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Od 25 maja 2018 roku obowiązuje Rozporządzenie Parlamentu Europejskiego i Rady (UE) 2016/679 z dnia 27 kwietnia 2016 r. oraz dyrektywy 95/46/WE ("RODO"). W związku z tym chcielibyśmy poinformować o przetwarzaniu Twoich danych oraz zasadach, na jakich odbywa się to po dniu 25 maja 2018 roku. Szczegóły znajdują się tutaj.

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Abstracts

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

 

WWI opened the door to a new phenomenon – the growth in the number of women studying at universities, and the growth of their significance in social and scientific environment. Our investigation will be devoted to the largely unknown and mostly forgotten history of female candidates of PhD degree in mathematics at the German University in Prague over its existence (1882–1945).
 
We plan the following deliverables: an analysis of the background to women’s studies in the Czech lands, a statistical overview of all PhD degrees in mathematics awarded at the German University in Prague, a survey of female doctoral procedures and an analysis of the social and historical background of their life stories, professional activities and fates of their families and relatives.

References:
[1] M. Bečvářová: Matematika na Německé univerzitě v Praze v letech 1882 až 1945 [Mathematics at the German University in Prague from 1882 until 1945], Karolinum, Praha, 2016 (Czech with the long English resume).
[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).
 
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Juozas Banionis (Vilnius), Samuel Dickstein and his publication on I.Domeyko‘s master‘s thesis at Vilnius university.
 
Samuel Dickstein  founded the journal Wiadomości Matematyczne in Warszaw  and in the years 1897-1939 he  edited and published 47 volumes . In one of them (XXV volume, 1921) was presented the Scientific Work (Thesis) of famous 19th century scholar and teacher  -  Ignacy Domeyko (1802-1889), which was written in 1822 in order  to obtain a Master's degree in Philosopy at the University of Wilno ( now Vilnius).
 
According to S. Dickstein's publication, this report will introduce the master theses written by I. Domeyko, which will reveal the circumstances and content of the work.
 
Keywords: S. Dickstein, I. Domeyko, Master Thesis, mathematics, exhaustion method, differential calculus, metaphysics.
 
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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)
 
In the period 1891-1914 in Göttingen lectures courses and seminars were counduacted by outstanding mathematicians: Klein, Hilbert, Schwarz, Minkowski, Landau and Runge. In those time nine young Poles, fellows of the Academy of Learning in Kraków and the Jagiellonian University, were studying in Georg-August University and were attending some of those courses and seminars. We are going to present extracts from the reports written by them and make an analysis of surprising information included in their reports.

Moreover, we will present basic facts about Gałęzowski, Kretkowski and Klimowski Funds supporting studies of young Poles abroad.
 
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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
 
Вопрос об актуальной бесконечного оказался одним из центральных как в творчестве математика академика Н.Н. Лузина, так и богослова,  философа и естествоиспытателя отца Павла Флоренского. Один подходил к ней как математик, другой с позиций богословия. Результатом стала дискуссия, обнаружившая их кардинальное расхождение во взглядах.  Если Флоренский безоговорочно встал на позицию Г. Кантора, то Лузин оказался среди сторонников Э. Бореля, не принявших свойственного Кантору свободного обращения с актуальной бесконечностью и признававших «право гражданства» в математике лишь объектов, допускающих эффективное построение. Так объектом их критики стал канторовский несчётный континуум: множество эффективно конструируемых (то есть реально существующих !) вещественных чисел счётно.
 
Infinity in mathematics and in theology: to the discussion of academician N.N. Luzin and father Pavel Florensky
 
The question of the actual infinite turned out to be one of the central issues in the work of the mathematician academician N.N. Luzin and of the theologian, philosopher and naturalist father Pavel Florensky. One approached it as a mathematician, the other from the standpoint of theology. The result was a discussion that revealed their fundamental divergence of views.  If Florensky unconditionally accepted the position of G. Cantor, then Luzin was among the supporters of E. Borel, who did not accept free circulation with actual infinity inherent to Cantor and recognized in mathematics only the objects allowing effective constructions.  So the Cantor uncountable continuum became the object of their criticism: the set of effectively constructed (that is for them really existing!) real numbers is countable.
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Stanisław Domoradzki (University of Rzeszów), Małgorzata Stawiska (American Mathematical Society), Mykhailo Zarichnyi (University of Rzeszów),Mathematical center and other scientific centers in Lvovbefore WWII.
 
In the talk we will discuss the process of forming a mathematical center in Lvov taking into account various relationships with the then developing scientific centers: philosophical, logical, physical, astronomical, medical, chemical, statistical,  cartographic, and others.
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Roman Duda (Wrocław), Formation of national mathematical communities in the Central-Eastern Europe
 
In the XIX and XX centuries the Central-Eastern Europe was the scene of reviving some old and emerging new nations, identified by their languages. Main task of their activists was to adapt the language to modern needs, in particular raising national mathematical terminology to the level fit of teaching and doing research. The process is of tremendous cultural importance. It does widely promote understanding mathematics, while on the other hand it also allows its development by using different language tools. An important problem of intercommunication of researchers using  different languages is solved practically by refering to one of a few internationally recognized languages. The aim of this article is make a review of the hitherto existing research of that process.
 
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Marzena Fila, Definitions of continuous function from Bolzano to Russell
 
We study various definitions of continuous function given in mathematics throughout the 19th century: starting   with  (Bolzano, 1817) and (Cauchy, 1821), through   (Weierstrass, 1988), (Heine, 1872), (Dedekind, 1872), (Stolz, 1885),  (Dini, 1892), to (Whitehead & Russell, 1910-1913).  We focus on how  requirements given first in natural languages  have  finally reached a symbolic  form presented  in Principia Mathematica, § 234. To this end, we employ a formalization method that consists of  rewriting sentences specified  in natural languages  into formulas (symbolic characters). The main concern during the formalization is to assure equivalence of the final translation and the original.
 
Explicit definitions of continuity are but a  starting point in our search for an adequate formula for continuous function. We also examine proofs which employ definitions of continuity, as well as examples of continuous and discontinuous functions provided by the discussed authors. We show that a notion of discontinuous function is by no means a negation of continuous function. We show that the final  definition of continuous function as written in symbols captures  the notion of continuity exploited in proofs, rather than a linguistic form of the discussed definitions.
 
References:
  1. 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.
  2. Cauchy, A. (1821), Cours d’Analyse, Paris.
  3. Dedekind, R. (1872), Stetigkeit und irrationale Zahlen, Braunschweig.
  4. Dini, U. (1892), Grundlagen für eine Theorie der Functionen einer verӓnderlicher reellen Grӧsse, Leipzig.
  5. Heine, E. (1872), Elemente der Functionenlehre, Journal für die reine und angewandte Mathematik 74, 172-188.
  6. Stolz, O. (1885), Vorlesungen über allgemeine Arithmetik. Nach den neueren Ansichten, Leipzig.
  7. Whitehead A. & Russell B. (1910-1913), Principia Mathematica, Cambridge.
  8. 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).
 
The traditions of seminars in Lvov University begins in the second half of the 19th century, since 1852 the philosophical-historical seminar was initiated. The mathematical seminar was organized on the basis of a decision of the Austro-Hungarian Ministry of Religion and Public Education on 1 December 1893.

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. 
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Romualdas Kašuba (Vilnius), The art of arithmetics and the mystique of the solution.
 
Mathematics or, modestly speaking, the temple of beauty and perfectness, is huge and nice. In that temple you might serve as a servant who is sometimes able to present a small part of the whole – that is, to show how to understand the arithmetical problem. If successful, that understanding shows the way to the answer.
 
Sometimes the problems in front of you are not difficult but might require an elegant solution, or they might stump you for a bit, or just remain a mystery.
 
In my opinion, a nice arithmetic problem is a remarkable unit where, after understanding what is to be done, you find a way to achieve it without an absurd effort on your part.
 
As an example of such a task let us consider the problem. Each point in the plain is colored by one of two colors – white or red and both colors are present. Prove that there exist two points of different colors the distance between which is (exactly) 1 (or 2019).  

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
 
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Roman Murawski (Poland), Mathematics and mathematicians in Polish encyclopaedias (1910−1940).
 
In 1918 Poland regained its independence after the 125 year period of partitions when the country was under Prussian, Russian and Austro-Hungarian rule. The state and its institutions, in particular the whole system of science and education should be restored. The period 1918−1939 was the time of an intensive development of mathematics – one should mention here Polish School of Mathematics with two main centres: Warsaw and Lvov. Also logic and (analytic) philosophy have been developed (Lvov-Warsaw School of Philosophy and Warsaw School of Logic).
 
This development found its reflection also in the domain of encyclopedias. In the interwar period there have been published in Poland nine universal encyclopedias and a number of subject and thematic ones. Our aim is to consider which place have found mathematics in them and how it was presented. We shall pay also attention to  the presentation of logic − as Poland was at that time one of the most important centres of it. Special attention will be paid to a specific publication Guide for Autodidacts which had an encyclopedic character.

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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.

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Zdzisław Pogoda (Kraków, Jagiellonian University), Some remarks about the Wilkosz's book on the topology of the plane.
 
Witold Wilkosz (1891-1941), a professor at the Jagiellonian University, was known for his varied interests. He is also the author of a book on topological properties of the Euclidean plane. During the lecture we will discuss selected facts from Wilkosz's book. We will also present the figure of this  talented mathematician. 
 
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Antonín Slavík (Prague), The interplay between graph theory and other mathematical disciplines in the work of Dénes König.

 

The Hungarian mathematician Dénes König (1884-1944) is well known for his landmark contributions to graph theory, including the authorship of the first textbook in this field. In this talk, we point out that some of König's graph-theoretic results were closely connected with (or even motivated by) problems in other mathematical disciplines, such as set theory, linear algebra, or recreational mathematics.
 
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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. 

 

 

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