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Alfred Tarski

Polish–American mathematician (1901–1983)

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Alfred Tarski; photo was scanned without modifications, like colour restoration; border cropped from File:Alfred Tarski 1968 (as-is).jpg
George Bergman · CC BY-SA 4.0

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Educated in Poland at the University of Warsaw, and a member of the Lwów–Warsaw school of logic and the Warsaw school of mathematics, in 1939 he immigrated to the United States, where in 1945 he became a naturalized citizen. Tarski taught and carried out research in mathematics at the University of California, Berkeley, from 1942 until his death in 1983.

His biographers Anita Burdman Feferman and Solomon Feferman state that, "Along with his contemporary, Kurt Gödel, he changed the face of logic in the twentieth century, especially through his work on the concept of truth and the theory of models."

Life

Early life and education

Alfred Tarski was born Alfred Teitelbaum (Polish spelling: "Tajtelbaum") to Polish-Jewish parents in comfortable circumstances. He first showed mathematical ability in secondary school, at Warsaw's Szkoła Mazowiecka. Nevertheless, in 1918 he entered the University of Warsaw intending to study biology.

After Poland regained independence in 1918, Warsaw University came under the leadership of Jan Łukasiewicz, Stanisław Leśniewski, and Wacław Sierpiński and quickly became a world-leading research institution in logic, foundational mathematics, and the philosophy of mathematics. Leśniewski recognized Tarski's potential as a mathematician and encouraged him to abandon biology.

Tarski attended courses taught by Łukasiewicz, Sierpiński, Stefan Mazurkiewicz, and Tadeusz Kotarbiński and in 1924 became the only person ever to complete a doctorate under Leśniewski's supervision. His thesis, O wyrazie pierwotnym logistyki (On the Primitive Term of Logistic), was published in 1923.

Tarski and Leśniewski soon grew cool to each other, mainly due to Leśniewski's growing anti-semitism. In later life, however, Tarski expressed the warmest praise (which was reciprocated) for Kotarbiński.

In 1923, Alfred Teitelbaum and his brother Wacław changed their surname to “Tarski”. The brothers also converted to Roman Catholicism, Poland's dominant religion, even though Alfred was an avowed atheist.

Career

After becoming the youngest person ever to complete a doctorate at Warsaw University, Tarski taught logic at the Polish Pedagogical Institute, mathematics and logic at the university, and served as Łukasiewicz's assistant. Because these positions were poorly paid, from 1925 Tarski also taught mathematics at the Third Boys’ Gymnasium (secondary school) of the Trade Union of Polish Secondary-School Teachers (later the Stefan Żeromski Gymnasium). Before World War II it was not uncommon for European intellectuals of research caliber to teach secondary school. Until his departure for the United States in 1939, Tarski wrote several textbooks and many papers – a number of them ground-breaking – while supporting himself mainly by teaching secondary-school mathematics.

In 1929 Tarski married fellow teacher Maria Witkowska, a Catholic Pole who had served during the Polish–Soviet War (1919–1921) as a courier for the Polish Army. They had two children: son Jan Tarski, who became a physicist; and daughter Ina, who married mathematician Andrzej Ehrenfeucht.

Tarski applied for a chair of philosophy at Lwów University, but on Bertrand Russell's recommendation it was awarded to Leon Chwistek. In 1930 Tarski visited the University of Vienna, lectured to Karl Menger's colloquium, and met Kurt Gödel. Thanks to a fellowship, he was able to return to Vienna during the first half of 1935 to work with Menger's research group. From Vienna he traveled to Paris to present his ideas on truth at the first meeting of the Unity of Science movement, an offshoot of the Vienna Circle.

Tarski's academic career in Poland was affected by his heritage. In 1937, when he applied for a chair at Poznań University, the chair was abolished to avoid assigning it to Tarski – indisputably the strongest applicant – because he was Jewish.

Tarski's ties to the Unity of Science movement likely saved his life, because they resulted in his being invited to address the Unity of Science Congress held in September 1939 at Harvard University. He left Poland in August 1939, on the last ship to sail from Poland for the United States before the German and Soviet invasion of Poland and the outbreak of World War II. Tarski left reluctantly, because Leśniewski had died a few months before, creating a vacancy which Tarski hoped to fill. Oblivious to the Nazi threat, he left his wife and children in Warsaw, not to see them again until 1946. During the war, nearly all his Jewish extended family were murdered by the German occupiers.

In the United States, Tarski held a number of temporary teaching and research positions: at Harvard University (1939), at City College of New York (1940), and thanks to a Guggenheim Fellowship, at the Institute for Advanced Study at Princeton (1942), where he again met Gödel. In 1942 Tarski joined the mathematics department at the University of California, Berkeley, where he spent the rest of his career. In 1945 he became an American citizen. Although emeritus from 1968, he taught until 1973 and supervised Ph.D. candidates until his death. At Berkeley, Tarski acquired a reputation as an astounding and demanding teacher, as noted by many observers:

His seminars at Berkeley quickly became famous in the world of mathematical logic. His students, many of whom became distinguished mathematicians, noted the awesome energy with which he would coax and cajole their best work out of them, always demanding the highest standards of clarity and precision.

Tarski was extroverted, quick-witted, strong-willed, energetic, and sharp-tongued. He preferred his research to be collaborative — sometimes working all night with a colleague — and was very fastidious about priority.

A charismatic leader and teacher, known for his brilliantly precise yet suspenseful expository style, Tarski had intimidatingly high standards for students, but at the same time he could be very encouraging, and particularly so to women — in contrast to the general trend. Some students were frightened away, but a circle of disciples remained, many of whom became world-renowned leaders in the field.

Tarski supervised twenty-four Ph.D. dissertations, including those of – in chronological order – Andrzej Mostowski, Bjarni Jónsson, Julia Robinson, Robert Vaught, Solomon Feferman, Richard Montague, James Donald Monk, Haim Gaifman, Donald Pigozzi, and Roger Maddux, as well as Chen Chung Chang and Jerome Keisler, authors of Model Theory (1973), a classic in the field. He also strongly influenced the dissertations of Adolf Lindenbaum, Dana Scott, and Steven Givant.

Five of Tarski's students were women, remarkably so, given that men were then the overwhelming majority of graduate students. He had extramarital affairs with at least two of the women. After he showed the work of another female student to a male colleague, the colleague published it himself, causing the woman to break off her graduate studies and later move to a different university.

Tarski lectured at University College, London (1950, 1966), the Institut Henri Poincaré in Paris (1955), the Miller Institute for Basic Research in Science at Berkeley (1958–60), the University of California at Los Angeles (1967), and the Pontifical Catholic University of Chile (1974–75).

Among many distinctions garnered over his career, Tarski was elected to the United States National Academy of Sciences, the British Academy, and the Royal Netherlands Academy of Arts and Sciences in 1958; and received honorary degrees from the Pontifical Catholic University of Chile in 1975, from Marseille's Paul Cézanne University in 1977, and from the University of Calgary, as well as a Berkeley Citation in 1981.

Tarski presided over the Association for Symbolic Logic, 1944–46, and the International Union for the History and Philosophy of Science, 1956–57; and was an honorary editor of Algebra Universalis.

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