Bogdan Bojarski and Tadeusz Iwaniec on Polish Mathematics

We give below thoughts about Polish mathematics by Bogdan Bojarski and by Tadeusz Iwaniec who was advised by Bojarski.

1. Bogdan Bojarski on Polish Mathematics.

This is based on an interview Bogdan Bojarski gave at the Institute of Mathematics, Academia Sinica on 30 November 2006.

https://www.math.sinica.edu.tw/interviewindexe/journals/4792?keywords%5B%5D=Bogdan+Bojarski

Bogdan Bojarski on Polish Mathematics.

Maybe the tradition of modern mathematics in Poland should be traced back to the beginning of the last (i.e. 20th) century or the two last decades of the 19th century. Actually, there were two main sources of modern Polish mathematics. One was France with Henri Lebesgue and other French mathematicians in complex function theory, set theory and general topology, Paul Montel, Émile Borel, Maurice Fréchet …, also, even somewhat earlier, Émile Picard, Henri Poincaré (Geometry, Analysis, Differential equations) influenced a group of Polish mathematicians studying in France, who started and formed a Polish mathematical school. So that was in Lebesgue's school and in Montel's school of complex analysis. But there were also at the beginning of the twentieth century, last century, very good and fruitful contacts with Moscow mathematicians. So, for instance, Wacław Sierpiński, whose role in the development of Polish mathematics was crucial, was very closely related to Nikolai Luzin and the Moscow school. An active group of talented young Polish mathematicians arose around Sierpiński. Nikolai Luzin, Andrey Kolmogorov and also Pavel Aleksandrov were from the beginning engaged in active fruitful contacts with that group. And so, in Poland, a positive step forward was made by Zygmunt Janiszewski.

Zygmunt Janiszewski, a very young mathematician, after returning from his studies in France, had the idea to organise a new mathematical journal "Fundamenta Mathematicae". Together with a group around him, a programme for the development of Polish mathematics, later called the Janiszewski Programme, was proposed. The principal new concept of the programme was that young Polish mathematicians should rather concentrate their thinking and research efforts on arising new areas of mathematical research than to compete on the international "research market" with the established, should we say classical, chapters of mathematics. As the new promising directions, the Janiszewski Programme named three: the first was set theory and topology, the second real analysis together with the emerging functional analysis, and the third was foundations of mathematics and logic. It was considered that in these areas Polish mathematicians had good chance of developing new ideas in their creative work, and obtain important new scientific results at the front line of contemporary mathematics.

Important mathematical names appeared in the foundations of mathematics and mathematical logic. Let us recall that Jan Łukasiewicz was the father of many ideas, but later the great figure of Alfred Tarski appeared. Before him was Stanisław Leśniewski and Kazimierz Ajdukiewicz. Later, from the time which I still remember, Andrzej Mostowski was a mathematician of international importance. In the area of real analysis great names appeared also. Let's recall Stanisław Saks, Antoni Zygmund and Jozef Marcinkiewicz in complex and real analysis. At the parallel time Juliusz Schauder started his famous seminal activity in the area of newly arising functional analysis, infinite dimensional topology and in strong connections with new breakthrough concepts in linear and nonlinear problems of the newly emerging theory of partial differential equations. Before Juliusz Schauder, and somehow without direct contacts with the ideas of the new Polish school of mathematics, was the personality of Stanisław Zaremba who independently developed a relatively small but active group, mostly in Krakow, in the classical theory of partial differential equations and applications in theoretical mechanics. That group was developed on the basis of contacts with the French school, mostly the Henri Poincaré school and the Émile Picard school, in classical potential theory and partial differential equations. Stanisław Zaremba was associated with Poincaré's school. But a real analysis group was developing under the influence from Henri Lebesgue in Paris, and Nikolai Luzin and his group, Aleksandr Khinchin, Andrey Kolmogorov etc. in Russia. Later Stefan Banach appeared as the founder of general functional analysis. Both these directions were developed on the basis of the scientific activity of the groups of Wacław Sierpiński and Hugo Steinhaus.

Stefan Banach was undoubtedly the most influential Polish mathematician in the world of mathematics. But before him Zygmunt Janiszewski and his closest mathematical friends elaborated and formulated the general new concepts and a strategy of a research programme. Unfortunately, Zygmunt Janiszewski unexpectedly died at the age of 30 or so, a very early age, and he was active only at the start of the 20th century Polish school of mathematics. After him came Mazurkiewicz and the famous Banach, later Stanisław Saks, Zygmund, Marcinkiewicz, Juliusz Schauder in analysis, Bronisław Knaster, Kazimierz Kuratowski, Karol Borsuk, Samuel Eilenberg in topology. Many Chinese mathematicians knew Kuratowski. But of course, again predominant were his contacts with French-Russian school. Pavel Sergeevich Alexandrov was influencing Kuratowski and so was Pavel Urysohn, also from Moscow. Unfortunately, Pavel Urysohn also died at the early age of 26. As a matter of fact, quite a number of mathematicians active at the beginning of Polish school and Russian school died young.

The classical fields, for example complex analysis, classical analysis, even differential equations have not been much developed in Poland in the early decades of the 20th century. Later in the thirties it was mainly Juliusz Schauder who studied everything and was able to achieve remarkable progress in partial differential equations, functions spaces, boundary value problems for linear and non-linear equations. It is enough to recall the concepts of Schauder: à priori estimates or Leray-Schauder index theory in infinite dimensional topology. Also Tadeusz Ważewski from Krakow should be recalled for his seminal works on ordinary differential equations. There also was another remarkable, very deep mathematician, with a broad range of research activity who started his career in Poland. This was Leon Lichtenstein.

Lichtenstein was a Polish mathematician. He started his scientific activity in Krakow, most active in the years 1908-1916. Later after the first world war he moved to Germany, and he settled in Leipzig. He was working in classical analysis and under the influence of the German school in partial differential equations, potential theory and hydrodynamics. In the thirties he published in German the monograph Hydrodynamik, in the famous Grundlehren series of Springer Verlag. This series of mathematical monographs contributed very much to the progress in mathematics research in the 20th century; that's the Yellow Series. So I think that Hydrodynamik of Leon Lichtenstein is a suitable book to start the study of the problems of hydrodynamics. When I was a student, I liked this book because it describes the hydrodynamical problems in realistically clear terms and at the same time in a mathematically rigorous way. So it is suitable to all levels of expectation of rigour. It's unlike most of the books on hydrodynamics and mechanics, which are very difficult to follow for a mathematician and are not fully convincing about the formulated scientific statements.

2. Tadeusz Iwaniec on Polish Mathematics.

This is based on an interview Tadeusz Iwaniec gave speaking to Grzegorz Jasiński at the jubilee meeting of Polish mathematicians on the centenary of the Polish Mathematical Society. He gave the interview on Saturday, 7 September 2019.

Tadeusz Iwaniec on Polish mathematics during the German and Soviet occupation.

Remembering the successes of Polish mathematics in the interwar period, we cannot forget what happened to it during the German and Soviet occupation. Polish mathematics in the interwar period was outstanding, but then came the dark night of occupation. We should not forget about it. It is perhaps more important to talk about it sometimes today than about the merits of mathematics that are known, recorded forever. I was raised in the atmosphere of great Polish mathematicians, I am grateful to them, not only for what they created for us before, but also for their patriotism.

These dark moments for Polish mathematics during the German and Soviet occupation, we must remember today, when we enjoy the beauty of mathematics. We must remember those whose great scientific career was brutally ended during World War II. Maybe I should, very briefly, give a few names. Stanisław Saks, a Pole of Jewish origin, specialised in complex analysis, was shot by the Gestapo in Warsaw at Aleja Szucha, the Gestapo Headquarters, in 1942 for participating in the underground movement. Juliusz Paweł Schauder, also of Jewish origin, was shot in Lviv during his escape in 1943. He dealt with differential equations. He was also an inspiration for me. Similarly Józef Marcinkiewicz, a Polish patriot, was probably murdered in Katyn, although this is not proven. He was a student of Antoni Zygmund, also a great Polish mathematician, who emigrated to Chicago. I even wrote a paper that I dedicated to Marcinkiewicz. When I look at all these people, I have the following thoughts. What is the difference between true Polish patriots, including Jews, and the rest of us? On Polish soil we had outstanding mathematicians, Polish patriots who gave their blood for Poland.

I also wanted to mention Professor Stanisław Zaremba, who together with the great David Hilbert directly created the method of variational calculus. It was 1908, at the congress in Rome. Zaremba was the first president of the Polish Mathematical Society, and at the time when the Jagiellonian University was closed in November 1939, he worked in the underground University. His student, Tadeusz Ważewski, after returning from the concentration camp in Sachsenhausen, created the so-called Krakow school of differential equations. This is my specialty today. You could say that in this way the academic community in Krakow fought against the occupier without weapons.

Today I deal with the applications of the calculus of variations to mathematical models of the theory of elasticity. Stanisław Zaremba's method is the basis for proofs of the existence of so-called hyperelastic mappings or deformations, i.e. transformations with the lowest energy. Using the method of the calculus of variations we can predict where cracks will occur in elastic materials and how these cracks propagate in these materials. These phenomena are a strong motivation, not only in theoretical mathematics, but also in engineering research. In mathematics there is no end to new questions, which are in effect the key to progress in theoretical science and in applications ...

Last Updated June 2025