Alfred Tarski

Alfred Tarski was a Polish-American logician and mathematician who taught at the University of Warsaw before emigrating to the United States, where he spent most of his career at the University of California, Berkeley. Tarski is best known for his semantic theory of truth, formulated in a 1933 paper on the concept of truth in formalized languages, which gave a rigorous mathematical definition of truth for formal languages via the Convention T criterion and became foundational to modern model theory. He proved Tarski's undefinability theorem, showing that a sufficiently strong formal system cannot define its own concept of arithmetical truth within itself, a result closely related to Godel's incompleteness theorems. With Stefan Banach, Tarski co-discovered the Banach-Tarski paradox, showing that a solid ball can be decomposed into finitely many pieces and reassembled into two balls identical to the original, a consequence of the axiom of choice. Tarski also developed an axiomatization of Euclidean geometry and made lasting contributions to abstract algebra, topology and algebraic logic through structures such as cylindric algebras.