The Swedish Mathematical Society was named Svenska Matematikersamfundet. It was founded in 1950 with the first meeting taking place in June of that year. The first President of the Society was Arne Beurling. The first secretary was Bror Gustaver and the first treasurer was Nils Erik Fremberg. Its aim was:-
... to promote mathematics, including by improving contacts between professional mathematicians, both nationally and internationally, and by spreading information about the growing importance of mathematics in society.Many of members of the Society are high school teachers while virtually all mathematicians at Swedish universities and colleges are members. Today the Society has over 500 members.
Discussions about producing a publication were held in a meeting of the new Society which took place in November 1950 when Beurling explained to members that there was a proposal to produce two new international mathematics journals published jointly by the Scandinavian mathematical societies, one a high level research journal, the other an elementary journal concerned with the teaching of mathematics :-
Negotiations among Scandinavian mathematicians started with a wish to create an international research journal accepting papers in the principal languages English, French and German, and expanded quickly into negotiations on another more elementary journal accepting papers in Danish, Norwegian, Swedish, and occasionally in English or German. The mathematical societies in the Nordic countries Denmark, Finland, Iceland, Norway and Sweden were behind both journals and for the elementary journal also societies of schoolteachers in Denmark, Finland, Norway and Sweden.The Swedish Mathematical Society was keen to participate in this venture but, fearing that the proposals might not materialise, they also made some preliminary plans to produce their own journal if necessary.
The second annual meeting of the Society took place in Lund in June 1951. Further important decisions on publishing the two international Scandinavian journals were taken at that meeting. The title of Mathematica Scandinavica was chosen as the title for the high level journal 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 also first appeared in 1953. At first the Swedish Mathematical Society were less keen on the elementary journal since Sweden already published the journal Elementa.
Ake Pleijel became the second President of the Swedish Mathematical Society, holding this position from 1952 to 1957. He became the first Swedish editor of Mathematica Scandinavica. Nils Erik Fremberg, the first treasurer of the Swedish Mathematical Society :-
... played an important role in supporting the Swedish participation in the elementary journal, he was appointed editor by the Swedish Mathematical Society of this journal, but he died unfortunately of cancer in September 1952 before the journal had started.A recent article by Klas Markström, the President of the Swedish Mathematical Society in 2017,  gives an up-to-date account of the Society. You can read a version of his article at THIS LINK.
The statutes of the Society, last modified in 2005, state that as well as individual members, institutions, schools and other legal identities may join. The Society meets at least twice a year. The Society is run by a Board :-
The Board shall consist of five persons, the chairman, vice-chairman, treasurer, secretary and an ordinary Board member. Representation on the Board for the younger mathematicians and mathematicians active in schools and in areas of application should be pursued. These are elected at the annual general meeting. In order for a board decision to apply, it is required that at least three Board members are present and agree on the decision.The Swedish Mathematical Society cooperates other organizations in arranging a variety of activities, such as Education Days, Mathematics Competitions and Sonja-Kovalevsky-Days, for high school teachers and students.
At each Swedish university and in other places where the circumstances merits it, the Society has a local representative. Their task should be to keep in touch with the active mathematicians at that locality and inform them of matters related to the Society. All local representatives are elected at the annual general meeting.
High School Mathematics Competition
At Danderyd's Gymnasium there has been a special mathematical competition, called Mathematics Gymnasium Competition since 1986. For the Swedish upper secondary schools, a mathematical competition was started in 1961. The mathematics initiative at Danderyd's Gymnasium led to the decision to start a competition for the country's high schools. The High School Mathematics Competition started in 1988 as a local mathematics competition for all high schools in the Stockholm area. Two years later, the competition was extended to the whole country and became a nationwide mathematical competition. Today, the High School Mathematics Competition is organized by an independent competition committee in collaboration with, among others, Danderyds Gymnasium, which is still hosting the final competition, and the Swedish Mathematical Society.
The Sonja Kovalevsky Days
The Sonja Kovalevsky Days are aimed at high school students interested in mathematics. It was organized for the first time in World Mathematics Year 2000 and became a clear success with many satisfied participants. The goal of the Sonja Kovalevsky Days is to increase the interest in mathematics studies among young people and to encourage them to choose that subject at university. Each upper secondary school with science programmes is invited to send two students to the Sonja Kovalevsky Days. Students are chosen among those who show a lively interest in the subject of mathematics. The Principal Teacher appoints the pupils, preferably a girl and a boy student who are in their final year in high school. The days aim to give the participants a picture of the importance of the role of mathematics in our society, give an understanding of the rapid development of mathematics in the last hundred years, give the opportunity to meet inspirational role models in education, research and business, and to give an understanding of the need for good mathematics skills in a future professional life.
Swedish Mathematical Society Wallenberg Prize
The Swedish Mathematical Society awards the Wallenberg Prize to promising young Swedish mathematicians. The Wallenberg Prize has been awarded since 1983 but it has had the name 'Wallenberg Prize' only since 1987 when funding for the award was received from the Marianne and Marcus Wallenberg Foundation. It has been distributed to especially promising younger Swedish mathematicians who have graduated with a Ph.D. but who have not yet received a permanent research position. The Wallenberg Prize has been the most prestigious award that a younger Swedish mathematician could have in the country. The stated intention of the prize has been to encourage mathematical research. Most of the prize-winners have gone on to have their career as a mathematician at a Swedish university, and most of the prize-winners today are professors. For a list of winners of the prize, see THIS LINK.
List of References (4 books/articles)
Other Web site Society Web-site (in Swedish)