**Poul Heegaard** was a Danish mathematician who (with Max Dehn) was the first to classify compact surfaces.

- At this stage Heegaard decided that he would benefit for international experience and received a stipend to support a year's study abroad.
- It has often been assumed that Heegaard's interest in Poincaré's work started in Paris.
- In order to support himself while working on his dissertation, Heegaard took a number of jobs teaching in high schools as well as undertaking some tutoring at the Polytechnic Institute.
- Heegaard submitted his dissertation Forstudier til en topologisk Teori for de algebraiske Fladers Sammenhaeng Ⓣ(Preliminary studies towards the topological theory of connectivity of algebraic surfaces) and successfully defended it in 1898.
- His friends encouraged him to apply for Thiele's chair of astronomy following his retiral in 1906 but Heegaard knew he lacked the necessary experience as an astronomer so did not apply.
- Another important mathematical contribution by Heegaard is his 1907 survey article (with Max Dehn) Analysis Situs where the authors set out the foundations of combinatorial topology.
- After his dissertation, Heegaard taught at various military schools in the Copenhagen area for more than 10 years.
- Many of Heegaard's friends encouraged him to apply but he was reluctant since he had little in the way of publications and he could not see how he could survive financially if appointed since the salary was only a fifth of the income he had at the time from his various posts.
- Reports in the Danish Press at the time suggest that Heegaard's resignation may have had something to do with Harald Bohr, who was a professor at the Polytechnic Institute and wanted a position at the more prestigious University of Copenhagen.
- Shortly after his resignation, Heegaard received an offer from the University of Kristiania (now Oslo) in Norway.
- Lie's papers appeared in six volumes, edited by Heegaard and Friedrich Engel, with extensive annotations by the editors.
- Engel did most of the editorial work on Volumes 3 to 6 while most of the work on Volumes 1 and 2, covering Lie's geometric work, was done by Heegaard.
- Often Heegaard's annotations are twice the length of Lie's original articles.
- This work led Heegaard to publish three papers generalising ideas in Lie's papers.
- At this time Heegaard was dean of the faculty of mathematics and natural science and he played a large role in the Congress.
- Heegaard represented the rector of the university at a reception held in the Aula for the participants and their families on the evening of Monday 13 July.

Born 2 November 1871, Copenhagen, Denmark. Died 7 February 1948, Oslo, Norway.

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Astronomy, Origin Denmark, Topology

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