## 3.1 Hugo Steinhaus

*Mathematics mediates between the spirit and the matter. H. Steinhaus*

Hugo Steinhaus was born in 1887 in Jasło. He seemed brilliant since his childhood, showing a tremendous talent for languages and sciences. His family wanted to make him an engineer, but he was more attracted to mathematics. And rightly so, because he is one of the most prolific Polish mathematicians of the 20th century.

After graduating from high school, he began studying at the University of Lviv. After a year, he transferred to the University of Göttingen, then the most important mathematical center in Europe. In Göttingen he studied under eminent mathematicians, including David Hilbert, with whom he defended his doctoral thesis, and Felix Klein. The paths of great minds often cross, and so Steinhaus, while in Göttingen, met Wacław Sierpiński.

After returning to Poland, he continued his scientific research in Jasło and Cracow with a break for his service in the army during World War I. In 1916 he made his greatest scientific discovery (his own words), namely the discovery of Stefan Banach. It so happened that Banach, together with Otto Nikodym, while waiting for his friend Witold Wilkosz, were discussing Lebesgue integrals. This interested Steinhaus, who was passing nearby. He was surprised to hear engaged conversations about very advanced mathematics in such an unusual place. During the meeting, Steinhaus shared with the young men a mathematical problem he was just working on. To his surprise, after a few days Stefan Banach approached him with a solution, which they eventually published together. This was Banach’s first paper and the beginning of a very interesting friendship. A friendship of very different personalities. Banach liked to have fun and did not care about conventions, Steinhaus was an abstinent, a language purist, always wearing a tie. However, they shared a common passion and love for mathematics.

Together with Banach, they created the Lwów school of mathematics, which at its peak brought together more than 20 prominent mathematicians.

While still in Lwów, Steinhaus encouraged mathematics students to look into applications of mathematics. Often saying, *A mathematician will do it better* encouraged students to face problems in other fields, since often a strict way of thinking helps solve a wide variety of problems.

He himself also bore witness to this claim. He willingly collaborated with biologists, doctors, economists and researchers in other specialties. For example, after he had already moved to Breslau, collaboration with Ludwig Hirszfeld (immunologist, founder of seroanthropology, known for his research on blood groups) led to the development of a mathematical theory of paternity investigation. In collaboration with Dr. Rozenzweig, he conducted research on the optimal electricity tariff from the perspective of the energy producer. He invented and patented the introvizor – an instrument for locating objects using X-rays. He invented the *longimeter* – a simple device for estimating the length of irregular curves, which has found many applications in geography.

In Wroclaw, he served as head of the Natural and Economic Applications Department of the Mathematical Institute of the Polish Academy of Sciences. He called his laboratory a ,,mathematical clinic’’ where anyone can go with their ,,mathematical diseases’’ for advice. It is estimated that more than half of his more than 200 articles deal with applications of mathematics.

Steinhaus was also a well-known aphorist. Many of his aphorisms, which were called hugonotes, have gone down in history. They could be found, among other things, in the magazine *Problemy*, in the column *Cicer cum caule* (Latin for peas with cabbage), run by Julian Tuwim (Yes, that Tuwim, poet, writer, scamandrite). Legend has it that
when Tuwim first heard the aphorism ‘Ball and chain - the Earth’ he knelt in awe of Steinhaus (‘Ball and chain’ in Polish is ‘Kula u nogi’, which literally translated is ‘A ball by your leg’).

*Geniusz – gen i już. H. Steinhaus*

He was also interested in popularizing mathematics. Back in the interwar period, he wrote *Mathematical Kaleidoscope*, a popular science book intended to show the different faces of mathematics. This book lived to see many editions and translations.

Hugo Steinhaus inspired mathematicians even after his death. For example, in 1990, the Hugo Steinhaus Center was established at the Wrocław University of Technology to promote and develop applications of mathematics in other fields of science. Steinhaus was also a promoter of many active scientists, who in turn were promoters of many more scientists. Today, his *mathematical family tree* (see Mathematics Genealogy Project) lists more than 2940 mathematicians, an unusually high number for such a short time. One of Steinhaus’ *mathematical descendants* is also the author of this book.