Probability in 1919/20: the von Mises-Pólya-Controversy |
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Authors: | Reinhard Siegmund-Schultze |
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Institution: | (1) Faculty of Sciences, Agder University College, N 4604 Kristiansand |
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Abstract: | The correspondence between Richard von Mises and George Pólya of 1919/20 contains reflections on two well-known articles by
von Mises on the foundations of probability in the Mathematische Zeitschrift of 1919, and one paper from the Physikalische Zeitschrift of 1918. The topics touched on in the correspondence are: the proof of the central limit theorem of probability theory, von
Mises' notion of randomness, and a statistical criterion for integer-valuedness of physical data. The investigation will hint
at both the fruitfulness and the limits of several of von Mises' notions such as ``collective', ``distribution' and ``complex
adjuncts' (characteristic functions) for further developments in probability theory and in ``directional statistics'. By
pointing to the selectiveness of Pólya's criticism, the historical analysis shows the differing expectations of the two men
with respect to the further development of the theory of probability and its applications. The paper thus gives a glimpse
of the provisional state of the theory around 1920, before others such as P. Lévy (1886–1971) and A. N. Kolmogorov (1903–1987)
stepped in and created a new paradigm for probability theory. |
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