The Danish Mathematical Society, named Dansk Matematisk Forening, was founded in 1873. It was not founded as the 'Danish Mathematical Society' but rather as the 'Mathematical Society'. The initiative for the creation of the Society came from Thiele and the first Board set up to run the Society consisted of Thiele, Zeuthen and Petersen. The original aim of the Society, as drawn up by the Board, was to (see for example ):-
... promote a vivid cooperation for the benefit of the science of mathematics and its practical applications.
Later a further aim was added, to:-
... benefit the teaching of mathematics.
At this stage the Society was associated entirely with the University of Copenhagen. All the three Board members were professors at the University of Copenhagen at the time the Society was created: Zeuthen had appointed as an extraordinary professor of mathematics in 1871; Petersen held the chair of mathematics; and Thiele was professor of astronomy. The Society arranged lectures but at first these were all given by members of the Society. It also built up a library of books and journals to help mathematical research in Denmark.
The first foreign speaker to the Society was Mittag-Leffler in 1900. The number of foreign speakers then grew and from 1921 an invitation was given every second year to a leading mathematician to give a series of lectures. The first series was given in 1921 by Hilbert. The outbreak of World War II caused this lecture series to stop. In this same year of 1921 the Society discussed whether it should join the International Mathematical Union, but there was strong opposition since the Union was actively discriminating against mathematicians from countries on the losing side in World War I. Harald Bohr was one of the strongest opponents of the Society joining the Union because of its political stance and, after heated debate, the Society decided that it would not join.
There was a Danish mathematical journal, Matematisk Tidsskrift, published before the Mathematical Society was founded. Matematisk Tidsskrift was founded in 1859 and Zeuthen became an editor in 1871. He held this role for 18 years. Shortly after he ended his editorial duties, the journal split into two parts in 1890. Series A published work on elementary mathematics, while series B published advanced mathematical research. The Mathematical Society took over the publication of these journals in 1919.
After World War II many changes came about in the running of the Society. Harald Bohr was President of the Society but now the Society worked to help create an International Union which all could support. This Union came about in September 1951. Even before this, proposals had been put forward for a Scandinavian mathematical journal to replace Matematisk Tidsskrift and they were put before the Society. Some members of the Board were enthusiastic for such a publication, while others opposed the idea principally on the grounds that they feared it would damage Acta Mathematica. Discussions took place with leaders of other Scandinavian mathematical societies despite the reluctance of some members of the Board. The title of Mathematica Scandinavica was chosen by votes taken in the participating mathematical societies in January 1952. The first meeting of the editorial board was in May and the journal was first published in 1953. Although negotiations for the joint publication of Nordisk Matematisk Tidskrift took a little longer to finalise, it first appeared in 1953.
In fact the Mathematical Society had changed into the Danish Mathematical Society during the discussions about publishing a Scandinavian journal. The Danish Mathematical Society was established in 1952 and the statutes changed from those of the Mathematical Society. Since its foundation the Mathematical Society was run by a Board of three members, but the statutes of the new national Society had a larger Board consisting of five members. The new statutes are given in full in .
In  Branner writes of the changes to the activities of the Society in the years following 1954 when more mathematical seminars were organised by individual Danish university mathematics departments, and fewer by the Danish Mathematical Society:-
The Society still arranges lectures in the Copenhagen area, but less frequently than before. During the last ten years regular meetings have been organised once or twice a year, alternating between the different mathematical departments, with lectures and discussions of common interests.
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