Hugo Steinhaus

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Hugo Steinhaus bigraphy, stories - Polish mathematician

Hugo Steinhaus : biography

January 14, 1887 – February 25, 1972

Władysław Hugo Dionizy Steinhaus (January 14, 1887 – February 25, 1972) was a Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the Jan Kazimierz University in Lwów (now Lviv, Ukraine), where he helped establish what later became known as the Lwów School of Mathematics. He is credited with "discovering" mathematician Stefan Banach, with whom he gave a notable contribution to functional analysis through the Banach–Steinhaus theorem. After World War II Steinhaus played an important part in the establishment of the mathematics department at Wrocław University and in the revival of Polish mathematics from the destruction of the war.

Author of around 170 scientific articles and books, Steinhaus has left its legacy and contribution on many branches of mathematics, such as functional analysis, geometry, mathematical logic, and trigonometry. Notably he is regarded as one of the early founders of the game theory and the probability theory preceding in his studies, later, more comprehensive approaches, by other scholars.

Mathematical contributions

Steinhaus authored over 170 works. Unlike his student, Stefan Banach, who tended to specialize narrowly in the field of functional analysis, Steinhaus made contributions to a wide range of mathematical sub-disciplines, including geometry, probability theory, functional analysis, theory of trigonometric and Fourier series as well as mathematical logic. He also wrote in the area of applied mathematics and enthusiastically collaborated with engineers, geologists, economists, physicians, biologists and, in Kac’s words, "even lawyers".

Probably his most notable contribution to functional analysis was the 1927 proof of the Banach–Steinhaus theorem, given along with Stefan Banach, which is now one of the fundamental tools in this branch of mathematics.

His interest in games led him to propose an early formal definition of a strategy, anticipating John von Neumann’s more complete treatment of a few years later. Consequently he is considered an early founder of modern game theory. As a result of his work on infinite games Steinhaus, together with another of his students, Jan Mycielski, proposed the Axiom of determinacy.

Steinhaus was also an early contributor to, and co-founder of, probability theory, which at the time was in its infancy and not even considered an actual part of mathematics. He provided the first axiomatic measure-theoretic description of coin-tossing, which was to influence the full axiomatization of probability by the Russian mathematician Andrey Kolmogorov a decade later. Steinhaus was also the first to offer precise definitions of what it means for two events to be "independent", as well as for what it means for a random variable to be "uniformly distributed".

While in hiding during World War II Steinhaus worked on the "cake-cutting problem": how to divide a resource in a manner which is "fair" according to precisely defined criteria, such as proportionality and envy-free.

Steinhaus was also the first person to conjecture the ham-sandwich theorem, and one of the first to propose the method of k-means clustering.

Academic career

Interwar Poland

During the 1916-1917 period and before Poland had regained its full independence, which occurred in 1918, Steinhaus worked in Kraków for the Ministry of the Interior in the ephemeral puppet state of Kingdom of Poland.

In 1917 he started to work at the University of Lemberg (later Jan Kazimierz University in Poland) and acquired his habilitation qualification in 1920. In 1921 he became a profesor nadzwyczajny (associate professor) and in 1925 profesor zwyczajny (full professor) at the same university. During this time he taught a course on the then cutting edge theory of Lebesgue integration, one of the first such courses offered outside of France.

While in Lwów, Steinhaus co-founded the Lwów School of Mathematics and was active in the circle of mathematicians associated with the Scottish cafe, although, according to Stanislaw Ulam, for the circle’s gatherings, Steinhaus would have generally preferred a more upscale tea shop down the street.