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Creators of the Polish mathematical school

Vladimir Petrovich Odinets read the paper Forerunners and first creators of the Polish mathematical school (Russian) at the St Petersburg Department of Steklov Institute of Mathematics of the Russian Academy of Sciences on 5 December 2013. We give a version of that talk in an English translation.

The Russian version can be read at THIS LINK


Forerunners and first creators of the Polish mathematical school [Note 1]

As is known, in 1795 the Third Partition of Poland was completed. Its territory was finally divided between three states: the Russian Empire, the Austro-Hungarian Empire and the Kingdom of Prussia [Note 2].

In 1871, the Kingdom of Prussia became part of the German Empire and its eastern border already included the entire Baltic coast with the renamed cities of Stettin and Danzig (present-day Szczecin and Gdansk), the Greater Poland lands with the main city of Posen and Silesia with the city of Breslau (present-day Poznan and Wroclaw). Let us note right away that none of these cities had higher education institutions where mathematics was taught.

The major Polish cities that entered Austria-Hungary included the city of Krakow and the capital of the future Galicia: Lemberg (Lviv). The rest of the territory of Poland, including the cities of Warsaw, Vilnius, Lodz, Lublin, and Aleksandrovsk (Pulawy), became part of the Russian Empire as the Kingdom of Poland.[1]

Speaking about the prerequisites for the emergence of the Polish mathematical school after the restoration of independence (in November 1918) of the Polish state, we will divide the problem of "growing" professional Polish mathematicians into two parts (Russian and Austrian) in accordance with the territorial Partition of Poland, including not only Polish territories, but also the university cities of the respective Empires. As for Germany, its university cities: Berlin, Heidelberg, Göttingen, Munich, Leipzig - were used not only for the study of mathematics by Polish students, but above all for scientific internships and the preparation of dissertations. However, this also applies to Paris and Zurich. In this case, we will limit ourselves to the time frame of 1860-1922, considering only those Polish mathematicians who habilitated as mathematicians [Note 3] no later than December 1922 - the time of the death of the first President of Poland, Gabriel Narutowicz (1865-1922) [Note 4], four years before the May (1926) coup of Józef Pilsudski (1869-1935). [2] In 1927, the First Congress of Polish Mathematicians took place, which drew a line under the period of formation of the Polish mathematical school [4].

It should be noted right away that the period from 1800 to 1860 was not marked by any new scientific results in mathematics in the Polish lands. [Note 5] There is, however, one exception - this is the creative life of the mathematician and philosopher Józef Maria Wroński (1776-1853), who took the surname Wroński at the age of 35, and before that bore the surname of his father, the Czech architect Hoene. Józef Wroński was born in the town of Wolsztyn (75 km southwest of Poznań) in the territory that was ceded to Prussia in 1793. As a mathematician, he became famous for introducing the Wronskian - the determinant of a matrix of order n×nn \times n, composed of the values ​​of nn functionsf1,…,fnf_{1}, … , f_{n}, (having derivatives up to order (n−1)(n-1) inclusive on the interval (a,b)(a, b)) and their derivatives up to order (n−1)(n-1) inclusive. [5][6] (The term Wronskian was introduced in 1882 by the Scottish mathematician Thomas Muir (1844-1934)).

It should also be noted that another famous Polish scientist, Jan (Ivan Andreevich) Sniadecki (Jan Baptyst Sniadecki: 1756-1830), had his main scientific works on astronomy. It was for these works that he was elected a corresponding member of the St Petersburg Academy of Sciences in 1811. He also wrote a number of textbooks on mathematics and was one of the creators of mathematical terminology in Polish. [7]

1. The Kingdom of Poland and Russia in the period 1860-1915

In 1862 (25 November, old style), the Warsaw Main School began operating in Warsaw, essentially resuming the activities of the University of Warsaw, which had opened on 20 September 1817. [Note 6] In 1969, the Main School was closed, and in its place, in 1870, the Imperial University of Warsaw was created. Poles then and now call this university Uniwersytet Cesarski, i.e. Tsar's University, taking into account that teaching there was conducted mainly in Russian [Note 7] .

Through the efforts of the then Minister of Public Education D A Tolstoy (1823-1889) (see [3], p. 11), this university began training in mathematics within the framework of the new Physics and Mathematics Faculty.

During the first three years (1869-1872) mathematics were taught there by Władysław Zajączkowski (1837-1898), and from 1876 to 1885 by Marian Aleksander Baraniecki (1848-1895) [Note 8] [3]. The relations between these eminent Polish mathematicians were far from cloudless, as evidenced by a paragraph from Władysław Zajączkowski's work "The Theory of Determinants {=Tensors} of Order p" [Note 9] [10]

Of course, strong Russian mathematicians also taught at the Imperial University of Warsaw. Here, first of all, we should mention Georgy Feodosyevich Voronoy (1868-1908), Corresponding Member of the St Petersburg Academy of Sciences (since 1907), who taught in Warsaw from 1894 to 1908 [Note 10] and "became the forerunner of the Polish school in number theory." [11].

Among those who graduated from the Main School in Warsaw on the eve (1869) of the transformation of this school into a university, Samuel Dickstein (1851-1939) should be especially noted. The role of this man in the creation of the Polish School of Mathematics is unprecedented. S Dickstein gave his entire fortune to the development of Polish mathematics. After defending his master's thesis in 1879 at the Imperial University of Warsaw, he directed all his seething energy to creating conditions for the unification of Polish mathematicians and the presentation of their scientific achievements.

Already in 1884, he (together with Aleksander Chaevich (Aleksander Czajewicz (1843-1926)) [Note 11] organised the Physics and Mathematics Library in Warsaw, the purpose of which, in addition to storing and providing readers with the physics and mathematics literature, was to publish (in Polish) scientific works on mathematics and physics.

In 1888, together with Władysław Gosiewski and the brothers Edward and Władysław Natanson [Note 12], he began publishing the journal "Prace Matematyczno-Fizyczne". By 1951, 49 volumes had been published.

In 1897 he founded the mathematical journal "Wiadomości Matematyczne". By 1 September 1939 (the beginning of World War II), 47 volumes had been published. (Publication was resumed in 1951).

It was a mathematical journal in Polish. In addition to scientific articles on mathematics, reviews, articles on the history of mathematics, book reviews, it contained information on the mathematical life of Europe, as well as obituaries of famous mathematicians. In 1890, S Dickstein was elected a Corresponding Member of the Polish Academy of Sciences in Krakow. He wrote and published textbooks on mathematics and physics for Polish secondary schools. With the resumption of the activities of the University of Warsaw (in 1915) during the occupation of Warsaw by the Germans, S Dickstein was invited to teach at the university. He taught algebra, number theory and the history of mathematics. In 1919 he was awarded the title of "Honorary Professor".[12] In 1937, due to the anti-Semitic campaign that had begun in Poland, he was deprived of the opportunity to teach, dragged straight from the department. [13] S Dickstein died during the bombing of Warsaw on 28 September 1939.

Of course, in addition to the University of Warsaw, Poles living in the territory of the Russian Empire could study mathematics at other universities and institutes, and, above all, at the University of St Petersburg. [Note 13]

Thus, in 1866, Julian Sokhotsky (1842-1927), born in Warsaw, completed his studies at the University of St Petersburg. He began his studies back in 1860, but after the January 1863 uprising in Poland, he left St Petersburg and went to Poland, having managed to attract the attention of P L Chebyshev (1821-1894). It was Chebyshev who helped Sokhotsky to be reinstated at the University, and under his supervision in 1868 he defended his master's thesis "Theory of Integral Residues with Some Applications". I note that Sokhotsky's master's thesis was devoted to the inversion of the Lagrange (1736-1813) power series using the theory of residues, as well as the expansion of analytic functions into continued fractions. Investigating in this work the behaviour of the values ​​of the function
f(z)=sin⁡((z−b)−1)f(z) = \sin((z-b)^{-1})
in any neighbourhood of an essentially singular point z=bz = b, he arrived at the formulation of the famous theorem on the behaviour of an analytic function in the neighbourhood of an essentially singular point. [Note 14] ("If for a given function ff the point z=z0z = z_{0} is essentially singular, then the set of limit values ​​of the function ff at this point must take "all possible values""). [Note 15]

In 1873, Sokhotsky defended his doctoral dissertation. This dissertation laid the foundation for the theory of singular integral equations. In it, for the function f(t)(t−x)−1f(t)(t-x)^{-1}, the function f is sought [Note 16] [15].

In 1882, Sokhotsky was elected an ordinary professor at St Petersburg University. In the same year, his original course, "Higher Algebra," was published. Another 11 years later, his treatise on the theory of algebraic numbers was published: "Principles of the greatest common divisor as applied to the theory of divisibility of algebraic numbers," which contained the results of A A Markov (1856-1922), E I Zolotarev (1847-1878) and Sokhotsky himself.[16].

It should be noted that Sokhotsky translated most of his works into Polish, and they were available in Warsaw.

Another Pole who became an ordinary professor of mathematics at St Petersburg University in 1897 was Julian Sokhotsky's student Jan Ptaszycki (1854-1912), who was born in Kaluga Governorate to a Polish family. In 1860, his father Leon Ptaszycki moved to Vilnius, and then to the Baranowice estate near Bielsk (Grodno Governorate). After graduating from the gymnasium in Vilnius in 1872 (with a gold medal), Jan Ptaszycki enrolled in the Physics and Mathematics Department of St Petersburg University, where he eventually became the favourite student of J Sokhotsky. Already in his fourth year, Ptaszycki wrote a paper, "On the integration of algebraic differentials in finite form," which received high marks from specialists. In 1881, he defended his master's thesis, "On the integration of irrational differentials in finite form." [Note 17] In 1882, Ptaszycki received the position of privat-docent at St Petersburg University. In 1888, he defended his doctoral dissertation, "On the integration of elliptic differentials in finite form," continuing and enriching with his own results the research of J Liouville (1809-1882), P L Chebyshev (1821-1894), and N Abel (1802-1829).

In 1891 Jan Ptaszycki was invited to teach mathematics at the Mikhailovskaya (Artillery) Academy, and in 1897 he became an extraordinary professor at St Petersburg University. His works, generalising Hermite's results on elliptic and hyperelliptic integrals and published in the "Bulletin des sciences mathématiques et astronomiques" and "Mathematische Annalen", made his name known in Europe [Note 18] [17].

It is no coincidence, therefore, that as a representative of Russia, he took an active part in the work of the Second Congress of Mathematicians in Paris (1900), being one of the secretaries of this Congress [18].

In 1901 Jan Ptaszycki became an ordinary professor at St Petersburg University, and in 1908 he received the title of "Distinguished Professor". Poles also studied mathematics at other universities, in particular at Kharkov University and Novorossiysk University, opened on 1 May 1865 in Odessa.

The future professor of logic at the Jagiellonian University, Jan [Note 19] (Ivan Vladislavovich) Sleszyński (1854-1931), studied at Novorossiysk University from 1876 to 1880. After passing his master's exams in 1880, Sleszyński was given the opportunity to continue his studies at the University of Berlin under the supervision of K Weierstrass (1815-1897). Upon his return from Germany in 1883, he taught at the university and at one of the Odessa gymnasiums. It should be noted that Sleszyński became an "Emeritus Professor" of Novorossiysk University in 1908. In addition to logic, he also taught algebra and probability theory. His most significant works should be recognised as the two-volume "Theory of Proofs" (volume 1 - 1925; volume 2 - 1929), published already in independent Poland, as well as "Theory of Determinants" (1926) [20].

In 1905, Anton (Pavlovich) Przeborski (Antoni Bonifacy Przeborski: 1871-1941) became an ordinary professor at Kharkov University. In 1921, he was an ordinary professor at Stefan Batory University in Vilnius, and from 1922 - at the University of Warsaw. [21]. The fate of A Przeborski in Russia in many ways resembles the fate of J Ptaszycki. After graduating with a gold medal from the gymnasium in Nikolaev in 1890, where his father served as a doctor in the Black Sea Fleet, Przeborski entered the same year the mathematics department of the physics and mathematics faculty of St Vladimir University in Kyiv. After graduating from the university in 1894, Przeborski was left there for 2 years "to prepare for the professorship." In 1895, he received the Professor I I Rachmaninoff Prize [Note 20] for his work "On the methods of Abel, Jacobi, Liouville and Weierstrass in the theory of elliptic functions." Przeborski defended his master's thesis in 1902 at Moscow University. But even earlier, in January 1898, he began working at the Kharkov Technological Institute in the full-time position of associate professor of mechanics. In 1899 he was invited to Kharkov University to the position of privat-docent in the mathematics department, and already in the autumn of 1902 Przeborski became acting extraordinary professor there. In 1904 Przeborski went on an internship to Heidelberg and Göttingen, after which he received invitations to a permanent position at various universities, including the Jagiellonian University in Krakow. However, he returned to Kharkov University, and there, in 1908, he defended his doctoral dissertation "Research in the Theory of Analytic Functions. The Problem of Continuing the Taylor Series." In the same year, he became an ordinary professor of the mathematics department.

The echo of the turbulent events after the 1917 revolution reached Kharkov: Przeborski was elected rector of Kharkov University, then arrested as a "Polish hostage" during the Soviet-Polish war. As a result, in August 1921, he turned to the Ministry of Religious and Public Education of Poland with a request to help him move to Poland for permanent residence. His request was granted, and in 1922, after a month's stay in Vilnius, he, with the assistance of Wacław Sierpiński (1882-1969), came to Warsaw, where he was elected full professor in the Department of Theoretical Mechanics at the University of Warsaw. He worked in this department until 1939 - the beginning of World War II.

The scientific research that Przeborski carried out in Poland was mainly related to classical mechanics. He obtained new results on the dynamics of nonholonomic systems and on nonanalytic integrals of nonlinear differential equations. In addition, his textbook "Variational Calculus" and two volumes of "Lectures on Theoretical Mechanics" were published in Warsaw. [Note 21] [22].

Listing the universities where Poles studied mathematics in the second half of the 19th and early 20th centuries, I said nothing about Moscow University. I will not presume to judge the reasons, but with the exception of Bolesław (Kornelievich) Młodzeevski (Bolesław Mlodzeevski: 1858-1923), I do not know of any prominent Polish mathematicians who influenced the development of the Polish mathematical school from the walls of this university. [Note 22] B Mlodzeevski himself was born in Moscow, graduated from the 5th Moscow Gymnasium in 1876 with a gold medal and entered Moscow University the same year. He graduated from the Physics and Mathematics Department in 1880, defending his thesis "Classification of plane curves of the 3rd order." [Note 23] In 1886, Mlodzeevsky defended his master's thesis "Research on the bending of surfaces."

This work was far ahead of its time. In essence, it was addressed in his research several decades later by A V Pogorelov (1919-2002).

In 1890, Mlodzeevsky defended his doctoral dissertation "On manifolds of many dimensions", and he was given the opportunity to go on an internship in Zurich, Paris and Göttingen for a year. Upon returning to Moscow, he received the position of extraordinary professor in the department of pure mathematics, and already in 1899 he became an ordinary professor in the same department [23]. It is interesting that from 1880 to 1900 (with a break in 1891) Mlodzeevsky also taught in a secondary school (Usachevsko-Chernavskoye School) [24]. In 1910, he was awarded the title of "Honoured Professor", and a year later, in solidarity with the rebellious students, he left Moscow University, returning there only in 1917. Mlodzeevsky did not have any special ties with Poland [Note 24]. Nevertheless, he tried to help those Polish mathematicians who turned to him for help. In particular, he agreed to be an opponent of Przeborski's dissertation when (in 1902) the local authorities did not allow him to defend his dissertation on the basis of the "anti-Polish" decree of 1864!

It is also appropriate to say that B Mlodzeevsky was the secretary of the Moscow Mathematical Society from 1891 to 1905, its vice-president (associate of the Chairman) from 1905 to 1921, and from 1921 until his death (1923) he headed this society. (It is worth adding here that Yulian Sokhotsky headed the St Petersburg Mathematical Society from 1894 to 1917.) Finally, it can be noted that B Mlodzeevsky was the Chairman of the Organizing Committee for the 2nd All-Russian Congress of Mathematics Teachers (January 1914) in Moscow and opened this congress. More than 20 teachers from Polish territories participated in the work of the congress [25], [26].

In addition to universities, many Poles studied at engineering universities in Russia, where mathematics was also studied. [Note 25] Later, some of them became professional mathematicians. [Note 26]

It is no coincidence that the first permanent metal bridges in St Petersburg (across the Bolshaya Neva) and Warsaw (across the Vistula) were built under the supervision of the Polish engineer Stanisław Kierbedź (1810-1899) [Note 27] [27].

It is also no coincidence that already in independent Poland (after 1918), the Polytechnic Institutes (Politechniki) became the workplaces of many prominent Polish mathematicians.

2. Austro-Hungarian Empire.

Let us now consider the situation with the development of mathematics in the Polish lands that became part of Austria-Hungary. Let us start with Krakow. It should be noted that in this city there has been a university called the Jagiellonian University [Note 28] (abbreviated UJ) since 1364. There were no specialised mathematical departments there until 1783 [Note 29].

On the other hand, mathematics was taught there before 1783. It is no coincidence that it was studied (along with astronomy and theology) by Nicolaus Copernicus (1473-1543), who studied at UJ in 1491-1493.

Despite the presence of specialised mathematical departments at UJ in the 19th century, serious mathematical works appeared there only at the end of the century. Their appearance is usually associated with the scientific work of only two mathematicians: Kazimierz Żórawski (Paulin Kazimierz Stefan Żórawski: 1866 - 1953) [Note 30] [29] and Stanisław Zaremba. We will return to these mathematicians later, but for now we will note that as early as 1816 the Krakow Scientific Society appeared, which existed until 1872. This society, together with the UJ, published yearbooks, which also included works on mathematics, in particular by Karol Huba [Note 31].

In 1872 the Krakow Scientific Society was transformed into the Academy of Knowledge (Academia Umiejętności), abbreviated AU. In 1919 the AU was transformed into the Polish Academy of Knowledge (Polska Academia Umiejętności), abbreviated PAU.

Franciszek Mertens (1840-1927), who received a mathematical education at the University of Berlin, defended his doctoral dissertation there in 1864, and since 1865 as a professor at the University of Krakow, actively participated in the work of AU at the very beginning of its activity. F Mertens brought new topics to the scientific activity of AU: the development of potential theory, the development of analytical number theory. In 1874, he published a proof of a theorem, which was included in all textbooks on analysis, on the convergence of the product of two series, one of which is convergent and the other is absolutely convergent (See, for example, [30], v.2, p. 392, p. 330). F Mertens worked at the University of Krakow until 1884, and then moved to Austria ([31], p. 25).

In 1882, at the meeting of the AU Natural Sciences and Mathematics Department on 12 June 1882, Dr W Kretkowski offered a prize of 500 francs for the solution of a problem identical to Hilbert's Third problem, spoken abour by the latter at the Second International Congress of Mathematicians in Paris in 1900. [Note 32] Hilbert's problem was solved in 1901 by Hilbert's student Max Dehn (1878-1952) using a new invariant (Dehn). The solution to Kretkowski's problem was obtained by Ludwik Antoni Birkenmajer (1855-1929), a future professor at the Jagiellonian University, even before 31 December 1883. [Note 33]

Let's return to the activities of K Żórawski and S Zaremba mentioned above.

K Żórawski studied physics and mathematics at the University of Warsaw in 1884-88. He continued his studies in Leipzig, Göttingen, and Paris (until 1892), defending his doctoral dissertation in 1891 in Leipzig. Even before the defence (in 1890), he was elected a Corresponding Member of the AU, and in 1900 - a full member. In 1892-95 he lived in Lviv, being a privat-docent at the Lviv Polytechnic. Later he became a professor at the University of Krakow (and even the rector of UJ in 1917-1918). In 1919 he became a professor at the University of Warsaw and the Warsaw Polytechnic. Żórawski's scientific interests and most of his works related to the theory of differential equations, differential geometry, group theory and theoretical mechanics. Żórawski's services in uniting Polish scientists are great. In 1921-31 he was the Chairman of the Warsaw Scientific Society, and in 1919 he was one of the founders of the Krakow Mathematical Society. During World War II K Żórawski lived through the years of German occupation (in his father's former estate [Note 34]). A few months before his death (in 1952), he became a full member of the Polish Academy of Sciences.

In 1890, Stanisław Zaremba became a professor at the Department of Mathematics at the University of Krakow. His main scientific works are concentrated on partial differential equations and equations of mathematical physics. His other works, however, also gained wide recognition. In particular, his books: "Theoretical Arithmetic" (1912) and "Introduction to Analysis" (1915 and 1918) are still cited. In the thirties, S Zaremba began publishing a multi-volume "Theoretical Mechanics". But before the beginning of World War II, only two volumes were published.

It is curious that on the initiative of V A Steklov in 1924, Zaremba was elected a foreign corresponding member of the USSR Academy of Sciences. This, however, is not surprising - they corresponded for more than 15 years. [32]. It remains to add that S Zaremba was one of the founders (in 1919) of the Polish Mathematical Society. S Zaremba died in Krakow in November 1942 [31].

Now let's go back to 1875. That year, Józef Puzyna (1856-1919), son of the magnate Włodzimierz Puzyna and Felicja Rudzki, graduated from high school in Lemberg (Lviv), and then entered the University of Lemberg (the Faculty of Philosophy), but two years later he was forced to interrupt his studies, as he was called up for a year of military service. He completed his studies at the university in 1880, and began to engage in scientific work. Two years later, he passed the exams for the right to teach mathematics and physics in secondary schools and began teaching at the high school, without interrupting his scientific work. In 1883, he received a doctorate from the University of Lemberg. He spent the academic year 1883/84 in Berlin as an intern with K Weierstrass, where he prepared a paper on the theory of analytic functions, which served, upon his return to Lemberg, as the basis for defending his habilitation [Note 35]. In 1889 he became an extraordinary professor, and in 1892 an ordinary professor and head of the Department of Mathematics at the University of Lemberg. In 1904/1905 he was rector of the University, and in the following academic year - vice-rector. From 1900 he was a corresponding member of the AU. In 1898-1900 he published two volumes of "The Theory of Analytic Functions", containing extensive fragments of set theory and group theory necessary for the main topic of the work. In 1908, he invited Wacław Sierpiński, then still a doctor, to Lemberg, who defended his habilitation in Lemberg that same year. Among the students to whom J Puzyna lectured on mathematics in 1905/1906, he singled out student Hugo Steinhaus, advising him to continue his studies in Göttingen. When H Steinhaus found himself in Lemberg at the beginning of 1917, J Puzyna helped him organise the defence of his habilitation and subsequent work at the University. In the same year of 1917, it was J Puzyna who initiated the creation of the Polish Mathematical Society in Lemberg. J Puzyna died in March 1919. Among those who studied with J Puzyn, in addition to H Steighaus, one can also note Otto Nikodym (Otto Marcin Nikodym: 1887-1974) and Antoni Łomnicki (Antoni Łomnicki: 1887-1941) ([34], p. 52).

Let us now return to 1896. In that year, Kazimierz Twardowski (Kazimierz Jerzy Skrzypna-Twardowski: 1866-1938), born in Vienna to a Polish family, received the position of professor at the University of Lemberg. He graduated from the University of Vienna, where he defended his doctoral dissertation in 1892 under the supervision of Robert Zimmermann (1824-1898) "On the Difference between Clear and Distinct Perception {= Perception} and Clear and Distinct Idea in Descartes". In 1894, he defended his habilitation "Zur Lehre vom Inhalt und Gegenstand der Vorstellungen" [Note 36], and after a year of teaching at the University of Vienna, he went to Lemberg.

Here he taught courses in philosophy and logic. His work "O tzw. prawdach względnych" (On the so-called relative truths) from 1900 is said to be the beginning of the birth of fuzzy sets. The circle of his students who defended their dissertations under his supervision includes future outstanding Polish philosophers and logicians [35]. Among them, Tadeusz Kotarbiński (1886-1981), the author of the new concepts of "reism" [Note 37] and "good work" in philosophy, Stanisław Leśniewski (1886-1939), the creator of mereology (the general part of ontology and applied logic), which found its application in the theory of artificial intelligence and in the creation of artificial languages [Note 38], and Jan Łukasiewicz (1878-1956), the creator of multi-valued logics [Note 39] [35], deserve special mention.

It is no coincidence that K Twardowski is called the "father" of Polish logic [36]. It is interesting that Stefan Banach (1892-1945) was also among those who wrote their doctoral dissertation under his supervision. However, a much greater role in the life of S Banach was played by Hugo Steinhaus (1887-1972), the son of a Jewish entrepreneur Bogusław Steinhaus (mother - Ewelina Lipszyc), who converted to Catholicism, from the town of Jasło (120 km southeast of Krakow). H Steinhaus graduated from high school in Jasło in 1905. He spent one academic year (1905/06) at the University of Lemberg, and then studied for five years in Göttingen, where he received his doctorate in 1911. In 1914/15 he was called up for military service and participated in World War I as part of the Polish Legions [Note 40]. In 1917, based on his work "On Some Properties of Fourier Series", he defended his habilitation at the University of Lemberg. In 1918, he published "Additive und stetige Funktionaloperationen" (Additive and Continuous Operators), the first Polish work on operators over functions.

From November 1918 to the summer of 1920, Steinhaus, having returned to Jasło, worked as a mathematician in the gas distribution bureau. In the summer of 1920, Hugo Steinhaus was offered the post of extraordinary professor of mathematics at Lviv University and the head of the First Department of Mathematics [39]. (He headed it until 1939).

In 1929, he founded (together with S Banach) the specialised journal "Studia Mathematica", which soon became one of the most authoritative international mathematical journals. In 1935, together with S Kaczmarz (Stefan Marian Kaczmarz: 1895-1939), he published the monograph "Theory of Orthogonal Series", which soon became world famous. In the same year of 1935, under the supervision of H Steinhaus, one of his favourite students, Marek Kac (1914-1984) [Note 41], began preparing his doctoral dissertation. After the arrival of the Red Army (in September 1939) and the entry of Galicia into the USSR, H Steinhaus was appointed head of the analysis department at Lviv University and, in addition, became a research fellow at the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR (in Kyiv).

On 29 June 1941, Lvov was occupied by the Germans. Many Polish professors were shot, not to mention the Jews. H Steinhaus hid in the vicinity of Lvov until the arrival of the Red Army. In 1945, he returned to Poland and headed the creation of a mathematical school in Wrocław, paying special attention to the applications of mathematics to various sciences. Dissatisfied with the generally accepted axiomatics of Kolmogorov, he began to develop the construction of probability theory based on the concept of independent functions, essentially close to the ideas (1917) of N S Bernstein (1880-1968) [40] (See also [41]). He was an internationally recognised mathematical educator - his popular book "Mathematical Kaleidoscope" (first published in 1938) was translated into more than 10 languages.

Two years older than H Steinhaus, Franciszek Leja (1885-1979) studied in 1904-1908 at the Faculty of Philosophy of the University of Lemberg. In 1909 he passed the exam for the right to teach mathematics and physics in secondary schools, and taught at the school until 1912. He spent the academic year 1912/13 on an internship in Paris. With the outbreak of World War I, he joined the Polish Legions. Since 1916, he became associated with the UJ, defending his doctoral dissertation there, and in 1924 - his habilitation. [Note 42] F Leja's main works were related to the theory of differential equations, the theory of topological groups, and the theory of analytic functions. F Leja was the author of the well-known textbook "Functions of a Complex Variable". [Note 43] [38], pp.389-390.

In the presentation of the biography of H Steinhaus, Stefan Banach was mentioned only once, but Steinhaus himself quite seriously called "his greatest discovery - the discovery of S Banach".

So, what do we know about Banach? This is not a rhetorical question, since S Banach himself learned about his origin only a year and a half before his death [42].

Stefan Banach was born in Krakow on 30 March 1892 in the St Lazarus Hospital and was baptised there. [Note 44] The baptismal certificate does not contain the father's surname, but it does contain the mother's first and last name: Katarzyna Banach, 25 years old, housekeeper. His father was Stefan Greczek (1867-1967), who at that time served in the Austrian army as an orderly for the same officer for whom Banach's mother worked as a housekeeper. Since soldiers in the Austrian army did not have the right to marry, S Banach's parents [Note 45] gave him to be raised by a childless laundry owner, Franciszka Plowa (18??-1927), for whom S Banach's mother had once worked. In Krakow, Banach graduated from high school (1910) and entered the Polytechnic Institute (in Lemberg), where he studied for 4 years until the beginning of World War I. S Banach spent the years 1914-1920 in Krakow. It was during this period that Steinhaus met Stefan Banach. Having received a chair at Lviv University in 1920, Steinhaus immediately approached S Banach with a proposal to become an assistant to the extraordinary professor A Lomnicki (Antoni Marian Łomnicki: 1881-1941) [Note 46] at the Polytechnic School, although Banach did not graduate from it. Banach accepted the offer, and in the same year he defended his doctoral dissertation at Lviv University [Note 47], and two years later (1922) he defended his habilitation there. In 1924, a department was opened at Lviv University especially for Banach, which he actually headed not only until 1939, but also in the period 1939-1941. In 1931, his famous "Theory of Operations. Vol. I. Linear Operations" was published in Warsaw in Polish, and a year later it was published in French.

A group of mathematicians formed around Banach, who began to intensively develop a new section of mathematics: functional analysis, not forgetting classical analysis, in particular the theory of functions of a complex variable and approximation theory. This group included S Mazur (Stanisław Mazur: 1905-1981), O Nikodym (Otton Marcin Nikodym: 1887-1974), J Schauder (Juliusz Pawel Schauder: 1899-1943), W Nikliborc (Władysław Michał Nikliborc: 1899-1948), A Zygmund (Antoni Szczepan Zygmund: 1900-1992), S Kaczmarz. (For more details, see [4] and [38], pp. 375-418).

Finally, it remains to write about the first creators of set-theoretic topology: Wacław Sierpiński, Zygmunt Janiszewski (1888-1920), Stefan Mazurkiewicz (1888-1945) and Kazimierz Kuratowski (1896-1980).

W Sierpiński was born in 1882 in Warsaw. In 1900, he graduated from high school and entered the Physics and Mathematics Department of the Imperial University of Warsaw (IUW), where his graduate (candidate's) thesis was supervised by G F Voronoy. In the 1904/05 academic year, Sierpiński was a teacher at a gymnasium in Warsaw, and was then accepted as a scholarship holder at the Warsaw Polytechnic Institute, "to prepare for a professorship." In 1906, he received a doctorate from the University of Krakow. He spent 1907 in Göttingen. From 1908, he began living in Lemberg; in 1908, he defended his habilitation there and began teaching at the local university. After the outbreak of World War I and the occupation of Lemberg by Russian troops, Sierpiński was interned, sent to Vyatka, but received permission to live in Moscow, where he collaborated extremely fruitfully with Luzin until the end of the war, developing problems in set theory. [Note 48]

He was one of the first to study the properties of sets, which were called fractal sets much later. The most famous of them is the so-called "Sierpiński gasket". [Note 49] In 1917 he was elected a corresponding member of the AU. At the end of 1918 he returned to Warsaw and in 1919 he was nominated for the post of full professor at the University of Warsaw (abbreviated, UW) and occupied the First Department of Mathematics. Together with Z Janiszewski he founded the mathematical journal "Fundamenta Mathematiсae", which received worldwide recognition. (The first issue was published in 1920). In 1921 he became a full member of PAU ([38], pp. 404-405). Before the beginning of World War II he published over 350 mathematical works, mainly in the field of set-theoretical topology [Note 50] [44].

Z Janiszewski, like Sierpiński, was born in Warsaw (in 1888). However, he was unable to complete high school in Warsaw due to the outbreak (in 1905) of a strike movement that also affected schools. He went to Lemberg, and there in 1907 he passed his final exams. Later he studied in Göttingen, Munich, Zurich and Paris. There, at the Sorbonne, he received a doctorate in 1911. [Note 51] In 1913, he returned to Lemberg and defended his habilitation. With the outbreak of World War I, he was at the front in the ranks of the Polish Legions. In December 1916 he returned to the University of Lemberg, formally remaining attached to the Polish Legions. [Note 52] It was at this time (in the spring of 1917) that he wrote a 6-page article [45], which became a programme for the development of Polish mathematics until 1939. [Note 53] Having refused to "take the oath of allegiance", Z Janiszewski hid from the summer of 1917 until June 1918, when he was hired by the University of Warsaw (UW). In April 1919 he was appointed, albeit as an extraordinary professor at UW, but with the receipt of the Second Department of Mathematics. Together with Sierpiński's student Stefan Mazurkiewicz, he conducted the first seminar on topology. At the same time he began (together with Sierpiński) to prepare material for the first issue of the journal "Fundamenta Mathematicae". The journal was published in 1920, but Z Janiszewski never saw it; he died suddenly in Lvov on 3 January 1920. [38]

Stefan Mazurkiewicz was born in Warsaw in 1888. He studied at a gymnasium until 1905. Due to the school strike that had begun, he transferred to the private school of Pavel Chrzanowski (1846-1914) [Note 54], from which he graduated in 1906. Since private schools did not grant the right of admission to universities in Austria-Hungary, S Mazurkiewicz went to Krakow and passed his final exams at one of the gymnasiums. He initially began studying at the philosophy department of the University of Krakow, continuing his studies at the universities of Munich, Göttingen and Lemberg. Under the supervision of W Sierpiński, he defended his doctoral dissertation at the University of Lemberg in 1913. From 1915 to 1939 he taught at the University of Warsaw (UW); he defended his habilitation there in 1919. From 1920 he was an ordinary professor at UW. In 1922 he was elected a corresponding member of PAU for his work in set-theoretic topology. His results on the properties of sets of type G−δG-\delta - the intersection of a countable number of open sets - became classics of topology. S Mazurkiewicz was repeatedly elected dean of the Faculty of Natural Sciences and Mathematics. He died in June 1945 in a suburb of Warsaw ([38], p. 394, [44]).

The last person to be discussed in this work is Kazimierz Kuratowski, born in 1896 in Warsaw. [Note 55] After graduating from the private Polish gymnasium of P Chranowski in 1913, wishing to continue his studies in Britain, he went to Oryol (in western Russia), where he passed his final exams. In Glasgow, he entered the Polytechnic Institute, but was expelled before the end of the first semester, allegedly for non-attendance. [Note 56] K Kuratowski returned to Warsaw, and in August 1914, World War I began. After Warsaw was occupied by the Germans, they decided to open a Polish university in Warsaw. It began functioning in 1915, and K Kuratowski enrolled in its philosophy department. He studied mathematics at the UW for four years, and in 1921 he defended his doctoral dissertation, initially supervised by Z Janiszewski, and after his death by W Sierpiński. The dissertation, which consisted of two parts, contained in the first part an axiomatic definition of topology using closed sets, and in the second, based on the doctoral dissertation of Z Janiszewski, it solved the problems of irreducible continua (i.e. irreducible topological spaces that are both compact and connected). At the end of 1921, K Kuratowski defended his habilitation based on the solution of some problems in set theory posed by a number of Belgian mathematicians, in particular, Baron de La Vallée Poussin (Charles Jean de La Vallée Poussin: 1866-1962). K Kuratowski worked at the University of Warsaw (UW) until 1927, when he was appointed as a profesor in the Third Department of Mathematics at the Lviv Polytechnic. The Lviv period [Note 57] of K Kuratowski's life also includes the publication in Polish of the world-famous monograph "Topology", Vol. I (1933). [Note 58] From 1934 to 1952, Kuratowski was an ordinary professor at UW, simultaneously heading the Department of Mathematics. During World War II, he was in hiding, but participated in the work of the secret university. From 1945 he was a full member of PAU, and from 1952 a member of PAN.

In 1948-1968 he was the director of the Mathematical Institute of the Polish Academy of Sciences, and from 1968 until his death (1980) he was the Chairman of the Scientific Council of this Institute. From 1952 he was the editor-in-chief of the Bulletin of the PAN, and the editor and editor-in-chief of the journal Fundamenta Matematicae ([38], pp. 388-389, [44]). Among his many students, Samuel Eilenberg (1913-1998), Stanislaw Marcin Ulam (1909-1984), and Andrzej Stanisław Mostowski (1913-1975) deserve special mention.

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