# Abstracts

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**Martina Bečvářová** (Prague), *Female Candidates of Doctorates in Mathematics at the German University in Prague.*

References:

[2] M. Bečvářová: Doktorky matematiky na univerzitách v Praze 1900–1945 [Female Doctors in Mathematics at the University in Prague 1900–1945], Karolinum, Praha, 2019 (Czech with the long English resume).

**Juozas Banionis**(Vilnius),

*Samuel Dickstein and his publication on I.Domeyko‘s master‘s thesis at Vilnius university.*

**Piotr Błaszczyk**(Kraków),

*WHERE THE MODERN CONCEPT OF MATHEMATICAL PROOF COMES FROM*

**Danuta Ciesielska**, (L.&A. Birkenmajer Institute for the History of Science, PAS Warsaw, dciesielska@ihnpan.waw.pl, https://orcid.org/0000-0002-3190-5617),

*Fellows of the Academy of Learning and the Jagiellonian University studying mathematics in Göttingen (1891-1914)*

Moreover, we will present basic facts about Gałęzowski, Kretkowski and Klimowski Funds supporting studies of young Poles abroad.

**Sergey S. Demidov**(president of International Academy of the History of Science; M.V. Lomonosov Moscow State University),

*Бесконечность в математике и богословии: к дискуссии академика Н.Н. Лузина и отца Павла Флоренского*

*Infinity in mathematics and in theology: to the discussion of academician N.N. Luzin and father Pavel Florensky*

**Stanisław Domoradzki**(University of Rzeszów),

**Małgorzata Stawiska**(American Mathematical Society),

**Mykhailo Zarichnyi**(University of Rzeszów),

*Mathematical center and other scientific centers in Lvovbefore WWII.*

**Roman Duda**(Wrocław),

*Formation of national mathematical communities in the Central-Eastern Europe*

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**Marzena Fila**, Definitions of continuous function from Bolzano to Russell

**References:**

- Bolzano, B. (1817), Rein analytischer Beweis des Lehrsatzes, daß zwischen je zwei Werthen, die ein entgegengesetzes Resultat gewӓhren, wenigstens eine reelle Wurzel der Gleichung liege, Prague.
- Cauchy, A. (1821), Cours d’Analyse, Paris.
- Dedekind, R. (1872), Stetigkeit und irrationale Zahlen, Braunschweig.
- Dini, U. (1892), Grundlagen für eine Theorie der Functionen einer verӓnderlicher reellen Grӧsse, Leipzig.
- Heine, E. (1872), Elemente der Functionenlehre, Journal für die reine und angewandte Mathematik 74, 172-188.
- Stolz, O. (1885), Vorlesungen über allgemeine Arithmetik. Nach den neueren Ansichten, Leipzig.
- Whitehead A. & Russell B. (1910-1913), Principia Mathematica, Cambridge.
- Wierestrass, K. (1988), Ausgewählte Kapitel aus der Funktionenlehre, Leipzig.

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**Olena Hryniv**,

**Yaroslav Prytula**(Lviv),

*The Mathematical Seminar at the Lvov University (1894 – 1918).*

There were two parts: higher seminar and lower seminar. The heads of seminars were Józef Puzyna, Jan Rajewski, Marcin Ernst, Wacław Sierpiński in different years.

In our talk we will discuss the themes of works written by the members of the seminar, the seminar works which became doctoral and persons who wrote chronicles of the seminar. The biographies of members of the seminars will be described as well.

**Romualdas Kašuba**(Vilnius),

*The art of arithmetics and the mystique of the solution*.

As human beings, we can still be impressed by something in the physical world or by new constructions of the mind. That sense of discovery seems to be inexhaustible. One of the most classical examples of that (at least, in the field of mathematics) is the fact that the set of all primes is infinite.

As educators, we are very eager to believe that the set of acceptable arithmetical problems, solving of which showcases the complex beauty of finishing a challenging task, finding the unexpected approach and the elegant journey to solution is inexhaustible as well.

During the long years of attractive problem posing and solving the author used not only his mother tongue but also boldly tried you use other accessible languages – between them not only English and Russian but also German and Polish as well.

That usage of a language different from the mother tongue provides not only some unavoidable tension but also develops inventiveness and other highly useful human qualities and in fact is also a source of a real satisfaction – the felling which is naturally very well-known also by all simultaneous translators.

References:

[1] Kašuba R. (2017) From the Lifetime Experience of a Seasoned Math Educator—Thoughts, Hopes, Views and Impressions. In: Soifer A. (eds) Competitions for Young Mathematicians. ICME-13 Monographs. Springer, Cham, p. 271 - 301

**Roman Murawski**(Poland),

*Mathematics and mathematicians in Polish encyclopaedias (1910−1940)*.

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**Christine Phili** (Athens xfili@math.ntua.gr), *On the special character regarding the development of mathematics in Greece during the 19th century and the beginning of the 20th century*.

Under Ottoman rule Greece at the periphery of Europe struggles to gain its cultural identity. Before the proclamation of the War of Independence in 1821 many mathematical textbooks were published in Greek in Europe. Later when Greece won its independence, the establishment of the Military School(1829), of the University of Athens (1838), as well as this of the Polytechnic School( 1838) contributed to the development of mathematics in Greece.

**Zdzisław Pogoda**(Kraków, Jagiellonian University),

*Some remarks about the Wilkosz's book on the topology of the plane.*

**Antonín Slavík **(Prague), *The interplay between graph theory and other mathematical disciplines in the work of Dénes König*.

**Jan Woleński** (Kraków), *SAMUEL DICKSTEIN AND THE FOUNDATIONS OF MATHEMATICS*

Inspecting mathematical textbooks published in Poland in the 2nd half of the 19th century, we can find no remarks concerning the foundational problems. This situation documents that Polish mathematicians were not interested in such problems. This attitude changed due to activities of Samuel Dickstein. His role in the growing foundational interests in Poland was twofold. Firstly, Dickstein, as the editor of journals and series of books, popularized the foundations of mathematic in Poland. In particular, he inspired translating into Polish works of such mathematicians as Riemann, Helmholtz, Dedekind and others. Secondly, he published a book “Notions and Methods in Mathematics 1” (the projected next parts of this works did not appear) intended as the general treatise of basic concepts of mathematics. In this work, Dickstein critically review the current literature in the foundations of mathematics. Among other things, he quoted Frege and included a brief outline of set theory. Although Dickstein was influences by Hoene-Wroński’s very speculative philosophical ideas, he also tried to make technical developments in the foundations of mathematics independent of declared philosophy. In this sense, Dickstein can be viewed as a predecessor of typical attitude of Polish mathematical school that the technical side of mathematics is to be independent of philosophical assumptions.

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**Wiesław Wójcik **(Jan Dlugosz University in Czestochowa ), The work of Samuel Dickstein over the reception of the thoughts of Józef Maria Hoene-Wroński

One of the most important achievements of Samuel Dickstein as a historian of science and a mathematician is the presentation of the character of Hoene-Wroński and the analysis of his mathematical achievements. In 1896 a monograph Hoene-Wroński. Jego życie i prace was published, in which he faced showing the phenomenon of the figure of a great Polish scholar. At the same time, it was an attempt to embrace the scientific (especially mathematical) legacy of the Polish mathematician and philosopher, as well as to encourage others to undertake further work in this direction. Since the 1980s, Dickstein publishes a whole series of works devoted to the most important mathematical achievements of Hoene-Wroński. This is a part of his project of bringing closer the achievements of Polish mathematics. This caused that many Poles took up mathematics and exact sciences. The activity of Samuel Dickstein, not only as an outstanding publisher, organizer and popularizer of science, but also as a historian of mathematics and a mathematician, was significant for the creation of the Polish Mathematical School. In the article I would like to deal with this aspect of his scientific activity and highlight how he showed and built the continuity of the development of Polish mathematical thought.

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**Ewa Wyka** (L & A Birkenmajer Institute for the History of Science Polish Academy of Science, Warsaw Jagiellonian University Museum, Cracow), Instruments and didactic models in mathematics

The main goal of this paper will be the presentation of the evolution of instruments, which today we broadly understand as "mathematical". Historically, this name was used until the 18th century to describe a group of instruments, which, in their construction allowed for the conversion of various quantities. In today's meaning, under this term such instruments as drawing, calculation and didactic models are understood. Taking examples from Polish museums` collections the basic constructions of historical mathematical instruments and models will be presented.

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**Joanna Zwierzyńska** (Poland), PhD in mathematics in Göttingen ca. 1900 and its impact on further scientific career (joint work with Danuta Ciesielska)

Ca. 1900 Göttingen was undoubtedly one of the most important and prestigious scientific centres in the field of mathematics. Studying there was a dream - and a goal - of many young people. Several of them were able not only to study in Göttingen but also to earn there a PhD in mathematics.

What impact had a PhD in Göttingen on future scientific careers? We will discuss the case, showing examples of five Polish scientists who received their PhD in mathematics and its applications in Göttingen, between 1893 and 1922. Their supervisors were world-renowned scientists: Wilhelm Lexis, David Hilbert, Waldemar Voigt, and Edmund Landau. We will discuss their future careers and the impact of earning a PhD in Göttingen in their lives. Our talk will be based on many documents from archives in Germany, Poland, and Latvia, among others PhD thesis reviews, self-written CVs and PhD thesis.