**Hugo Steinhaus** was a Polish mathematician whose book *Mathematical Snapshots* has been very influential.

- However, by the time Steinhaus was born in Jasło, Austria had named the region the Kingdom of Galicia and Lodomeria and given it a large degree of administrative autonomy.
- Steinhaus studied for one year in Lemberg, spent one term in Munich but then spent five years studying mathematics at the University of Göttingen.
- There he was influenced by an amazingly strong group of mathematicians including Felix Bernstein, Carathéodory, Courant, Herglotz, Hilbert, Klein, Koebe, Edmund Landau Landau (although he only arrived in Göttingen after Steinhaus had been there three years), Runge, Toeplitz, and Zermelo.
- For his doctorate Steinhaus studied under Hilbert's supervision.
- The main influence on the direction that Steinhaus's research would take was none of the major mathematical figures at Göttingen but rather the influence came from Lebesgue.
- Steinhaus studied Lebesgue's two major books Leçons sur l'intégration et la recherche des fonctions primitives Ⓣ(Lessons on integration and research on primitive functions) (1904) and Leçons sur les séries trigonmétriques Ⓣ(Lessons on trigonmetric series) (1906) around 1912 after completing his doctorate.
- The mathematical society which Steinhaus proposed was started as the Mathematical Society of Kraków and, shortly after the war ended, it became the Polish Mathematical Society.
- Also at this time Steinhaus started a collaboration with Banach and their first joint work was completed in 1916.
- Steinhaus took up an appointment as an assistant at the Jan Kazimierz University in Lwów (as Lemberg University had become) and, around 1920, he was promoted to Extraordinary Professor.
- by Steinhaus and Banach, concentrated mainly on functional analysis and its diverse applications, the general theory of orthogonal series, and probability theory.
- Steinhaus was the main figure in the Lwów School up till 1941.
- Steinhaus published his second joint paper with Banach in 1927 Sur le principe de la condensation des singularités Ⓣ(On the principle of condensation of singularities).
- In 1929, together with Banach, he started a new journal Studia Mathematica and Steinhaus and Banach became the first editors.
- Another important publishing venture in which Steinhaus was involved, begun in 1931, was a new series of Mathematical Monographs.
- The series was set up under the editorship of Steinhaus and Banach from Lwów and Knaster, Kuratowski, Mazurkiewicz, and Sierpiński from Warsaw.
- An important contribution to the series was a volume written by Steinhaus jointly with Kaczmarz in 1937, The theory of orthogonal series.
- Steinhaus is best known for his book Mathematical Snapshots written in 1937.
- to understand and appreciate Steinhaus's mathematical style, one must read (or rather look at) snapshots.
- it expresses, not always explicitly and at times even unconsciously, what Steinhaus thought mathematics is and should be.
- To Steinhaus mathematics was a mirror of reality and life much in the same way as poetry is a mirror, and he liked to "play" with numbers, sets, and curves, the way a poet plays with words, phrases, and sounds.
- despite Steinhaus's attention to preparation, the lectures were too difficult for the average student.
- Steinhaus, who sometimes joined his colleagues in the Scottish Café, contributed ten problems to the book, including the final one written on 31 May 1941 only days before the Nazi troops entered the town.
- When the prospect of war was looming in 1938, Steinhaus proposed Lebesgue for an honorary degree from Lwów.
- In 1945 Steinhaus moved to the University of Wrocław but made many visits to universities in the United States including Notre Dame.
- Steinhaus, now in the University of Wrocław, decided that the tradition of the Scottish Book was too good to end.
- Let us finally examine some of Steinhaus's mathematical contributions which we have not mentioned above.
- In 1944 Steinhaus proposed the problem of dividing a cake into nnn pieces so that it is proportional (each person is satisfied with their share) and envy free (each person is satisfied nobody is receiving more than a fair share).
- Some of Steinhaus's early work was on trigonometric series.
- As we have noted above, other contributions by Steinhaus were on orthogonal series, probability theory, real functions and their applications.

Born 14 January 1887, Jasło, Galicia, Austrian Empire (now Poland). Died 25 February 1972, Wrocław, Poland.

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Origin Poland

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