Alfred Tarski

Tusk was born in a wealthy Polish Jewish family, formerly known as Alfred Teitelbaum. Some speculate that his intelligence was inherited from his mother, Rosa Prussak. His mathematics could initially be strengthened at the private high school Szko?a Mazowiecka in Warsaw. However, when he entered the University of Warsaw in 1918, Tusk originally wanted to study biology.

Following Poland¡¯s independence from Tsarist rule in 1919, the University of Warsaw quickly became the world¡¯s leading institution for logic, mathematical foundations and mathematical philosophy under the leadership of Jan Wukasziewicz, Stanisław Leżywski and Watswowski Serbinski. Leżywski met Tusk and discovered his genius by chance, and thus persuaded him to give up biology for mathematics. Later, Tusk trained courses by Wukasziewicz, Sergewski, Stefan Mazurkiewicz and Tadeusz Kotarbiński, and became the only doctor who could graduate from Leniewski.

In 1923, Alfred Tetburg and his brother Wacaw invented the new surname "Tarski", which sounded more Polish and was easier to spell and pronounce, and changed it to "Tarski" (many years later Tarski actually met someone with his same name in Northern California). The Tarski brothers also converted to Roman Catholicism, the dominant religion of the Poles, although Alfred claimed to be an atheist at the time. Alfred realized that he was facing graduation, and that it was difficult for a Jew to find a formal job in the new Polish university system. At that time, Tarski had Polish nationality and regarded himself as a native Polish. Even after moving to the United States, Tarski still spoke Polish at home.

In 1929 Tarski married a fellow teacher, Maria Witkowska. Maria Witkowska is a native Polish and Catholic descendant who worked as a postman for the army during the Polish War of Independence. They had a son and a daughter. The son, Jan Tarski, later became a physicist, and the daughter married mathematician Andrzej Ehrenfeucht.

After graduating as the youngest PhD in the history of the University of Warsaw at the time, Taski taught logic at the Polish Teacher¡¯s College, taught mathematics and logic at the University of Warsaw, and served as an assistant to Wukasziewicz. Because of these three jobs, Taski was still teaching mathematics at a high school in Warsaw. In Europe before World War II, the research talents taught at the high school were comparable. So before leaving Europe from 1923 to 1939, Taski wrote a few textbooks and papers alongside the middle school teachers¡¯ vacancies, some of which achieved breakthrough achievements. Taski had applied for a philosophical position at the University of Lviv, but this position was obtained by Leon Chwistek, recommended by Bertrand Russell.

In February 1930, Tarski was invited by Karl Menger to visit the University of Vienna to give three lectures, and at the same time met Kurt Godel. Thanks to a research grant, Tarski visited Vienna again in the first half of 1935 to work with Menger's research group. From Vienna, he visited Paris and explained his concept of truth at the first meeting of the movement for scientific unification initiated by the Vienna School. Therefore, Harvard University invited him to the United States to attend the scientific unification conference in the autumn of 1939, which indirectly saved Tarski's life from the Nazis. Tarski left Poland in August 1939 on the last ship to the United States before Germany launched the Polish campaign. At that time Le? niewski had died, leaving a faculty vacant, and Tarski hesitated. He was unaware of the threat of the Nazis, so that he left his wife and children in Poland when he left, but he didn't expect to be reunited until 1946. During World War II, most members of the Tarski family were killed by the Nazis.

After arriving in the United States, Tasky held several temporary teaching and research positions, including: in 1939 at Harvard University, in 1940 at the New York City College, and in 1942 funded by the Guggenham Foundation at the Princeton Institute of Higher Education and reunited with Godel. In 1942, Tasky was hired at the University of California at Berkeley and worked at Berkeley until his retirement. In 1945, Tasky joined the United States. In 1968, Tasky retired from Berkeley, but continued to teach until 1973 and taught PhD students until his death. In Berkeley, Tasky was recognized as a strict teacher:

Tarsky's discussion board in Berkeley quickly became a powerhouse of logic. Most of his students are now outstanding mathematicians. In their memory, Tarski used his terrible energy to cunningly guide them to the best work, and always demanded the highest standards of clarity and precision. "Times obituary." Tarski is extroverted, quick-thinking, strong-willed, energetic and sharp-tongued. He enjoys collaborative research-sometimes working all night with a colleague -and was very fastidious about priority. " (Gregory Moore, "Alfred Tarski" in Dictionary of Scientific Biography. "Tarsky was a charismatic leader and teacher, who was very strict in thinking and hesitant in explanations. Tarsky demanded his students with horribly high standards, but sometimes encouraged, especially to women. Some students were scared away by him, but others stayed, many of whom became world-renowned mathematical leaders in their fields." Tarski supervised a total of 24 PhDs, including 5 women, and deeply influenced the doctoral dissertations of Alfred Lindenbaum, Dana Scott, and Steven Givant. His students include : Andrzej Mostowski, Julia Robinson, Robert Vaught, Solomon Feferman, Richard Montague, J. Donald Monk, Donald Pigozzi, Roger Maddux, and Chen-Chun Chang and Jerome Keisler, authors of the classic textbook on model theory. Tarski lectured at University College London (1950, 1966), Henri Poincaré Institute in Paris (1955), Miller Institute for Basic Sciences in Berkeley (1958-1960), UCLA (1967), and Pontificia Universidad Católica de Chile (1974-75). Tarski was a member of the National Academy of Sciences and the British Academy of Sciences, and served as president of the Symbolic Logic Society from 1944 to 1946 and the International Union for the History of Science and Philosophy of Science from 1956 to 1957.

Tasky's interest in mathematics is widespread among mathematical logicists.His dissertation has a length of 2,500 pages, and most of it is about mathematical branches beyond logic.

Tuskie published his first paper, Content Collection Theory, at the age of 19, in 1924 in collaboration with Stefan Panah, demonstrating that a spherical surface can be cut into limited blocks and then crunched into a larger spherical surface, or two spherical areas of the same size as the original spherical surface. It is now known as the Panah-Tasky paradox.

In a paper entitled "The Approval of Primary Generations and Geometry", Tasky's Approval of Quantitative Abolition Proves that only the theory of multiplication and multiplication can be judged (although Tasky came to this conclusion only late in 1948, he completed the proof in 1930 and mentioned it in a paper in 1931).This conclusion is interesting because Alonso Church in 1936 proved that the true proposition in the logic of the primary generations was indiscriminate. In 1953, Tasky and his collaborators together in the book The Theory of Indiscriminacy proved that many mathematical systems (including the theory of equity, radiography, internal generations, group theory) were indiscriminate.

In 1941, Tuskie published an important paper on binary relationships, which opened up his study of relational algebra and its metallic mathematics. Though Tuskie's further research and Roger Lyndon's related work revealed some important limitations of relational algebra, he also demonstrated that relational algebra can express the most collective theory and piano arithmetic theory. At the end of the 1940s, Tuskie and his students developed circular algebra, which has a relative importance to one-layer logic as well as binary bulldogic relativity.

Alfred Tuskij was one of the greatest logic scientists of the twentieth century. He achieved significant achievements before he arrived in the United States. The most famous is the Panakhtasky puzzle. Another achievement of Tuskij's early days was the process of writing sentences in the language of real arithmetics. These sentences can be written with variables in the range of whole numbers, operating symbols plus and multiplied, equal to and number and non-symbols, or, containing and existing. Tuskij created an algorithm that determines whether such sentences are true.

For philosophers, Tasky¡¯s greatest achievement is his fierce criticism of the concept of truth. He can accurately define a language sentence as true under appropriate conditions. The condition is that the language is entirely formalized and has a clear syntax. The language in which the truth is generated is generally separate from the language in which the true value of that sentence is to be proved. Gotthard proposes a language that can be made as its own primary language. But in this case, Tasky can prove his famous theory of truth¡¯s indeterminability: in general, the concept of the ¡°true value¡± of a language¡¯s sentence cannot be defined in the same language.

Tarski lives unruly. As a teacher who is strict with his students, his 24 students have made outstanding achievements. He convinced the University of California, Berkeley of the importance of logic and got enough resources to make the Berkeley Department of Mathematics the world's logic center.