**In its 120 anniversary, the Austrian Mathematical Society (ÖMG) awards Matthew Kwan from the Institute of Science and Technology Austria (ISTA) its frontline prize. With his group ** *Combinatorics and Probability***, the 32-year-old assistant professor explores the interplay of these two mathematical fields, tackling some of the grand questions of modern mathematics.**

Each year, the Austrian Mathematical Society (ÖMG) awards prizes in three categories. This year, its main prize, which one could consider "Austria’s Fields Medal", goes to Matthew Kwan from the Institute of Science and Technology Austria (ISTA). He is known for combining ideas from disparate mathematical areas to gain new insights into randomness and combinatorics. After Julian Fischer, he is the second ISTA faculty member to receive the award.

Matthew Kwan: "I’m very thankful to the Austrian Mathematical Society. This award is great validation of the importance of the research directions I’ve been pursuing since joining the Institute in 2021."

**Contributions to mathematics**

Kwan has a track record of alloying ideas from mathematical communities that usually do not interact. Because of this, his research interests have continuously broadened throughout his academic career. His biggest contributions to mathematics surfaced within the last few years. Most notably, in 2022, he and three junior collaborators resolved a decades-old Erdos conjecture by bringing probabilistic ideas to design theory. "Matthew’s approach can be viewed as a paradigm change in the extremal theory of hypergraphs," says ISTA mathematician László Erdos in his laudation (not related to Paul Erdos, whose conjecture Kwan solved). The paper was recently accepted for publication in the *Annals of Mathematics*, the most renowned mathematics journal in the world.

Lately, Kwan has also been building connections between Ramsey theory, which concerns how "disordered" complex systems can be, and the study of polynomials of random variables. He used these concepts to crack another conjecture by Erdos and McKay. Now, the bridging goes even further. "Together with Michael Anastos and Benjamin Moore, two postdocs in my group, we have been working on a topic somewhere between maths and computer science called graph isomorphism testing," says Kwan. The upcoming result is about getting some theoretical understanding of why simple algorithms seem to work well in practice.

"All these results just within the last few years would trump the lifetime achievements of many senior mathematicians," concludes laudatory speaker László Erdos of ISTA.

**Kwan’s mathematical life path**

Born in Sydney, Kwan’s abilities were already recognized during his undergraduate studies at the University of New South Wales, Australia. Also, his doctoral institution, the ETH in Switzerland, awarded him the university medal for his achievements in mathematics. After three years at Stanford University, where Kwan served as Szego Assistant Professor, he joined the Institute of Science and Technology Austria (ISTA) in 2021, back then as the youngest faculty member. In 2023, he received an ERC Starting Grant to achieve a deeper understanding of the role of randomness in combinatorics.