## Alfred TarskiyAn outstanding Polish-American mathematician, logician and founder of the formal theory of truth.
Date of Birth:
14.01.1902Country: USA |

**Content:**

## Biography of Alfred Tarski

Alfred Tarski, born Alfred Taitelbaum, was an outstanding Polish-American mathematician and logician, renowned as the founder of the formal theory of truth. He was born into a well-off family of Polish Jews. His inclination towards mathematics first manifested itself during his school years. However, in 1918, he entered the University of Warsaw with the intention of studying biology. That same year, Poland, which had been under the rule of the Russian Empire, became an independent state, and the University of Warsaw gained capital status. With the introduction of Jan Lukasiewicz, Stanislaw Lesniewski, and Waclaw Sierpinski, the university quickly became a global leader in logic, the foundations of mathematics, and the philosophy of mathematics. Tarski's mathematical talent was discovered by Lesniewski, who dissuaded the young Alfred from pursuing biology in favor of mathematics. Later, under Lesniewski's guidance, Tarski wrote his dissertation and obtained a Ph.D. degree in 1924. He became the youngest doctor in the history of the University of Warsaw. In 1923, Alfred and his brother Waclaw changed their surname to "Tarski." This last name was chosen because it was simple, not very common, and sounded Polish. Tarski tried not to publicize his Jewish origin, as he identified himself as a Pole and sought to be accepted as such.

After defending his dissertation, Tarski remained a lecturer at the university, assisting Lesniewski. During this time, he published a series of works on logic and set theory that brought him worldwide recognition. In 1929, Tarski married Maria Witkowska, and they had two children, Ina and Jan. In August 1939, he traveled to the United States to attend a scientific congress, just shortly before the invasion of German forces into Poland. This circumstance, apparently, saved his life, as almost all the members of his family who remained in Poland perished at the hands of the Nazis during the war. With no choice but to stay in the United States, Tarski temporarily settled at Harvard University, then moved on to several other positions at various American universities until finally obtaining a professorship at Berkeley in 1948, where he continued to work until his death. Here, he established his famous school and earned a reputation among his students as a strict and demanding supervisor.

## Contributions

Tarski made a series of important contributions concerning the decidability and undecidability of formal theories in first-order logic. His most famous positive results in this area include the theorems on the decidability of real linear arithmetic and Euclidean geometry. In the first case, he developed and successfully applied the method of quantifier elimination, which became one of the main methods for proving the decidability of first-order theories. In the second case, Tarski had to develop his own axiomatization of Euclidean geometry, which turned out to be more successful than the previously known axiomatization by Hilbert. He also made significant contributions to set theory. One of his early results in this field was the Banach-Tarski paradox, discovered jointly with Banach in 1924. The paradox essentially showed that a sphere in Euclidean space could be divided and rearranged to form two spheres of the same volume. The explanation for the paradox lies in the fact that the concept of volume cannot be adequately interpreted for arbitrary sets, and "sets without volume" temporarily arose in the construction process. The paradox had significant implications for the development of measure theory.

## Influence

Throughout his life, Tarski supervised a total of 24 students who obtained their Ph.D. degrees under his guidance. Among them are well-known names such as Andrzej Mostowski, Julia Robinson, Solomon Feferman, Richard Montague, Robert Vaught, as well as the authors of the renowned Model Theory, Jerome Keisler and Chen-Chung Chang. In addition to his direct students, Tarski maintained contacts with many other scholars and exerted a significant influence on their work. Some of these scholars include Alfred Lindenbaum, Dana Scott, and Leonard Gillman.

**Mathematicians**

Honore Fabri | Leopold Kronecker | Karl Gauss |

Witold Hurewicz | Gosta Mittag-Leffler | Evklid |