**Karl Sundman** was a Finnish mathematician who used analytic methods to find a solution to the three-body problem.

- Karl's health was poor as he was growing up and he certainly did not have a very easy time studying on his own without a teacher so that he could take the baccalaureate examinations, which he did on 18 May 1893.
- After qualifying to enter university, Sundman went to Helsinki (Helsingfors) where he began his studies in the autumn of 1883.
- The University was an ancient one, founded in 1640, and there Sundman excelled academically although he had to battle against financial difficulties.
- After graduating Sundman went to Pulkovo Observatory to continue his research on astronomy.
- Sundman, however, was interested in the theoretical aspects of astronomy.
- In this work Sundman examined the perturbations of minor planets whose period of revolution round the sun is in the ratio of 1:2 of that of Jupiter.
- In 1902 Sundman was appointed as a lecturer at the University of Helsinki, being promoted to extraordinary professor of astronomy there in 1907.
- The most famous contribution of Sundman was his solution of the three-body problem which he accomplished using analytic methods to prove the existence of an infinite series solution.
- In 1913 the Academy of Sciences in Paris awarded Sundman their Pontécoulant prize for his outstanding work on this problem.
- One of the reasons why the Academy was so impressed by Sundman's solution was that it was a problem to which Henri Poincaré had devoted much effort.
- To regularize the singularity of the differential equations of motion, in the 1912 paper mentioned above, Sundman introduced a new independent variable which regularizes the motion within a band of finite breadth.
- it is possible to show the existence of two different research programs, one related to Levi-Civita's works, the other to Sundman's investigations, which include for the first time a complete regularization of the three-body problem.
- Sundman will always be known for his remarkable solution to the extremely difficult three-body problem, but he did other important work.
- Such a machine will necessarily be very complicated and Sundman describes the project in detail using well-known techniques and construction capabilities in a field unrelated to astronomy.
- In the 1940 paper Sundman gave a new and elegant demonstration of the theorem of Poisson on the invariability of the major axes of the planetary orbits which had been demonstrated in several ways.
- This last statement suggests that Sundman may not have been pleased had he realised that 60 years after his death a biography describing his remarkable achievements would be placed on the web!

Born 28 October 1873, Kasko, Vaasa, Finland. Died 28 September 1949, Helsinki, Finland.

View full biography at MacTutor

Astronomy, Origin Finland

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive