Even as a Polish-trained mathematician with active interests in philosophy and history of mathematics and science (who took two courses from Prof. Woleński, among others), I am hard pressed to think of three mathematicains/logicians/philosophers who would have good motivation for reading Principia and were “liquidated by Hitler”.
To be sure, Leon Chwistek is the strongest contender. He worked on theory of types and corresponded with Russell, who (successfully) recommended him for the chair of logic at the Lwów University in 1928. Mark Kac, a student in Lwów in 1930s, wrote the following words about Chwistek in his autobiography “Enigmas of chance”: “Rumor had it that he was the only one who, except for the authors, had read all three volumes of Principia Mathematica (pp. 42-43).” However, Chwistek died of a kidney failure in Moscow in 1944 (there were rumors about his poisoning).
As noted by other participants in this discussion, several strong candidates cannot be counted because of when and how they died. But it is still worth recalling some of the evidence of their reading Principia, along with a little of biographical information, since not all are household names.
Jan Sleszyński (1854-1931), a Pole who was first a professor in Odessa (under the name of Ivan Sleshinskii), then in Kraków, started out working in number theory and analysis, later turning to logic. His lecture notes in proof theory, published in Kraków by the Mathematics and Physics Student Circle in 1925-29, discuss extensively the history of logic up to (and including) the contributions of Russell and Whitehead. (see the book by Roman Murawski, Philosophy of mathematics and logic in the inter-war Poland). According to A. Hoborski, O Śleszyńskim, wspomnienie pośmiertne [On Śleszyński, an after-death reminiscence], Wiadomości Matematyczne, 36 (1934), he sought to eliminate any hidden rules from deductive reasoning, which prompted him to study Principia Mathematica (private information from Lidia Obojska).
Zygmunt Zawirski (1882-1948) was a philosopher with some mathematical background, a student of Kazimierz Twardowski. In 1937 he became a professor in Kraków. He was interested in application of logic to natural sciences. He had hoped that Russell’s theory of types would help eliminate logical antinomies arising in quantum physics (this information after Irena Szumilewicz-Lachman: Zygmunt Zawirski. His life and work. With selected writings on time, logic and the methodology of science. Kluwer Academic Publishers, 1994).
Of course, the names of Alfred Tarski and Stanisław Leśniewski are much better known among mathematicians. Regarding whether Tarski read Principia, one can note that he considered the concept of membership and in a lecture in 1966 he quoted Principia Mathematica to support his view that it is a logical notion:
“Using this method [of Principia Mathematica], it is clear that the membership relation is certainly a logical notion. It occurs in several types, for individuals are elements of classes of individuals, classes of individuals are elements of classes of classes of individuals, and so on. And by the very definition of an induced transformation it is invariant under every transformation of the world onto itself” (quotation after Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/tarski/).
Tarski’s PhD advisor Leśniewski tried to provide foundations for mathematics in a very unique manner, bypassing the set theory and the type theory. He referred to Principia Mathematica at least by criticizing its terminology, which he found confusing (“Foundations of a General Theory of Sets I”, 1916; after http://plato.stanford.edu/entries/lesniewski/).
My personal bets (if speculation is allowed), besides Chwistek, are Władysław
Hetper and Witold Wilkosz.
Hetper was a student and coauthor of Chwistek (and a close friend and roommate of Mark Kac in their student days), who received his PhD in 1937 and his habilitation in 1939. He was imprisoned by the Soviets and executed by them, probably in Kharkov in 1941.
Wilkosz was a professor of mathematics in Kraków, Banach’s high school classmate, a PhD student of Giuseppe Peano in Turin, and a polymath with multiple interests, including logic. Not quite ”liquidated”, he died in 1941 (during the German occupation of Poland) of natural causes, but the time he spent in German prison in 1939 and subsequent wartime deprivation made his condition worse. Wilkosz explicitly referred to Russell and his arguments with Peano when discussing equivalence relations in the paper “O definicji przez abstrakcjȩ” [On defining through abstraction], Kwartalnik Filozoficzny 14 (1938), 1-13 (see Murawski’s book cited above). Hetper in his work credited some unpublished results of Wilkosz.
All three (Chwistek, Hetper, Wilkosz) died during WWII. Russell either did not know the details of their death (in the cases of Chwistek and Hetper, these are still not fully confirmed and were not public knowledge in communist Poland) or else he was reluctant to blame the Soviets.
There was also Stanisław Bilski, a graduate in mathematics and a doctor in philosophy (from the Jagilellonian University in Kraków) in 1926, whose thesis title was “A priori knowledge in Bertrand Russell’s epistemology”. he was a communist activist in Poland, subsequently liquidated in the USSR in the Great Purge of 1934 (hence again by Stalin, not by Hitler). But his name was rather unknown.
Finally, a popular account in Polish of Russell’s antinomy was written in 1927 (Przegla̧d Filozoficzny, vol. 30, issue 4, pp. 291-292) by the Lwów mathematician Lucjan Emil Boettcher, who worked mainly in iteration theory. He died of natural causes in 1937, before WWII and German occupation.
The only sure conclusion of all this is that Russell’s works were studied by
Poles (and in Poland, when it was reborn in 1918) before 1939.