**Prof. Hugo Steinhaus**

Hugo Steinhaus was born at Jas³o on January 14, 1887. On graduation from classical secondary school in 1905, he entered Lwow University where he studied philosophy and mathematics. A year later, he moved to Gottingen and attended lectures by Hilbert, Klein, Minkowski, Runge, Landau, Caratheodory, Toeplitz and others.

In 1920, he was nominated Associate Professor at the Lwow University and in 1923 - Professor. He became a member of the Lwow Scientific Society in 1926, and in 1929 he founded, together with Stefan Banach, the periodical "Studia Mathematica", devoted mainly to functional analysis. From the very beginning (1931) of the series "Monografie Matematyczne", Steinhaus has been a member of the editorial committee.

In 1945 at Cracow, he contributed to the organization of the Wroc³aw
University, where he was appointed to a department, later called the Department
of Application of Mathematics. In November of that year he settled in Wroc³aw
and was the organizer and first dean of the Faculty of Mathematics, Physics and
Chemistry (at that a *de facto* common faculty of the University and the
Technical University). Steinhaus was the first chairman of the Wroc³aw Branch
of the Polish Mathematical Society, one of the founders and the first
secretary-general of the Wroc³aw Scientific Society.

Twice - in 1947 and 1951 - Steinhaus was awarded the Banach Prize of the Polish Mathematical Society, in 1950 that of the Polish Academy of Sciences, in 1951 a National Prize first class, in 1959 the City of Wroc³w Prize, and in 1960 a prize from the periodical "Problemy" for popularization.

He was decorated in 1954 with the Officer's Cross of the Polonia Restituta Order, in 1957 - Commander's Cross with Star of the same Order, and in 1959 a Banner of Labour, First Class.

Steinhaus was awarded doctorates *honoris causa* as follows, in 1958 -
Warsaw University; in 1961 - the Wroc³aw Medical Academy; in 1963 - Poznan
University; and in 1965 - Wroc³aw University.

He passed away in Wroc³aw on February 25, 1972.

Steinhaus's early achievement, including his habilitation thesis, were
concerned with the *theory of trigonometric series* in which he became an
expert. He was the first to give and examples of trigonometrical series
everywhere divergent, with coefficients tending to zero. He proved that a
trigonometric series is a Fourier's series if and only if its Cesaro sums fulfil
the Cauchy condition in the mean. The theorems and counterexamples by Steinhaus
are already acknowledged as classsical.

The fundamental theorem concerning *functional analysis* at that time
coming to the fore, was the result of collaboration in the twenties of Steinhaus
with Stefan Banach. Steinhaus's theorem on the form of a linear functional in
the space of integrable functions and the theorems proved with Banach on
sequences of functionals, and, above all, the theorem called principle of
condensation of singularities are already universally known and still applied
and described in all monographs and textbooks in this field.

Various authors stress in their works the precursory role played by Steinhaus. For example, Norbert Wiener states that he was inspired by Steinhaus's ideas when he was developing the theory of stochastic processes. The connections of probability with measure and real functions began to work in the opposite direction, too: the papers by Steinhaus on series with random coefficients, and further on independent functions (the series of papers initiated in 1935 together with M.Kac) are among those works which started the penetration of probabilistic ideas and methods into different branches of mathematics - principally analysis).

From his early years Steinhaus, engaged in *popularization* of
mathematics. He delivered popular lectures, wrote articles to various
periodicals, and published "What Mathematics Is and What Is Not" (1923 in
Polish). Later, he wrote the "Kalejdoskop Matematyczny", which appeared also in
English under the title "Mathematical Snapshots" (1938). A considerable place in
the latter publications is occupied by the problems of chess, draughts and other
games. The earlier article on games (1929), defining the fundamental notion of a
determined game, caused Steinhaus to be seen as a pioneer of the rapidly
developing *theory of games*. In particular, Steinhaus was the first to
observe that pursuit is an example of a game in the sense of that theory.

Steinhaus has always been interested in various practical problems of
biology, medicine, geography and sometimes technology. His works on
*applications of mathematics* to those and also other fields began to
appear in 1924. There are practical problems at stake as regards measuring areas
and lengths and later of what is known as Groer's law of patergy concerning
infant tuberculosis (1934). Steinhaus designed and instrument for localization
of strange bodies in the body of a sick person by means of X-rays, based on a
simple and elegant geometrical conception (1938).