The dramatic episode of Sundman
type: Item
instance of: scholarly article
title: The dramatic episode of Sundman
zbMATH Open document ID: 1193.01037
author: June Barrow-Green
published in: Historia Mathematica
publication date: 2010-05-31T00:00:00Z
full work available at URL: Sundman final.pdf
review text: 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 consider…
reviewed by: Horst-Heino von Borzeszkowski
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 70-03
Mathematics Subject Classification ID: 70F07
Mathematics Subject Classification ID: 34-03
zbMATH DE Number: 5714282
zbMATH Keywords: Karl Sundman
zbMATH Keywords: three-body problem
zbMATH Keywords: Ernst Lindelöf
zbMATH Keywords: Gösta Mittag-Leffler
zbMATH Keywords: Finland
MaRDI profile type: Publication
Wikidata QID: Q29999793
OpenAlex ID: W2029232438
cites work: Q4174811
cites work: Q5687997
cites work: Q4544174
cites work: Q5557227
cites work: Some Recent Results in the Problem of Three Bodies
cites work: Q4287093
cites work: Painlevé's conjecture
cites work: Q3931217
cites work: Q5843404
cites work: Karl F. Sundman in memoriam
cites work: Q5822045
cites work: Karl Frithiof Sundman's investigations in celestial mechanics. I: The astronomer Sundman
cites work: Q4483998
cites work: Mathematics Without Borders
cites work: Ernst Lindelöf in Memoriam [March 7, 1870 in Helsingfors (Helsinki) -- June 4, 1946 in Helsinki]
cites work: Q4947470
cites work: Q4174817
cites work: A Visit to the Newtonian N-Body Problem via Elementary Complex Variables
cites work: Q3023963
cites work: On the Modern Development of Celestial Mechanics
cites work: Q4070368
cites work: Rockefeller and the internationalization of mathematics between the two world wars. Documents and studies for the social history of mathematics in the 20th century
cites work: Q5758976
cites work: Q2761415
cites work: Q3995849
cites work: The global solution of the n-body problem
cites work: Q4001463
cites work: Q5803187
DOI: 10.1016/J.HM.2009.12.004
description: scientific article; zbMATH DE number 5714282