Poul Heegaard (1871 - 1948),

a home page, created by Ellen S. and Hans J. Munkholm.

Poul Heegaard was a professor of mathematics at Copenhagen University 1910 - 1917 and at Christiania (later Oslo) University 1918 - 1941.  Today he is best known for his contributions to the study of three-manifolds; in fact Heegaard splittings and Heegaard diagrams are household words in that area, unfortunately often with the name misspelled as Heegard or even Hegard.

In addition, many topologists will know that Heegaard gave a counter example to Poincaré's first formulation of his duality theorem, and that Heegaard and Dehn's article Analysis Situs (1907, in the Enz. der Math. Wissenschaften) marks the foundation of combinatorial topology

En biografisk artikel, Poul Heegaard (1871 - 1948), dansk - norsk topolog, af Ellen S. Munkholm og Hans J. Munkholm, findes her   i .html format. Den er næsten identisk med en artikel med samme titel, som er udkommet i NORMAT i 1998. Den har et noget andet sigte end den nedenfor omtalte engelsksprogede artikel.

A biographical article, Poul Heegaard,

by Ellen S. Munkholm and Hans J. Munkholm  appears in a volume on the history of topology, edited by Professor Ioan James for Elsevier. The .html file  of a preprint (with links to most of the illustrations) is available. So is the  .dvi file   (less the illustrations).  Five of the six illustrations from the preprint, as well as two auxiliary pictures, can be found here:

Figure 1 (from preprint). Picture from the obituary, by permission from the Norwegian Academy of Science and Letters.

Figure2 (from preprint). The first half page of Heegaard's Autobiographical Notes.

Figure 3 (from preprint). Poul Heegaard at his prime (unknown date). Original belongs to Lars and Rese Hjelle.

Figure 5 (from preprint). This photo of Poul Heegaard, and his father, Sophus Heegaard, was taken shortly after the death of Poul Heegaard's older sister, Henny. Original belongs to Lars and Rese Hjelle.

Figure 6 (from preprint) Poul Heegaard ("Bobo") as remembered by his granddaughter, Rese Hjelle. Original belongs to Lars and Rese Hjelle.

In 1917, the Danish tabloid Ekstrabladet had several articles about a feud between Harald Bohr and Poul Heegaard. This picture shows the text of one of these articles (in Danish) and an accompanying  cartoon of Harald Bohr who was a soccer player of a national reputation.

This shows the front page of a periodical that was published in Oslo 1941 - 45. In vol. 4, issue 2, one finds an article by Poul Heegaard on his genealogical interests. 

Heegaard's Autobiographical Notes (in Danish)

In preparation for the article Poul Heegaard, the authors searched the Internet for relatives of Poul Heegaard. One of the relatives found this way, Poul E. Heegaard, Trondheim, turned out to have in his possession roughly 130 pages of handwritten notes that were written (in Norwegian) by Poul Heegaard in 1945 and intended as a family history for Heegaard's children and grandchildren. The above link takes you to a transcript (in Danish) of the notes. 

Heegaard's radio causeries

In 1944 - 45, Heegaard gave a series of radio causeries on Naturvitenskabens høvdinger (The Chiefs of Natural Science) in the Norwegian Radio NRK. The manuscripts for this series have been preserved by Poul Heegaard's granddaughter, Rese Hjelle. To appreciate the effect of such a series on the contemporary Norwegian Society, one may take a look at two excerpts from Hans Frederik Dahl: Dette er London, NRK i krig 1940 - 45. On p. 309, one finds a government order from 1941 to hand in to the local authorities all privately owned radio sets. For the rest of the occupation period, radios were allowed only in those households which had a paid subscription to the official paper Fritt Folk and where a majority of the people were members of the Nazi party. The second excerpt, from p. 315, records the official number of NRK listeners in 1944 as 13,902, just around 2 % of the prewar figure of 650,000.
A list of the scientists portrayed in the series is on p. 2 of Heegaards radioforedrag i NRK, 1944 - 45 (in Danish).
The introductory paragraphs of the manuscripts concerning daVinci and Kant are available. On the back of the latter manuscript, Heegaard had penciled a brief submission note to the Norwgian radio, signed with the official Nazi signature Heil og sæl. 

Heegaard and  knot theory

Heegaard's work on three-manifolds, mentioned above, led him to a study of knots. This aspect
of his work has been studied by  Jozef Przytycki  in a  preprint from IMADA, Odense University.
In connection with this work,  Agata Przybyszewska  translated  a  part of Heegaard's dissertation into English.

Naturvidenskabens Stormænd indtil det attende Aarhundrede

In 1947, Heegaard revised the manuscripts for the above mentioned radio causeries to form the backbone of a manuscript (in Danish) ``Great Men of Natural Science until the Eighteenth Century''. The above link takes you to a transcript of the manuscript. In it, Heegaard has reproduced a drawing, made by one of his students, showing Pythagoras before and after his main discovery. 

Travelling in Finmarken

In March and April of 1920 Poul Heegaard went on a long trip to the Northernmost parts of Norway to give popular lectures on astronomy in several places, including the town of  Kautokeino . He has described this experience in a series of letters (in Danish) to his friend, High School Principal Karl Hude, Hillerød, Denmark. The letters were published as an irregular serial entitled ``Paa Reise til Finmarken'' by the local newspaper Frederiksborg Amts Avis during the months of May and June 1920. We have not found the date of the first letter; the last one appears in the newspaper on June 19, 1920. In the  autobiographical notes, Heegaard mentions the tour in section 19.9, and an anecdote from there is included in the above mentioned preprint. 

Poul Heegaard in the MacTutor History of mathematics archive
Last modified: March 29, 1999 

Hans J. Munkholm <>