Hugo Steinhaus

Hugo Steinhaus, a world-famous Polish mathematician, was born on 14th January, 1887 in Jasło (south-eastern Poland); he died on 25th February 1972 in Wrocław. He studied mathematics in Lviv and Göttingen. From 1916 to 1941 he was associated with the John Casimir University in Lviv. After the war, the Polish border changed and the Polish Lviv mathematical community moved, in large part to Wrocław, where Steinaus started to organise scientific activities. He became the first dean of the Faculty of Mathematics, Physics and Chemistry, which was then jointly managed by the University of Wrocław and the Wrocław University of Science and Technology. He was the creator of two schools of mathematics: functional analysis in Lviv (together with Stefan Banach), and applied mathematics in Wrocław. From 1945 he was a member of the Polish Academy of Arts and Sciences. His desire to popularise and visualise mathematics led him to write a book “Mathematical Snapshots”. It was published in 1938 at the same time in Polish and in English; it has since been translated into several languages and due to its popularity was reprinted many decades after. He founded internationally renowned journals that still exist today: "Studia Mathematica" (1929), "Colloqium Mathematicum” (1948) and “Zastosowania matematyki” (1953) now known as “Applicationes Mathematicae". His numerous achievements are important in mathematics to this day and were even celebrated in a poetry book.¹

After the war he was successfully developing applied mathematics cooperating with representatives of a broad spectrum of scientific and technological fields. His seminar on the applications of mathematics launched on 7th October 1948 and took place in the main building of the Wrocław University of Science and Technology. Later, the seminar was moved to the building of the State Institute of Mathematics (now called Institute of Mathematics of the Polish Academy of Sciences) at Kopernika street, located in the charming Park Szczytnicki and has become a famous meeting place for the Wrocław scientific community.

Let us try to answer whether Hugo Steinhaus was right with his thesis:

Cooperation - this is applied mathematics. There is no ready-made doctrine of applied mathematics. It is created when mathematical thought comes into contact with the surrounding world, but only when both the mathematical spirit and the natural matter are fluid. To achieve this, you need to realise that learning not only describes reality, but also creates a new reality whenever it becomes an active attitude, not waiting for questions, but posing them.²

We start our search for an answer by going back to Hugo's early years. His father Bogusław was a merchant and industrialist, and his uncle Ignacy was a famous lawyer and politician. They both founded Towarzystwo Kredytowe (Credit Company) in Jasło. Hugo spent his childhood there and after graduating from gymnasium, he started his university education in Lviv in 1905 studying philosophy and mathematics. Next year he moved to the University of Göttingen which at that time was the world capital of mathematics, where from 1906 to 1911 he studied pure mathematics as well as applied mathematical disciplines and astronomy. On 10th May 1911 he obtained his doctorate summa cum laude under the supervision of David Hilbert. The dissertation was titled “Neue Anwendungen des Dirichletschen Prinzips” (“New applications of Dirichlet's principle”).³

It is there where – probably due to the influence of Felix Klein, who founded the Association for the Promotion of Pure and Applied Mathematics in Göttingen, Carl Runge, director of the Institute of Applied Mathematics, and Constantine Carathéodory, then assistant professor of mathematics – Steinhaus developed affinity to the applications of mathematics. With the help of David Hilbert and Herman Minkowski in 1910 Steinhaus established a close contact with a well-known American physicist, 1907 Nobel Prize laureate, Albert A. Michelson, who even offered him position in Chicago as his mathematical assistant.⁴

However, this did not come to fruition because Steinhaus was tired from his long stay abroad. He returned to Jasło and – as he writes – he was a "private scholar" for some time, spending a lot of time on trips to Lviv, Kraków, and on longer journeys to Italy and France. During the First World War he served in the Polish Legions artillery and later he worked at Dyrekcja Odbudowy Kraju (Directorate of the Country Reconstruction) in Kraków. It was then, in 1916, when during a walk in Planty Park around the Kraków old city, he made his (as he stated himself) greatest mathematical discovery – he noticed Stefan Banach discussing advanced mathematical topics with his colleagues and recognised his enormous mathematical talent. Steinhaus obtained his habilitation at the John Casimir University in Lviv, and in 1918, after the end of the war, he started working as a mathematical expert for the Jasło-Krosno gas pipeline construction conducted by companies Gartenbarg, Waterkeyn and Karpaty. The pipeline connected the "Męcinka" mine near Krosno via Jasło with a refinery in Glinik Mariampolski near Gorlice and supplied methane to both the refinery and the surrounding towns. Steinhaus worked there under the supervision of a great engineering expert Alexander Dietzius. His office was in Niegłowice near Jasło, close to the refinery.

His academic career truly started after a nomination for an associate professor at John Casimir University in 1920. He started conducting research on trigonometric series, functional analysis and fundamentals of probability theory. In addition to mathematical research, he was interested in specific applications to various fields such as cartography, medicine or energy. As a result of cooperation with dr. I. Rozenzweig from the Department of Electrical Engineering at Lviv Polytechnic, he became interested in the problem of mathematical determination of the optimal electricity tariff. In a famous paper published in Bulletin of Swiss Electrotechnical Society 30, 134–136, 1939 he proposed the square tariff in which the price is a square root of the integral of squared consumed power, which promotes constant demand preferable to the producer.

The Second World War brutally interrupted the dynamic development of the Lviv school of mathematics. After Lviv was occupied by the Nazis Steinhaus, under the false name Grzegorz Krochmalny, hid in the hamlet Berdechów near the village Stróże. During this period he was engaged in the underground education of many subjects, while trying to continue his own scientific work. He wrote memoirs. At that time he built a sundial (solar clock) for his students and added the inscription "Grzegorz Krochmalny, solar watchmaker".

In Berdechów he returned to the topic of energy tariffs. He published the results obtained in 1947 in the form of a 50-page article in "Prace Wrocławskiego Towarzystwa Naukowego" (“Works of the Wrocław Scientific Community”) and in a series of five articles in magazines devoted to the mathematics and energetics. He wrote, inter alia:

It is in the interest of the power plant to receive a constant demand, or a demand close to constant. As the increased profitability of the company allows part of the profit to be passed on to consumers in the form of a discount on the electricity prices, the benefit of the power plant coincides here with the interests of the recipients.

The means to achieve this is the tariff, and the method is functional analysis. 16th January 1948 factory in Świdnica (which still functions under the contemporary name “Pafal”) produced a prototype of the electric counter compatible with the Steinhaus square tariff. It was not until 1997 that Poland established Urząd Regulacji Energetyki (Energy Regulation Office), which analyses and approves tariffs taking into account consumer's interest in mind and economic competition.

While in the USA in 1947, Steinhaus visited National Bureau of Standards, the famous Westinghouse company, hospital in Bethesda, Md., and the Pentagon, where he demonstrated his “introvisor” – a device that allows for detection of invisible items, and he arranged an American patent for this device. He discussed the square tariff with Friedman from The Cowley The Commission for Economic Research. In 1963, during his stay in Great Britain he analysed another energy industry problem, the so-called power reserve (since electricity cannot be stored, this reserve must be kept at an appropriate level so as not to run out during big blackouts like we had witnessed in the USA and several European countries). Hence, it is safe to consider Steinhaus as a forerunner of the electricity market. It is a good place to quote Steinhaus' words, which he addressed to us, students:

There is a widespread misconception that the United States is a much richer country than Poland. This is devoid of any basis, because Poland can afford to raise and educate great mathematicians and then have absolutely no use of their work. The United States cannot afford this.

Steinhaus was conducting intensive research in energetics in cooperation with engineers from the IASE (Institute of Energetical Systems Automatics). He also involved his students in this topic: Stanisław Trybuła and Stanisław Gładysz. It was Gładysz who later effectively applied the ergodic theory of Markov processes to design the transport network (the so-called excavator-conveyor belt-stacker system) in the "Turów" lignite mine. As Steinhaus writes in his Memoirs under the date 27th June 1964:

The mine management stated that Dr. Gładysz's advice, if known earlier, would have reduced investments in billions and that they will reduce operating costs by 10%. For this advice, “Turów” made Dr. Gładysz a consultant with a salary of 2,000 zł per month, i.e. lower than the average salary of miners in Turoszów.

It is worth mentioning that the term “industrial mathematics” was not known at the time… Steinhaus words “There is no ready-made doctrine of applied mathematics” are adequate here.

Professor Hugo Steinhaus from 1948 to 1962 headed the Applications Group at the Państwowy Instytut Matematyczny (National Institute of Mathematics). The name of this group was later changed to the Department of Applications in Fundamental Sciences, Economics and Technology. At subsequent meetings Zjazd Matematyków Polskich (Congress of Polish Mathematicians) in 1948 and 1953 he delivered plenary lectures such as: "The Ways of Applied Mathematics" and "Probability Calculus as a Research Tool in Natural Sciences and Production”. No wonder in 1953 he founded a new magazine “Zastosowania matematyki” (Applications of Mathematics), which he published until 1963. Steinhaus' motives and strategy can be found in one of his lectures from 1955:

The correct tactic here was to bridge from the mathematical bank to the opposite bank in place which is the broadest: one had to attack the camp of biologists and doctors, the furthest one and – apparently – the most difficult to conquer.

During the period 1953-1963 Steinhaus published 15 articles in his journal.

Wrocław mathematician Stefan Drobot, creator of the mathematical fundamentals of dimensional analysis⁵, famously gave the following definition of mathematics:

Mathematics is commedia dell'arte, it is like a theatre in which actors have no assigned roles, there is no precisely defined plot, there is no director, and there is only an agreement between the actors that they are on stage and something is supposed to happen. This something has been roughly discussed, and the rest is left to the talent of the actors and - not without due significance - to the audience's reaction.

It seems the Drobot’s definition aptly explains the credo of Wrocław School of Applied Mathematics. It also contains the key to understanding Steinhaus’ thesis “There is no ready-made doctrine of applied mathematics.” Traditions of this school are still vivid in Wrocław and in Hugo Steinhaus Center.

¹ S.H. Case, “The Scottish Café”, ‎Slapering Hol Press, New York 2022.
² H. Steinhaus, “Drogi matematyki stosowanej” (“The ways of applied mathematics”), Matematyka 3, 8-19, 1949.
³ H. Steinhaus, “Selected Papers”, PWN, Warsaw 1985.
⁴ H. Steinhaus, “Wspomnienia i zapiski” (“Recollections and notes”), 1st ed., Aneks Publishers, London 1992; 3rd ed., Wydawnictwo Atut, Wrocław 2010; R.G. Burns, I. Szymaniec, A. Weron (editors), "Hugo Steinhaus Mathematician for All Seasons. Recollections and Notes" Vol.1 (1887-1945), Birkhauser 2015, "Vol. 2 (1945-1968), Birkhauser 2016.
⁵ Publications in Zastosowania Matematyki (Applicationes Mathematicae) 1, 1954 and Studia Mathematica 14, 1954.