It was not a Society which aimed to support advanced mathematics. Rather its membership consisted of amateurs and :-
... schoolteachers, surveyors, bookkeepers, engineers, instrument makers, and other practically minded mathematicians.Strabbe, who became a member of The Hamburg Mathematical Society, chose as a motto for his own Society "Untiring labour overcomes all" which remains its motto to this day. However, it certainly didn't start off as a national Society, rather it was an Amsterdam mathematical society functioning at a time when several Dutch amateur mathematical societies arose in the late 18th and early 19th centuries :-
During the last decades of the 18th, and the first decades of the 19th century, the Netherlands saw the emergence of several other mathematical societies, whose existence has been forgotten.The young Society was small and rather insignificant during the first years of its existence; it had 95 members by 1782. At first it only met yearly, with lectures on the practical usefulness of mathematics and how it contributed to happiness, but the meetings became monthly during the nineteenth century as the level of mathematical research in The Netherlands rose sharply. It was during the early 19th century that the Society became a national one, including almost all the Dutch mathematical community. In  Beckers points out that the gap between the social classes in the Netherlands was not as large as in other regions of Europe which helped the Society to make the necessary changes to provide a link between amateur and professional mathematicians.
The Society published from shortly after it was founded with the Wiskundig Genootschap appearing in 1782. In 1856 the Archief first appeared and it 1875 it became the Nieuw Archief voor Wiskunde and was distributed to all members of the Society. Pieter Hendrik Schoute was an editor of this journal from 1898 until his death in 1923. He was also a founding editor of another Dutch Mathematical Society Journal Revue semestrielle des publications mathématique from 1893, when the journal was founded, again until his death in 1923. The Society continued to publish this journal until 1934 by which time 39 volumes had appeared.
Another major figure in Dutch mathematics and in the running of the Dutch Mathematical Society was Diederik Johannes Korteweg. He served the Society by being on the organising committee for 58 years. In more recent times L E J Brouwer, J A Schouten and T J Stieltjes have been important figures, and the Society published Stieltjes' Collected works in two volumes in 1914 and 1918, and Brouwer's Collected works in two volumes in 1975 and 1976.
A major event for the Society was hosting the International Congress of Mathematicians in Amsterdam in 1954 at which Kunihiko Kodaira and Jean-Pierre Serre were awarded Fields Medals. By 1965 the monthly meetings of the Society were becoming less well attended despite the increased membership of the Society. They were discontinued and yearly Dutch Mathematical Congresses were organized :-
This two day conference, which takes place in April, draws a large part of the Dutch mathematical community, including high school teachers and industrial and applied mathematicians.Once every three years the Brouwer Medal is awarded during the Dutch Mathematical Congress to a leading mathematician. The award of the medal was instituted in 1970 with the first award being made to René Thom. A Symposium aimed at high school teachers is run evey winter, and a special Section for Industrial and Applied Mathematics within the Society organizes Symposium each autumn and also runs a Study Group with Industry.
The Nieuw Archief voor Wiskunde is published quarterly for all members of the Society and, reflecting the way the Society began, it still contains a famous problem section. The Society has also published Pythagoras, a magazine for high school students, for a number of years.
List of References (8 books/articles)
Other Web site Society Web-site (in Dutch)