, including conferences and summer schools conducted in English, thus making it a popular and valuable meeting place for the global mathematics community. Reflecting on the Institute’s history, Professor Böröczky notes that fostering international collaboration has always been one of its defining ambitions. “Alfréd Rényi himself envisioned the Institute as a bridge between Hungarian mathematics and leading mathematicians abroad, and every director who followed him worked to strengthen that role. In 2019, András Stipsicz took these efforts to a new level by establishing the Erdős Center, creating an institutional framework for building international scientific connections. Many of the international professors I work with tell me that our organizational and administrative team is outstanding. They are particularly impressed that, with far more modest financial resources, we have built an organization capable of managing major scientific events at a level comparable to some of the world's leading mathematics research centers, such as SLMath in California, the Newton Institute in the United Kingdom, and the Hausdorff Center in Germany. These events are an essential part of the research infrastructure of mathematics. Major collaborative results, influential publications, and even entirely new research directions emerge from these extended programs, which may last for several months.”

Research professor Károly Böröczky’s contributions to scientific management are also highlighted by the Members of the Hungarian Academy of Sciences (Imre Bárány, Péter P. Pálfy, and András Stipsicz) who signed the official nomination letter recommending that he receive the 2026 Academy Award of the Hungarian Academy of Sciences in recognition of his outstanding contributions to several areas of mathematics, most notably geometry. As the nominators emphasize, “His achievements as a scientific leader are equally remarkable. He served as Chair of the Department of Mathematics at CEU for eight years. Since 2022, he has been Director of the Erdős Center at Rényi Institute. He also led an EU-funded Transfer of Knowledge project (2004–2008) involving five European institutions, and has organized numerous conferences, both in Hungary and internationally, including events hosted by the American Institute of Mathematics.” (Our news article about the award ceremony, featuring a photo provided by the Hungarian Academy of Sciences, is available HERE.)

He has achieved all this while maintaining an outstanding research career. (He could boast about these accomplishments if boasting were not completely at odds with his personality, as the editor cannot help but note.) His nominators also emphasize his impressive academic record. According to the Hungarian Scientific Bibliography (MTMT), he is the author of 139 scientific publications, which have received 1,726 independent citations. They also note that he has supervised six PhD students and mentored four postdoctoral researchers.

During his year at ETH Zurich, Károly Böröczky collaborated with Fields Medalist Alessio Figalli, who received the award in 2018. Together with Figalli and Brazilian mathematician João P. G. Ramos, whom they had first met when he was an early-career researcher, they co-authored the book titled "Isoperimetric Inequalities, Brunn–Minkowski Theory and Minkowski-Type Monge–Ampère Equations on the Sphere". The volume was published by EMS Press, the publishing house of the European Mathematical Society.

According to EMS Press's recommendation „This volume presents a rigorous study of the Brunn–Minkowski theory, the isoperimetric inequality, and their functional and analytic extensions. It develops the classical theory of convex bodies and mixed volumes, highlighting the geometric foundations of volume and surface-area inequalities. Building on this, the text examines isoperimetric problems in both the classical and measure-theoretic settings, including sets of finite perimeter, and establishes functional analogues of geometric inequalities. A significant part of the book is devoted to the interaction between these inequalities and curvature-related equations, with Monge–Ampère equations on the sphere serving as a principal example. The exposition emphasizes structural relations: how classical convex geometry informs functional inequalities, and how analytic methods extend geometric results to broader settings.

Asked by renyi.hu to elaborate the subject of the book, Károly Böröczky explains that the isoperimetric inequality is one of the oldest and most fundamental examples of a geometric inequality. Many later developments – including several key results in the Brunn–Minkowski theory – have grown out of it. Its history dates back to ancient Greece, where mathematicians were already studying the problem more than two thousand years ago. "In the plane, you can think of it like this: suppose you have a piece of string and want to enclose the largest possible area on a sheet of paper. The string has to form a circle. In three-dimensional space, if the volume of a body is fixed and you want its surface area to be as small as possible, then the body has to be a sphere. This is one of the reasons why so many objects in nature are spherical – they minimize surface energy. Even in everyday life, when we are cold, we instinctively curl up because we want as little of our body's surface as possible to be exposed to the cold air.” He continues: “The significance of this is that if you have a body of a given volume and you know that its surface area is close to the smallest possible value – that is, close to the surface area of a sphere – then you can also determine how close the shape itself is to a sphere. There are problems for which this kind of stability does not hold, but in general one can prove that if the surface area is nearly minimal, then the body must also be close to spherical. This is such a fundamental problem that one of its most important breakthroughs, proved only about fifteen years ago by Alessio Figalli and his collaborators, was among the achievements that led to Figalli receiving the Fields Medal.” (Prof. Figalli – who, together with Károly Böröczky and the Brazilian mathematician João P. G. Ramos, is one of the three authors of the newly published volume – officially received the Fields Medal “for contributions to the theory of optimal transport, partial differential equations, and probability.” (The editor hereby notes, however, that his work on geometric inequalities is also deeply connected with the Brunn–Minkowski theory, the isoperimetric inequality, and many classical problems in convex geometry.)
 

“The three of us worked together at ETH Zurich,” prof. Böröczky recalls. “Figalli is still based in Zurich, while Ramos is now in Rio de Janeiro, and I am back in Budapest. Results of this kind, as well as the proofs and theorems behind them, are of enormous theoretical significance. At the same time, they also have important practical implications. They play a role, for example, in the design of cars and aircraft, where minimizing air resistance or optimizing heat dissipation is essential.” Böröczky's own work focuses on the theoretical side of these questions. He points out that many researchers are dedicated to bridging the gap between theory and practice, identifying within theoretical results the key building blocks needed for real-world applications and translating them into concepts that design engineers can use. “Without these building blocks, there can be no engineering design,” he adds.

As both a mathematician and a researcher, prof. Károly Böröczky is convinced that although theoretical scientists are often accused of working merely “for their own amusement,” no one can know which fundamental building block of knowledge will prove useful twenty or fifty years later. “Even theoretical research is inspired by problems that arise from the real world. But it is impossible to predict what will ultimately prove useful, or why. What we do know is that if theoretical research develops organically, then sooner or later a substantial part of it is very likely to find important applications.” 

His extensive experience as a researcher, educator, and scientific leader both in Hungary and internationally lends particular credibility to this conviction. Böröczky earned his PhD at the University of Calgary in Canada. In addition to ETH Zurich, he has held research positions at New York University and University College London. Today, he spends most of his time in Hungary. Alongside his research and his work as Director of the Erdős Center, he teaches part-time at the Department of Geometry at Eötvös Loránd University.

“It never even occurred to me to stay abroad for life. Rényi Institute offers an environment in which being a researcher is, quite literally, a dream. The entire Institute is built around supporting research, and every one of its directors has strengthened this philosophy: giving us the freedom to pursue our work while helping us prepare increasingly competitive grant applications, so that we have the resources needed to do first-rate research. Equally important is that this is the place and culture I feel at home in. I have many dear colleagues abroad, but the people who understand me from half a sentence and whom I understand just as easily are mostly here in Hungary.”

As a closing thought, Böröczky offers a piece of advice to young researchers. “Both in science and in my personal life, I have found that if something truly matters to us, if we feel called to pursue it, and if we have the perseverance to stay on that path, we are likely to go far. The research that ultimately led to my Academy Award was something I only began working on around 2010, inspired by my time at NYU in Princeton, and it represented quite a sharp departure from my earlier research. In the end, it led to results that made such a distinction possible. I have seen the same pattern in my own children. Whenever they devoted real energy to a subject they genuinely enjoyed, or later to a particular scientific direction, they made remarkable progress. (Károly's son, who is still in high school, has already won a mathematics competition, while his daughter is preparing to pursue a PhD in pharmaceutical sciences.) What I have learned is that when an idea is matched with perseverance and passion, results eventually follow and the scientific community takes notice. That, to me, is one of the most important lessons of my life and career.”