The **Icelandic Mathematical Society** was founded on 31 October 1947 in Reykjavik on the 70th birthday of Ólafur Dan Daníelsson. Since Daníelsson plays such a major role we give some biographical details.

**Ólafur Daníelsson** (born 31 October 1877, died 10 December 1957) was born in Viðvík in Viðvíkursveit in Skagafjördur. He completed his matriculation examination from Laerða School in Reykjavík in 1897 and, later that year, entered the University of Copenhagen to study mathematics. He was awarded his Master's Degree in 1904 and, returning to Iceland, he applied for a vacant teacher position at the High School in Reykjavík where he had himself been a pupil a few years earlier. However, his did not get the position, the successful applicant being Sigurður Thoroddsen. Daníelsson earned money from giving private tuition and at the same time he undertook research for a doctorate. In 1909 he submitted his thesis to the University of Copenhagen and was awarded a doctorate, becoming the first Icelander to be awarded a doctorate in mathematics. He taught mathematics at High Schools in Iceland and wrote mathematical textbooks. He didn't give up research, however, and he published several research papers.

The Icelandic Mathematical Society's records contain information about the founding of the Society [2]:-

In addition to Ólafur Daníelsson, there were fifteen men present at the meeting at his home and these men must be considered as the founders of the Society. The fifteen are: Thorkell Thorkelsson, physicist, Brynjólfur Stefánsson and Árni Björnsson, actuaries, Bolli Thoroddsen, engineer; Sigurkarl Stefánsson and Leifur Ásgeirsson, mathematicians; Steinşór Sigurðsson and Trausti Einarsson, astronomers; Kr. Guðmundur Guðmundsson, security mathematician; Sveinn Þórðarson, physicist; Guðmundur Arnlaugsson, mathematician; Gunnar Böðvarsson, engineer; Thorbjorn Sigurgeirsson, physicist; and Björn Bjarnason, mathematician. We note that at this stage the Society had not adopted the name 'Icelandic Mathematical Society', but this was done later as we shall describe below.On Friday,31October1947, which was the seventieth birthday of Ólafur Daníelsson, he gathered in his home several men and set up a Society. The purpose of the Society is to promote co-operation and promotion of people in Iceland who have completed a university degree in a mathematical subject. The Society holds meetings at which individual members explain their mathematical topics and, if desired, discussions on the topic will be conducted.

It was the purpose of the Society that people should gather to discuss their mathematical work and introduce their ideas to each other. The first lecture was delivered by Ólafur Daníelsson himself. He spoke "about the circle transcribed by the outer circumference of the triangle" and calculated its length relative to the radius of the inscribed circle and the circumference of the triangle. He had recently published the result in the *Danish Mathematical Journal*. But it was something he had been thinking about for a very long time for the first fundamentals of this material is found in an article he wrote in the same journal as a twenty-two year old in 1900. In this sense, this was an old topic, but it is also a subject in which a new understanding had been achieved not long before his talk. In the first decade of the Society, four or five lectures were usually given each year. New members quickly joined the Society and delivered lectures. During the first few years, Bjarni Jónsson and Sigurður Helgason both gave lectures and both of them continued to attended meetings regularly and gave many lectures over the following years. In fact several leading international mathematicians have lectured to the Society, for example André Weil and Paul Erdős.

The Society collaborates with other Scandinavian mathematical societies in publishing *Mathematica Scandinavica* and *Nordisk Matematisk Tidskrift*. Danielsson agreed that the Society would participate in publishing these journals in 1951 and the two journals appeared in 1953. Because of the small population of Iceland compared with other Scandinavian countries, it was only required to contribute 1% to the financial costs *Mathematica Scandinavica*. In fact the Ministry of Education in Iceland was the first to give financial support and major grants were made for the setting up of *Mathematica Scandinavica* by Icelandic Life Insurance Companies. Now it was because of the Society's involvement in publishing *Mathematica Scandinavica* that it decided to adopt the name 'Icelandic Mathematical Society'. The minutes of a meeting of the Society in 1952 record that it had received a formal request from the Danish Mathematical Society to be involved in publishing *Mathematica Scandinavica*. The minutes record [2]:-

The Statutes of the Icelandic Mathematical Society were revised at the Society's Annual General Meeting on 12 January 2010. Here is an indication of these Statutes [2]:-In connection with this case, the meeting decided that the name of the Society should be called the 'Icelandic Mathematical Society'.

In fact the Society has made three people honorary members. The first of these was the founder of the Society, Ólafur Dan Daníelsson. We gave some details about Daníelsson above. The other two honorary members are Leifur Ásgeirsson and Sigurður Helgason. Let us give some biographical details of these two mathematicians.The Society is called the Icelandic Mathematical Society. Its home and base is in Reykjavík. The purpose of the Society is to:

(i)Be a forum for professional discussions for mathematicians and others interested in mathematics.

(ii)Introduce and promote mathematical research in Iceland.

(iii)Promote mathematical education and general mathematical knowledge in Iceland.

(iv)Promote the relationship between mathematicians within and outside the country and represent the members of the Society to related non-governmental organisations.

Members are required to have completed a university degree in mathematics or related subject and are then only considered after at least three years of university studies following graduation.

The Board of Directors of the Company shall be composed of five members, i.e. a chairman and four co-chairs. The chairman shall be elected for one year at each annual general meeting, but the board of directors for two years. The chairman handles the day-to-day management of the Society. The Annual General Meeting has the supreme authority in the affairs of the Society and will be held in January each year.

Those who have worked outstandingly for the Society's goals may be chosen as honorary members.

**Leifur Ásgeirsson** (born 25 May 1903, died 19 August 1990) graduated from the University of Reykjavík in 1927 and then undertook research at the University of Göttingen with Richard Courant as his supervisor. He graduated from Göttingen in 1933, and returned to Iceland where he was head of the district school at Laugum in Reykjadalur from 1933 to 1943. He became the first Icelander to receive extensive international recognition for mathematical research. He was appointed as a lecturer in mathematics at the University of Iceland in 1943 and became the first full-time professor of mathematics at the University of Iceland in 1945. For a long time he was the only professor of mathematics, first at the engineering department. He was the first Icelandic editor of Mathematica Scandinavica.

**Sigurður Helgason** (born 30 September 1927 in Akureyri, Iceland) attended the Gymnasium in Akureyri 1939-45 before entering the School of Engineering, University of Iceland where he studied for two years before going to the University of Copenhagen where he studied between 1946 and 1952. After graduating in January 1952 he travelled to the United States where he undertook research at Princeton advised by Salomon Bochner. Graduating with a Ph.D. in June 1954 he taught at Princeton University for most of his career, except for two years at the University of Chicago and two years at Columbia University. He became a full professor at Princeton in 1960. His research has been devoted to the geometry and analysis on symmetric spaces. He developed new integral geometric methods to establish fundamental existence theorems for differential equations on symmetric spaces. He also proved some new results on the representations of the isometry groups for these equations. He was made an Honorary member of the Icelandic Mathematical Society in 1997.

Let us looks at some other activities that the Society has undertaken. We have already mentioned their cooperation in publishing *Mathematica Scandinavica* and the Nordic mathematical journal - *NORMAT*. Since 2003, the Society has cooperated with the Physics Association of Iceland, the Chemical Society of Iceland and the Stjarna Sciences Association of Iceland in publishing *RAUST*, the journal of science and mathematics. Since 1952, the Icelandic Mathematical Society has given an innovative book award for outstanding achievement in mathematics at the matriculation examination. Sadly no complete record of the winners of this award exists despite strenuous efforts by the Society in 1989 to find the names of all the winners.

The Society played a major role in organising the Nineteenth Nordic Mathematical Congress held in Reykjavik in 1984. They organised another major conference in 1990 which was to honour Bjarni Jónsson on his 70th birthday. The conference was held at Laugarvatn.

**List of References**(2 books/articles)

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