The German Mathematical Society (*Deutsche Mathematiker-Vereinigung*) was founded in 1890 at a meeting of the Society of German Scientists and Physicians which took place in Bremen from 15 to 20 September. Few societies can have come into existence at a meeting at which so many leading mathematicians spoke, for at this meeting Cantor, Gordan, Hilbert, Klein, Minkowski, Study and Heinrich Weber all gave lectures.

This was the 63^{rd} meeting of the Society of German Scientists and Physicians and it was not the first one at which an attempt had been made to found a mathematics society. In 1867 Clebsch lectured on binary forms to the meeting of the Society of German Scientists and Physicians held in Frankfurt-am-Main. He proposed to the meeting the setting up of a separate mathematics society and a specialist journal. In part he was successful for *Mathematische Annalen* was founded in the following year (1868) as a consequence of discussions which had taken place between Clebsch and about 20 other mathematicians at Frankfurt-am-Main.

Clebsch continued to press the idea of a mathematics society which had support but its founding was continually delayed. When Clebsch died in 1872 his role as the leading advocate of a German mathematical society was taken up by Klein, who was Clebsch's student. However, it was not until Cantor made a strong push for the founding of the Society that eventually the idea turned into reality.

The first meeting of the new German Mathematical Society took place in Halle in 1891 at a meeting timed to coincide with the 64th meeting of the Society of German Scientists and Physicians. The statutes of the Society were agreed at this meeting and Cantor was elected president of the Society. He held this post until 1893. The aims of the Society, as set out in the statutes passed at this meeting, were [3]:-

... jointly to promote and to improve mathematics in all ways, to establish active connections and interaction among its various parts and scattered publications, to elevate it to its rightful place in the intellectual life of the nation, to offer its representatives and disciples the opportunity for free and friendly communication and for the interchange of ideas, skills, and hopes.

An executive committee was set up which was required:-

... to prepare for the annual meeting by arranging a full programme, comprised, if possible, of talks on the development of a single area of the science.

The meeting in Halle of the German Mathematical Society in 1891 is famous for another reason. At that meeting Cantor lectured on cardinal numbers and gave for the first time a proof that for any cardinal number *M*, the cardinal 2^{M} is strictly greater. His proof used the now familiar diagonal process. He ended his lecture with these words (see for example [3]):-

The potencies represent the simple and important generalisation of the finite cardinal numbers. These are nothing more than the transfinite cardinal numbers, and they possess the same reality and certainty as the former, except that the laws among them, that is to say the arithmetic related to them, is of a different kind from that of the finite realm. The further exploration of this field of enquiry is a project for the future.

Despite the bitter antagonism that existed between Cantor and Kronecker, Cantor invited Kronecker to address this first meeting of the Society in 1891 as a sign of respect for one of the senior and most eminent figures in German mathematics. However, Kronecker never addressed the meeting, since his wife suffered a serious accident prior to the meeting.

From the year of its foundation the German Mathematical Society published the *Jahresbericht* which was mainly a vehicle to publish major surveys of an area of pure or applied mathematics. In 1893 the German Mathematical Society requested a survey of algebraic number theory from Hilbert. His major report of 370 pages appeared the *Zahlbericht* in 1897.

We have indicated that Cantor was the first President of the German Mathematical Society from 1890 to 1893. Klein served as President in 1897, 1903, and 1908. Hilbert served as President in 1900, so he held this role at the time that he gave his famous talk on the mathematical challenges for the 20th century at the International Congress of Mathematicians in Paris. Other Presidents before the Second World War included Weyl who was President in 1932.

Problems began for the German Mathematical Society in 1933. On 30 January 1933 Hitler came to power and on 7 April 1933 the Civil Service Law provided the means of removing Jewish teachers from the universities, and of course also to remove those of Jewish descent from other roles. All civil servants who were not of Aryan descent (having one grandparent of the Jewish religion made someone non-Aryan) were to be retired. The German Mathematical Society heatedly discussed the issue in 1934, some pointing out that the Society could not carry out its aim *to elevate [mathematics] to its rightful place in the intellectual life of the nation* when 40% of its members were non-Aryan. Attempts to change the statutes failed, however, but in 1938 only those of Aryan descent were allowed to be members of the Society and all others were forced out.

The present activities of the Society are set out in [4]:-

Today, more than3000DMV members represent the German active mathematical community in universities, high schools, and industry. Besides protecting the scientific interests of its members, the DMV influences political decisions regarding research and education. For this purpose, the DMV takes positions on areas of great social importance, such as the teaching of mathematics.

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