胡戈·施泰因豪斯1887—1972

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

Early life and studies

Steinhaus was born on January 14, 1887, in Jasło, Austria-Hungary to a family with Jewish roots. His father, Bogusław, was a local industrialist, owner of a brick factory and a merchant. His mother was Ewelina, née Lipschitz. Hugo's uncle, Ignacy Steinhaus, was a lawyer and an activist in the Koło Polskie (Polish Circle), and a deputy to the Galician Diet, the regional assembly of the Kingdom of Galicia and Lodomeria.

Hugo finished his studies at the gymnasium in Jasło in 1905. His family wanted him to become an engineer but he was drawn to abstract mathematics and began to study the works of famous contemporary mathematicians on his own. In the same year he began studying philosophy and mathematics at the University of Lemberg. In 1906 he transferred to Göttingen University. At that University he received his Ph.D. in 1911, having written his doctoral dissertation under the supervision of David Hilbert. The title of his thesis was Neue Anwendungen des Dirichlet'schen Prinzips ("New applications to Dirichlet's principle").

At the start of World War I Steinhaus returned to Poland and served in Józef Piłsudski's Polish Legion, after which he lived in Kraków.

He was an atheist.

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.

World War II

In September 1939, after Nazi Germany and the Soviet Union both invaded and occupied Poland, as a fulfillment of the Molotov–Ribbentrop Pact they had signed earlier, Lwów initially came under Soviet occupation. Steinhaus considered escaping to Hungary but ultimately decided to remain in Lwów.

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.

Legacy

Steinhaus is said to have "discovered" the Polish mathematician Stefan Banach in 1916, after he overheard someone utter the words "Lebesgue integral" while in a Kraków park (Steinhaus referred to Banach as his "greatest mathematical discovery"). Together with Banach and the other participant of the park discussion, Otto Nikodym, Steinhaus started the Mathematical Society of Kraków, which later evolved into the Polish Mathematical Society. He was a member of PAU (the Polish Academy of Learning) and PAN (the Polish Academy of Sciences), PTM (the Polish Mathematical Society), the Wrocławskie Towarzystwo Naukowe (Wrocław Scientific Society) as well as many international scientific societies and science academies.

Steinhaus also published one of the first articles in Fundamenta Mathematicae, in 1921. He also co-founded Studia Mathematica along with Stefan Banach (1929), and Zastosowania matematyki (Applications of Mathematics, 1953), Colloquium Mathematicum, and Monografie Matematyczne (Mathematical Monographs).

He received honorary doctorate degrees from Warsaw University (1958), Wrocław Medical Academy (1961), Poznań University (1963) and Wrocław University (1965).

Chief works

Czym jest, a czym nie jest matematyka (What Mathematics Is, and What It Is Not, 1923).

Sur le principe de la condensation de la singularités (with Banach, 1927)

Theorie der Orthogonalreihen (with Stefan Kaczmarz, 1935).

Kalejdoskop matematyczny (Mathematical Snapshots, 1939).

Taksonomia wrocławska (A Wroclaw Taxonomy; with others, 1951).

Sur la liaison et la division des points d'un ensemble fini (On uniting and separating the points of a finite set, with others, 1951). One of multiple rediscoveries of Borůvka's algorithm.

Sto zadań (One Hundred Problems In Elementary Mathematics, 1964).

Orzeł czy reszka (Heads or Tails, 1961).

Słownik racjonalny (A Rational Dictionary, 1980).

Family

His daughter Lidya Steinhaus was married to Jan Kott.