**Stefan Kaczmarz** was a Polish mathematician whose work provided the basis for modern imaging techniques, including the CAT scan.

- When he was growing up, Stefan lived first in Kety, in the Silesian foothills east of Bielsko-Biala, where he attended primary school between 1901 and 1905.
- In September 1913 Kaczmarz began his studies of mathematics, physics and chemistry at the Jagiellonian University in Kraków.
- Kaczmarz, who was promoted to sergeant in July 1915, was involved in this Carpathian Campaign which was one of the most tragic of the whole war with great loss of life on both sides with little gained in the end.
- At the end of March 1918 Kaczmarz was released and he returned to his studies of mathematics, physics and chemistry at the Jagiellonian University in Kraków.
- In addition to this teaching, Kaczmarz also taught some classes at a girls' school in Kraków.
- (Lwów is now Lviv in Ukraine) Stefan Banach habilitated at the university in April 1922 and was appointed as an extraordinary professor of mathematics in July of that year.
- Hugo Steinhaus was also a professor at the Jan Kazimierz University of Lwów and Banach, very keen on building a major research centre at Lwów, arranged for an offer of a position to be made to Kaczmarz.
- At this stage Kaczmarz did not have a doctorate so, once on the staff at Lwów, he undertook research advised by Stanisław Ruziewicz (1889-1941).
- On 13 October 1924, Kaczmarz was awarded his doctorate for his thesis The relationships between certain functional and differential equations.
- In this paper, which contained results discovered in answering one of Banach's questions, Kaczmarz thanks Stanisław Saks and Stanisław Ruziewicz for helpful comments.
- In 1935 Kaczmarz published a book, Theorie der Orthogonalreihen Ⓣ(Theory of orthogonal series), coauthored with Hugo Steinhaus.
- From 1923 to 1939 Kaczmarz taught many university level courses at Lwów such as: Analytical Geometry, Higher Analysis, Integral Equations, Algebraic Curves, Trigonometric Series, Non-Euclidean Geometry and the Theory of Groups, and Differential Geometry.
- In addition to teaching at university level, Kaczmarz taught in the local secondary schools where his work received the highest praise.
- There are a number of aspects of Kaczmarz's mathematical contributions that we must mention in addition to those mentioned above.
- There is Kaczmarz's algorithm for the approximate solution for systems of linear equations which appears in his paper Angenäherte Auflösung von Systemen linearer Gleichungen Ⓣ(Approximate resolution of systems of linear equations) published in the Bulletin International de l'Académie Polonaise des Sciences et des Lettres in 1937.
- The iterative algorithm which Kaczmarz gave has proved particularly useful in applications, particularly to modern imaging technologies.
- A topic which Kaczmarz was embarking on at the time war broke out was a theoretical study of the curvature of railway tracks.
- Kaczmarz's greatest pleasure, other than mathematics, was to walk in the mountains.
- On the following day Kaczmarz was assigned to Warsaw as a lieutenant in the reserve.
- The second version is that Kaczmarz was killed by the Russians in the Katyn massacre in April or May 1940.
- It would appear that the theory he died in the Katyn massacre is the least likely of the possibilities, and that almost certainly Kaczmarz died in September 1939.
- Stanisław Ruziewicz, Kaczmarz's thesis advisor, also died during the war.

Born 20 March 1895, Sambor, Lwów, Austria-Hungary (now Sambir, Ukraine). Died after 4 September 1939, Poland.

View full biography at MacTutor

Origin Ukraine

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive