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Wrocławska szkoła matematyczna

Duda R., Weron A.

Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne

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2006

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[Z] 42

73-101

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Nieznane mowy Jana Śniadeckiego z lat 1784-1785

Wiąsław W.

Kwartalnik Historii Nauki i Techniki

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2005

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R. 50, nr 3/4

149--182

EN

The paper contains three lectures presented by Jan Śniadecki during scientific sessions held at the University of Cracow, then called the Main School of the Kingdom of Poland. Lecture One (1784): On the necessity of higher mathematics in understanding and perfecting physics. Lecture Two (read on 13 May 1785): On applications of mathematical sciences in the advancement of physics. Lecture Three (only an outline): On applying mathematics in physics. In these interesting lectures, Śniadecki pointed to the role of probability and statistics in conducting experiments, as well as the role played by logic where experiments were not necessary and where the results of one series of experiments needed to be verified by another. He mentioned astronomy, hydrodynamics and mechanics as those scientific domains in which mathematical analysis (calculus) was necessary. Śniadecki also stressed the essential role of differential equations in the physical sciences. It has been known from documents in the Archives of Jagiellonian University in Cracow that Śniadecki did lecture on the role of mathematics in physics in the years 1784-1785, but his manuscripts have so far been thought to be lost. In fact, six volumes of hitherto unknown manuscripts by Jan Śniadecki were kept in the years 1842-1986 in Russian, and then Soviet archives. They were returned to Vilnius (Wilno) in the late 1980s, and are now kept at the Historical Archives of Vilnius.

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Pietro Mengoli szeregi liczbowe prehistoria funkcji ζ Riemanna

Maślanka K.

Kwartalnik Historii Nauki i Techniki

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2004

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R. 49, nr 1

47--64

EN

The article deals with the work of the 17th-century Italian mathematician. Rev. Pietro Mengoli (1625-1686), who was the forerunner of research on numerical series.The legacy of Mengoli, a scientist well-known and well respected in Italy, but almost altogether forgotten in the West, has never been thoroughly analyzed in Polish historical writing. Yet it was Mengoli who first posed a number of problems related to finding the sums of an infinite number of fractions. He solved most of those problems, but he failed in one case - in the case of the sum of the inverse of squares of successive natural numbers. For fundamental reasons, which had not been understood until several dozen years later, Mengoli was unable to find a compact expression for the sum of this series. He himself, with a humility rarely found in the history of science, admitted that this problem required a "richer intellect". This series turned out to be the first example of a fundamental function investigated later by Euler and Riemann, and called, in honour of the latter mathematician, the Riemann ζ (dzeta) function. This function constitutes the key to solving one of the greatest mathematical puzzles of all times - the distribution of prime numbers. Connected with this riddle is also the most important and most difficult of the hitherto unsolved problems of the famous list presented in 1900 by Hilbert at the 2nd International Mathematical Congress in Paris, the Riemann hypothesis. The generalizations of the series considered by Mengoli continue to be researched by mathematicians today. The aim of the article is to show, on the example of Mengoli’s achievements and failures, a general regularity: the solution of a given mathematical problem is the result of the subtle interplay between, on the one hand, the scientists’s knowledge, talent and effort, and, on the other, the level of general knowledge at a given time, which stems from the collective achievements of many previous generations of mathematicians.

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Matematyka wileńska za czasów Adama Mickiewicza : personalia

Więsław W.

Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne

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2003

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[Z] 39

117-149