Poul Heegaard
Who was Poul Heegaard?
Danish mathematician (1871-1948)
Biographical data adapted from Wikipedia’s article on Poul Heegaard (CC BY-SA 4.0).
Biography
Poul Heegaard was born on November 2, 1871, in Copenhagen, Denmark. He became an important figure in early topology. He attended Metropolitanskolen for his secondary education and then studied mathematics at the University of Copenhagen from 1889 to 1893. After traveling and teaching math for a few years, he earned his doctoral degree in 1898 with a thesis that would become key to the new field of topology, specifically in the study of three-dimensional manifolds.
In his 1898 dissertation, Heegaard introduced what's now called the Heegaard splitting, a way to break down a three-dimensional manifold into two connected pieces. This method allowed him to critique Henri Poincaré, a leading mathematician at the time. Heegaard pointed out that Poincaré had missed the potential for torsion in the homology groups of a space, an important detail. The thesis also included a section on representing complex points on algebraic surfaces, and it has been translated into English for those interested in the history of mathematics.
After years of research and teaching, Heegaard became a professor at the University of Copenhagen in 1910. While there, he and German mathematician Max Dehn wrote a substantial article on combinatorial topology for an encyclopedia, which helped lay the groundwork for the field. This collaboration with Dehn resulted in one of the key reference works in early twentieth-century topology.
Heegaard's time in Copenhagen ended after a dispute involving his opposition to hiring Harald Bohr as a professor. Due to these tensions, he accepted a professorship in Oslo, Norway, where he continued his academic work until his retirement in 1941. He passed away in Oslo on February 7, 1948.
In recognition of his work, Heegaard was made a Knight of the Order of the Dannebrog in 1918. In 1936, he was President of the Third International Congress of Nationalists at the Nobel Institute in Oslo, adding complexity to his legacy. His work, especially from his doctoral thesis, remains influential in modern mathematics.
Before Fame
Poul Heegaard grew up in Copenhagen in the late 1800s, a time when Scandinavian universities were closely following developments in European mathematics. He attended Metropolitanskolen, a well-known high school in Copenhagen, before starting university in 1889. The math scene at the University of Copenhagen was influenced by French and German traditions, which later played a crucial role in Heegaard's research.
After finishing his studies in 1893, Heegaard spent a few years teaching and traveling. This practical experience, along with his interest in analysis situs (now called topology), helped him create his important thesis in 1898. Poincaré's work, which Heegaard would later critique, was also quite new at the time, making Heegaard's contributions even more significant in the early development of the field.
Key Achievements
- Introduced the concept of Heegaard splitting in his 1898 doctoral thesis, providing a foundational tool for the study of three-dimensional manifolds
- Identified a significant oversight in Henri Poincaré's work on homology, specifically the omission of torsion in homology groups
- Co-authored a landmark encyclopedia article on combinatorial topology with Max Dehn
- Appointed professor at the University of Copenhagen in 1910, where he advanced the study of topology in Scandinavia
- Awarded Knight of the Order of the Dannebrog in 1918 for his contributions to mathematics
Did You Know?
- 01.Heegaard's 1898 doctoral thesis identified an error in Henri Poincaré's work by showing that torsion in homology groups had been overlooked, a correction that influenced the subsequent development of algebraic topology.
- 02.The concept of Heegaard splitting, introduced in his thesis, remains an active area of research in three-manifold topology more than a century after its publication.
- 03.Heegaard co-authored a major encyclopedia article on combinatorial topology with Max Dehn, a work that served as a standard reference in the field for decades.
- 04.His opposition to the appointment of Harald Bohr, brother of physicist Niels Bohr and a distinguished mathematician in his own right, contributed to Heegaard's departure from the University of Copenhagen.
- 05.Heegaard was awarded the Knight of the Order of the Dannebrog in 1918, one of Denmark's oldest orders of chivalry, in recognition of his academic contributions.
Family & Personal Life
Awards & Honors
| Award | Year | Details |
|---|---|---|
| Knight of the Order of the Dannebrog | 1918 | — |