Alfred Tarski made considerable contributions to several areas of mathematics, including set theory and algebra, and his work as a logician led to important breakthroughs in semantics--the study of symbols and meaning in written and verbal communication. Tarski's research in this area yielded a mathematical definition of truth in language, and also made him a pioneer in studying models of linguistic communication, a subject that became known as model theory. Tarski's research also proved useful in the development of computer science, and he became an influential mentor to later mathematicians as a professor at the University of California at Berkeley.
Born Alfred Tajtelbaum in Warsaw, Poland (then part of Russian Poland), on January 14, 1901, Tarski was the elder of two sons born to Ignacy Tajtelbaum, a shopkeeper of modest means, and Rose (Iuussak) Tajtelbaum, who was known to have an exceptional memory. During his teens Tarski helped supplement the family income by tutoring. He attended an excellent secondary school, and although he was an outstanding student, he, surprisingly, did not get his best marks in logic. Biology was his favorite subject in high school, and he intended to major in this discipline when he first attended the University of Warsaw. However, as Steven R. Givant pointed out in Mathematical Intelligence, "what derailed him was success." In an early mathematics course at the university, Tarski was able to solve a challenging problem in set theory posed by the professor. The solution led to his first published paper, and Tarski, at the professor's urging, decided to switch his emphasis to mathematics.
Tarski received a Ph.D. from the University of Warsaw in 1924, the same year he met his future wife, Maria Witkowski. They got married on June 23, 1929, and later had two children, Jan and Ina. It is believed that the young mathematician was in his early-twenties when he changed his name from Tajtelbaum to Tarski. His son, Jan, told interviewer Jeanne Spriter James that this step was taken because Tarski believed that his new Polish-sounding name would be held in higher regard at the university than his original Jewish moniker. When Tarski was married, he was baptized a Catholic, his wife's religion.
Early Struggles in Academia
Tarski served in the Polish army for short periods of time in 1918 and 1920. While working on his Ph.D. he was employed as an instructor in logic at the Polish Pedagogical Institute in Warsaw beginning in 1922. After graduating he became a docent and then adjunct professor of mathematics and logic at the University of Warsaw beginning in 1925. That same year he also took a full-time teaching position at Zeromski's Lycee, a high school in Warsaw, since his income from the university was inadequate to support his family. Tarski remained at both jobs until 1939, despite repeated attempts to secure a permanent university professorship. Some have attributed Tarski's employment difficulties to anti-semitism, but whatever the reason, his lack of academic prominence created problems for the young mathematician. Burdened by his teaching load at the high school and college, Tarski was unable to devote as much time to his research as he would have liked. He later said that his creative output was greatly reduced during these years because of his employment situation. The papers he did publish in this period, however, quickly marked Tarski as one of the premiere logicians of the century. His early work was often concentrated in the area of set theory. He also worked in conjunction with Polish mathematician Stefan Banach to produce the Banach-Tarski paradox, which illustrated the limitations of mathematical theories that break a space down into a number of pieces. Other research in the 1920s and 1930s addressed the axiom of choice, large cardinal numbers, the decidability of Euclidean geometry, and Boolean algebra.
Tarski's initial research on semantics took place in the early-1930s. He was concerned here with problems of language and meaning, and his work resulted in a mathematical definition of truth as it is expressed in symbolic languages. He also provided a proof that demonstrated that any such definition of truth in a language results in contradictions. A London Times obituary on Tarski noted the groundbreaking nature of his work in this area, proclaiming that the mathematician's findings "set the direction for all modern philosophical discussions of truth." Tarski expanded this early work in semantics over the ensuing years, eventually developing a new field of study--model theory--which would become a major research subject for logicians. This area of study examines the mathematic properties of grammatical sentences and compares them with various models of linguistic communication.
Additionally, Tarski pursued research in many other areas of math and logic during his career, including closure algebras, binary relations and the algebra of relations, cylindrical algebra, and undecidable theories. He also made a lasting contribution to the field of computer science. As early as 1930 he produced an algorithm that was capable of deciding whether any sentence in basic Euclidian geometry is either true or false. This pointed the way toward later machine calculations, and has also had relevance in determining more recent computer applications.
Outbreak of World War II leads to New Opportunities
In 1939 Tarski left Poland for a conference and speaking tour in the United States, intending to be gone for only a short time. Shortly after his departure, however, the German Army invaded and conquered Poland, beginning World War II. Unable to return to his homeland, Tarski found himself stranded in the United States without money, without a job, and without his wife and children who had remained in Warsaw. The family would not be reunited until after the war, and in the meantime, Tarski set about finding work in America. He first served as a research associate in mathematics at Harvard University from 1939 to 1941. In 1940 he also taught as a visiting professor at the City College of New York. He had a temporary position at the Institute for Advanced Study at Princeton beginning in 1941, and in 1942 he obtained his first permanent position in the United States when he was hired as a lecturer at the University of California at Berkeley. The university would remain his professional home for the rest of his career.
Tarski became an associate professor at the university in 1945, was appointed to the position of full professor the following year, and was named professor emeritus in 1968. Tarski's contributions to mathematics and science were enhanced by his role as an educator. He established the renown Group in Logic and the Methodology of Science at Berkeley, and over his long tenure he taught some of the most-influential mathematicians and logicians to emerge after World War II, including Julia Bowman Robinson and Robert Montague. His stature was further enhanced through his service as a visiting professor and lecturer at numerous U.S. and international universities. In 1973 Tarski ended his formal teaching duties at Berkeley, but he continued to supervise doctoral students and conduct research during the final decade of his life. He died in 1983 from a lung condition caused by smoking.
Tarski received many awards and honors throughout his career. He was elected to the National Academy of Sciences and the Royal Netherlands Academy of Sciences and Letters, and was also made a corresponding fellow in the British Academy. In 1966 he received the Alfred Jurzykowski Foundation Award, and in 1981 he was presented with the Berkeley Citation, the university's highest faculty honor. He also was awarded numerous fellowships and honorary degrees, and was a member in many professional organizations, including the Polish Logic Society, the American Mathematical Society, and the International Union for the History and Philosophy of Science.
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