Mathematician Vera T. Sós, Full Member of MTA, Passes Away

Vera T. Sós (1930–2023) Photo: Academy Gold Medal film, 2015

The scientific work of Vera T. Sós and her work as a Hungarian and international school creator and science organiser contributed significantly to the explosive development of discrete mathematics over the last half century. She achieved pioneering results and initiated new research directions in two different branches of mathematics, number theory and combinatorics.

A much-cited result from her youth regarding number theory is the “three gaps” theorem, in which she proved a supposition of Steinhaus. In the field of graph theory, she became involved in the extreme graph theory research started by Pál Turán and Pál Erdős. With a deep understanding of the problems, she revealed the common roots of important lines of research investigation. Her fundamental insight was that the theory of uniform distribution, in number theory, and the field of Ramsey and Turán, in extremal graph theory, represent two different sides of the same general question: how closely can an infinite (continuous) structure be approximated by a finite (discrete) structure.

This led her to create discrepancy theory, in which she formulated fundamental questions not only in number theory and graph theory, but also in other areas of the phenomenon, which inspired the research of many of her students and other mathematicians worldwide. This led her to the theory of quasi-random graphs, within the framework of which she described (in a joint paper with Miklós Simonovits) the relationship between quasi-random graphs and Szemerédi’s regularity lemma. Through this, she arrived at a theory of graph lines, in which she co-authored a significant part of the papers that established the field.

Vera T. Sós taught at ELTE for more than fifty years, starting in 1952, laying the foundation for the regular teaching of combinatorics in Hungary. Ahead of other universities in the world, her work at ELTE introduced the teaching of important combinatorics fields such as extremal graph theory, matroid theory and the probability method. Almost all members of the new generation of combinatorics studied at her seminars and under her personal guidance.

In addition to combinatorics and graph theory, she also taught mathematical analysis. Her analysis lectures, planned with incredible care, were legendary. Her introducing of concepts in an intuitive way, her placing of the material in a larger context, her presentation of applications, and her precise structuring were in perfect harmony in her lectures, which served as a model for many of her students. This approach also characterised her university notes and textbooks used over many decades.

She took a role in almost all areas of public mathematical life: in academic, ministerial and university committees, as well as in the work of the János Bolyai Mathematical Society. She was the editor of well-known journals and one of the founders of the journal Combinatorica, one of the leading international papers in the field. She is also credited with managing the organisation of highly successful conferences and collaborative international projects.

Vera T. Sós’s domestic recognition is evidenced by the Academy Award, the Széchenyi Award, the Order of Merit of the Republic of Hungary, and the Academy Gold Medal, which she received in 2015. Her international recognition is indicated by numerous prestigious foreign invitations. In 1995, the Austrian Academy of Sciences elected her a corresponding member, and the Academia Europaea accepted her among its members in 2013. In 2018, she was awarded an honorary doctorate at the Hebrew University in Jerusalem.

Laszló Lovász, full member and former President of the Hungarian Academy of Sciences
Miklós Laczkovich, full member of the Hungarian Academy of Sciences and President of the Section of Mathematics