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Czesław Ryll-Nardzewski was one of the most outstanding Polish mathematicians, and his achievements have permanently inscribed his name in the history of world mathematics.
He was born in Vilnius on October 7, 1926. His parents, Janina and Czesław, were both physicians. After World War II, his father became a professor at the Medical Academy in Lublin and was a well-known and respected specialist in dermatology.
The young Ryll-Nardzewski spent the war period in Vilnius, where he passed his high school graduation exam in 1944 through clandestine courses. In 1945, he began studying mathematics at Maria Curie-Skłodowska University in Lublin. He earned his master’s degree in 1948 and, just a year later, defended his doctoral dissertation in the theory of distributions under the supervision of Professor Mieczysław Biernacki. Shortly afterward, he moved to Wrocław, where he became an assistant professor at the Department of Mathematics of the then-combined Wrocław University of Technology and University of Wrocław. From 1952 to 1954, he worked at the University of Warsaw. Between 1954 and 1959, he was affiliated with the Mathematical Institute of the Polish Academy of Sciences, dividing his time between Lublin and Wrocław once again. From 1959, he resided permanently in Wrocław, where he worked at the University of Wrocław until 1976; from 1964 to 1966, he served as Dean of the Faculty of Mathematics, Physics and Chemistry. Beginning in 1976, he worked at Wrocław University of Technology, where he played a crucial role in developing a prominent research and teaching center in mathematics. Between 1966 and 1987, he supervised 18 doctoral dissertations.
His early interests, developed in Lublin, focused on logic. His work in this area led to two fundamental theorems: one on the non-existence of a finite axiomatization of arithmetic, and the other on the omega-categoricity of theories. Both theorems now bear his name. He soon impressively broadened his research interests, obtaining significant results in ergodic theory, measure theory, functional analysis, harmonic analysis, probability theory, stochastic processes, topology, and descriptive set theory. In each of these fields, he achieved results now considered to be classic, with numerous applications. In mathematics, fixed-point theorems and selection theorems are powerful tools. Among the most important in both categories are theorems proved by Ryll-Nardzewski: the Ryll-Nardzewski fixed-point theorem for distal semigroups of mappings, and the Kuratowski–Ryll-Nardzewski measurable selection theorem. He never shied away from collaboration, whether with world-renowned mathematicians (such as K. Kuratowski, D. Blackwell, and J. Łoś) or with talented young researchers, including numerous students. A notable result from a later period is the Four Poles Theorem, concerning the possibility of constructing, in the sense of an ideal, a nonmeasurable sum from a pointwise finite partition of a Polish space into sets from the ideal (this applies, among other things, to Lebesgue measure and Baire category). His co-authors were J.&nsbp;Brzuchowski, J. Cichoń, and E. Grzegorek.
Professor Ryll-Nardzewski made highly significant contributions to the development of ergodic theory. One of his most renowned achievements in this area is the proof of ergodicity (with respect to the so-called Gaussian measure) of the transformation that maps a number from the interval [0,1] to the fractional part of its reciprocal — known as the Gauss map — which is directly related to continued fraction expansions. His application of methods from ergodic theory to the study of continued fractions was particularly innovative. This result is cited in virtually every book on continued fractions.
An example of Ryll-Nardzewski’s insightfulness was his formulation — several years before the pioneering work of V. Bergelson and B. Host with B. Kra (which led to the development of higher-order Fourier analysis and nilsystems) — of a question posed at a local seminar concerning return times with so-called fat intersections for triple iterations in ergodic systems. The theory of nilsystems, which later emerged, answered this question. Although Ryll-Nardzewski did not directly pursue this direction further (and it remains unclear whether his question reached or influenced subsequent authors), the mere fact that he posed it reflects his remarkable intuition and ability to anticipate future developments in mathematics. Notably, nilsystems were later used in the famous work by Green and Tao on the existence of arbitrarily long arithmetic progressions among the prime numbers.
Of course, a brief biography such as this cannot even begin to address the breadth and significance of Professor Ryll-Nardzewski’s extensive and important body of work (over 100 publications). The results mentioned above are merely illustrative examples of his remarkable contributions.
His brilliant mathematical career progressed rapidly. He received his professorial nomination in 1954, and in 1964 was appointed full professor. In 1967, he became a corresponding member of the Polish Academy of Sciences, and in 1973, a full member. He was also a member of the reactivated Polish Academy of Learning. He received numerous prestigious honors and awards, both state and academic, including the Stefan Mazurkiewicz Prize of the Polish Mathematical Society, the Stefan Banach Medal, the Officer’s Cross of the Order of Polonia Restituta, and the Prime Minister’s Award.
Throughout his scientific career, Professor Ryll-Nardzewski visited many universities and research centers abroad, including Berkeley, Moscow, and Oberwolfach.
His wife, Jadwiga née Grossman, was an actress and Polish philologist. In 1960, their son Wojciech was born. He was an accountant by profession and passed away in 2023.
Professor Czesław Ryll-Nardzewski passed away in Wrocław on September 18, 2015.
He was a wise man and a kind person.
“They used to say that his genius lay in the fact that whenever someone explained something entirely new to him, Professor Ryll-Nardzewski would instantly understand it better than the person explaining it.”