The dramatic episode of Sundman
After two nearly unnoticed precursors in 1907 and 1909, in 1912 \textit{K. F. Sundman} [Acta Math. 36, 105--179 (1912; JFM 43.0826.01)] published in Acta Mathematica the final form of his solution of one of the most famous mathematical problems, namely that of the three-body problem. It was the solution in a form that mathematicians of the caliber of Poincaré had believed impossible to achieve. And, astonishingly, it was provided by a little-known mathematical astronomer working in comparative isolation in Helsinki. In the present paper the author traces Sundman's career, beginning with a discussion of mathematical environment in Finland in the 19th and early 20th centuries. This is followed by an outline of his career and a detailed consideration of the time he spent abroad prior to his first publication on the three-body problem. Afterwards, the author turns to the problem itself, first describing it and its significance and difficulty a description that is supported by references showing that, from Newton to Hilbert, there was little hope to solve it. It is shown that Sundman became interested in the solution of the three-body problem because it was a first step in the solution of the many-body problem which gave answer to the question of the stability of the solar system. Then the author discusses main features of the solution, in particular the facts that Sundman attacked the problem by considering triple as well as binary collisions and introduced an auxiliary variable by which the coordinates and the time were generalized to complex values. This discussion is followed by paragraphs on the circumstances in which Sundman produced his publications and on their reception by the scientific community. This article brings to light the involvement of Ernst Lindelöf and Gösta Mittag-Leffler in Sundman's research and professional development. The article ends with a short description of two of Sundman's later papers which in different but connected ways can be considered as complementary to his publications on the three-body problem.
scientific article; zbMATH DE number 5714282
scientific article