What are mathematical problems? Why is it important to solve them? How exactly do we do it? These are some of the questions we are constantly asked as mathematicians. The daily work of a scientist remains mysterious for most people, especially when the science in question is mathematics. We will discover some of the important steps leading to a mathematical breakthrough by focusing on dramatic changes in physical systems — scholarly name: phase transitions. These happen all the time in our everyday life, for example when making coffee. This will give us an occasion to explore what motivates mathematicians, how they organize their work, and why beauty plays a key role in that process.
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Hugo Duminil-Copin is currently a Full Professor of mathematics at the University of Geneva, as well as Permanent Professor at the Institut des Hautes Études Scientifiques in Bures-Sur-Yvette. His work focuses on developing probabilistic models to analyse the ubiquitous physical phenomena of criticality and phase transitions. By using new connections between these models and developing a theory of so-called dependent percolation, Hugo Duminil-Copin has obtained transformative results, thus improving our understanding of critical phenomena in statistical physics. He has been awarded numerous prizes for his work during the past ten years, culminating in 2022 with the Fields Medal, the most prestigious award in mathematics.