**Adolf Lindenbaum** was a Polish mathematician, logician and topologist. He was executed by the Nazis.

- There are no records of Adolf's early years although we can assume that he was brought up in Warsaw.
- At the time that Lindenbaum was born, Poland did not exist as an independent country but had been partitioned between Austria-Hungary, Prussia and Russia.
- Lindenbaum, who was sixteen at the time, enlisted in an organisation set up by the Polish White Cross to help the soldiers.
- We should mention one of Lindenbaum's classmates at the Jana Kreczmara Gymnasium.
- This was Mojżesz David Kirszbraun (1903 or 1904-1942) who, like Lindenbaum, showed outstanding mathematical abilities at the school.
- He graduated at the same time as Lindenbaum and the two entered the University of Warsaw to study mathematics together.
- Lindenbaum and Kirszbraun were close friends and undertook joint research projects while at university.
- On 14 September 1922 Lindenbaum applied for admission to the Mathematics department in the Faculty of Philosophy of Warsaw University.
- During the five years of his university course, Lindenbaum was taught by some outstanding academics.
- Alfred Tarski taught at the Polish Pedagogical Institute in Warsaw from 1922 to 1925 but began teaching at the University of Warsaw in session 1925-26 when he taught on cardinal numbers, a course which Lindenbaum attended.
- Since Lindenbaum also attended Tarski's elementary mathematics (plane geometry) course in 1926-27 it looks likely that he was attending courses by a friend to give him support rather than to learn new mathematics.
- Lindenbaum also attended a logic course by Tadeusz Kotarbiński (1886-1981).
- Lindenbaum also attended a course on the history of philosophy given by Władysław Tatarkiewicz (1886-1880) who had taught in Wilno and Poznań before taking up an appointment in Warsaw in 1923.
- Tatarkiewicz was also an expert on aesthetics and the history of art, and taught a course on French art which Lindenbaum attended.
- Lindenbaum's student career ended in a slightly strange way.
- From 1929 to 1934 Lindenbaum worked on his habilitation thesis.
- After the two papers listed above, Lindenbaum published the following papers between 1928 and 1934: Sur quelques propriétés des fonctions de variable réelle Ⓣ(On some properties of functions of a real variable) (1928); Remarques sur une question de la méthode axiomatique Ⓣ(Notes on a question of the axiomatic method) (1930); (with A Kozniewski) Sur les opérations d'addition et de multiplication dans les classes d'ensemble Ⓣ(On the operations of addition and multiplication in the general classes) (1930); Sur les ensembles ordonnés Ⓣ(On ordered sets) (1931); Bemerkung zu den vorhergehenden "Bemerkungen ..." des Herrn J.
- After presenting his habilitation thesis, Lindenbaum became a docent in the Faculty of Mathematics and Natural Sciences.
- Courses taught by Lindenbaum were on set theory, measure theory, algebra, actuarial mathematics and the foundations of mathematics.
- In addition to the research that he was publishing, Lindenbaum and Tarski collaborated on writing the book Theorie der eineinendeutigen Abbildungen Ⓣ(Theory of unambiguous illustrations).
- As one might imagine, being Jewish, Lindenbaum had problems.
- In 1935 Polish universities adopted an anti-Semitic policy which meant that Lindenbaum had little chance of being promoted beyond docent.
- Janina had received a doctorate from Warsaw in 1926 advised by Tadeusz Kotarbiński who had also taught Lindenbaum.
- Both she and Lindenbaum had delivered papers at the First Congress of Mathematicians from Slavic Countries held in Warsaw in September 1929.
- Lindenbaum did other things which would later put his life in danger.
- Lindenbaum realised the danger he was in both as a Jew and as a known Communist.
- He knew that the Germans had lists of names of Polish Communists and other critics of Hitler's regime which, particularly because of the petitions and letters he had signed, terrified Lindenbaum.
- The Soviets set up the Białystok Pedagogical Institute and Lindenbaum was appointed as a docent at the Institute.
- Lindenbaum does not appear to have made any efforts to escape which is slightly strange given that he was fully aware of the danger he was in from the Germans.
- It is not known exactly when Lindenbaum was executed but it is believed that he too was murdered at Ponary soon after his arrest.
- described Lindenbaum as "a man of unusual intelligence".
- Mostowski once called Lindenbaum the most lucid mind in the foundations of mathematics.
- Legendary stories told by Lindenbaum's friends and colleagues document many cases of theorems discovered by him but proved by someone else, as he had no time to complete his ideas.
- Fraenkel had claimed to prove this but Lindenbaum and Mostowski in a 1938 paper, claim that there are errors and obscurities in Fraenkel's proof which they correct.
- Lindenbaum also worked on the propositional calculus and its connection to logical matrices.
- Two other significant achievements are what is today called the Lindenbaum algebra and the maximalisation theorem sometimes today called Lindenbaum's Lemma.
- Lindenbaum was a member of the Polish Mathematical Society from 1926, becoming treasurer of the Warsaw branch of that Society in 1938.

Born 12 June 1904, Warsaw, Russian Empire (now Poland). Died 1942, Ponary (now Paneriai), (near Vilnius), Lithuania.

View full biography at MacTutor

Origin Poland

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive