Stefan Kaczmarz

Stefan Marian Kaczmarz ( ; 20 March 1895 – 1939) was a Polish mathematician and a representative of the Lwów School of Mathematics. He is known for introducing the Kaczmarz method, which provided the basis for many modern imaging technologies, including the CAT scan.

Kaczmarz was a professor of mathematics in the faculty of mechanical engineering of Jan Kazimierz University of Lwów from 1923 to 1939, where he collaborated with Stefan Banach. After graduating with honours, Kaczmarz enrolled at the Jagiellonian University in Kraków to pursue studies in mathematics, physics and chemistry. His professors included some prominent figures of the time, such as Stanisław Zaremba, Marian Smoluchowski, Jan Śleszyński and Kazimierz Żorawski. In 1924, he obtained his doctorate based on his thesis entitled The relationships between certain functional and differential equations. His findings from the thesis were published in Fundamenta Mathematicae in the same year. In 1929, he received his habilitation. Kaczmarz also took part in the famous discussions at the Scottish Café attended by renowned mathematicians including Stefan Banach, Stanisław Mazur, Władysław Orlicz, Stanisław Ulam and Mark Kac.

In 1928, he married teacher Helena Firlcińcka in Nowy Sącz with whom he had two daughters. In 1932, after having been granted a scholarship by the National Culture Fund, he travelled to Cambridge where he met G. H. Hardy and Raymond Paley and participated in lectures on Fourier transform delivered by Norbert Wiener. He then spent brief time in Göttingen and came back to Lwów. In 1933, he became the recipient of the Cross of Independence. In 1935, he was appointed an assistant professor at the Lviv Polytechnic. The following year, he became a member of the Lwów Scientific Society. In 1937, he was awarded the Golden Cross of Merit.

Death The circumstances of Kaczmarz's death are unclear. In early September 1939, after World War II broke out, he was called up for Polish military service as a reserve lieutenant. He sent a letter to his wife on 4 September and was not heard from afterwards. Theories for his death include the possibility that he died soon after near Nisko (the source of his last letter to his wife) in a German bombing raid on a train he was traveling in, that he died later that month in combat against the Germans near Umiastów, or that he was murdered by the NKVD in April or May 1940 as part of the Katyń massacre. He mainly worked in algebra, real analysis, Fourier series, and orthogonal functions. He is perhaps most well-known for introducing the Kaczmarz method, an iterative algorithm for solving linear equation systems, which laid the foundation for developing many modern imaging technologies, including the CAT scan. It was originally published in his paper entitled Angenäherte Auflösung von Systemen linearer Gleichungen and appeared in the Bulletin International de l'Académie Polonaise des Sciences et des Lettres in 1937 after having been presented to the journal by Tadeusz Banachiewicz.