The **Hamburg Mathematical Society** (Mathematische Gesellschaft in Hamburg), founded in 1690, is the oldest mathematical society in the world which still exists today. It was not, however, the only society founded in Hamburg in the 17th century for, after the Thirty Years War (1618-1648), various citizens of Hamburg got together and formed societies of people with similar interests. For example, before the mathematical society, a medical society was founded in 1644 and a music society in 1660. The need for such a mathematical Society was shown by the quotes in [1]:-

To overcome these problems, the Society was founded as the 'Kunstrechnungsliebende Societät in Hamburg' byA writer from the beginning of our century(18th century)writes about the teachers of the time: "These extremely wretched schoolmasters came, like mushrooms from the earth, without any prior spiritual care to the school room," while a contemporary says, especially of the calculating masters, that: "These ignorant and unscrupulous youth-killers would have to be ashamed if they were asked to thoroughly explain one of their examples."

**Heinrich Meissner**(20 April 1644 - 1 September 1716) and Valentin Heins. Heinrich Meissner was a pupil at the Knackenrüggesche school in Hamburg, becoming a teacher there in 1669. In 1688 he became a teacher at the St Jacobi Church school where he taught writing and calculating until shortly before his death. He wrote several popular arithmetic textbooks. Valentin Heins, the son of a linen weaver, taught arithmetic from 1651 in Hamburg, then he studied theology from 1658 to 1659 at Jena and Leipzig. Returning to Hamburg, he became a teacher of writing and arithmetic at St Michael's Church school. He also wrote several popular arithmetic textbooks, in particular the

*Tyrocinium Mercatorio-Arithmeticum*(1694) which ran to 24 editions and was published until the beginning of the 19th century.

The 'Kunstrechnungsliebende Societät' did not originate as a society of the "learned society" type which exists today but rather a society for writing and calculating masters whose task was to teach practical counting in schools to those who would enter commercial occupations or study at a university. The early society aimed at spreading the mathematical art as widely as possible to anyone who was interested in calculation. Those applying for membership of the new Society had to sit an entrance examination to demonstrate their knowledge of how to solve quadratic and cubic problems, as well as understanding the basics of Euclidean geometry and Euclid's theory of irrational numbers. This was a demanding requirement and few school teachers would have been able to come up to this level. The new Society, therefore, had rather few members, in fact there were only fifteen founding members, six of whom came from Hamburg. The members were mostly interested in writing textbooks and they would support each other in that task. For example Heinrich Meissner published *Stern und Kern der Algebrae* in 1692 which begins with a discussion of basic arithmetic including the extraction of square and cubic roots. It then deals with the solution of quadratic and cubic equations. Meissner gives a single method for solving such equations and writes:-

Meissner believed that it was useful for merchants to know algebra and this was his motivation for this unusual work.... that by the grace of God one might one day come to a general rule of all the cousins.

**Valentin Heins** (15 May 1637 - 17 November 1704) published *Tyrocinium Mercatorio-Arithmeticum* (1694) which was a much more conventional commercial arithmetic. As well as his job as a writing and calculating master in St Michael's Church school, he worked as an accountant for the Guinean African Company and was able to include a host of examples problems about trade with gold, ivory and slaves from West Africa and sugar, rum and cotton from the West Indies.

Meissner, who died in 1716, was the last of the founding members. After that the Society only had three members from Hamburg and by 1717 only two remained. The Society, however, continued to exist because of its foreign members, in particularly the Dutch, Danes, and those from Schleswig-Holstein. It certainly did not flourish so the Society revised its statutes in 1774, and again in 1789-90 to distinguish itself from other societies that were starting up aiming to include scholars, lawyers and merchants wishing to improve trade and commerce. The Society chose a new name to mark its centenary, namely the 'Gesellschaft zur Verbreitung der mathematischen Wissenschaften in Hamburg'. The Society now had the aim of making mathematical truths known not only to the lovers of this science, but also for the benefit of the general public.

The 100-year old society soon had to contend with other difficulties. Napoleon began to lead French armies to attack various countries in Europe. The French occupied Hamburg in November 1806 but it was subsequently freed by Cossack troops. It was occupied again by the French in May 1813 and came under siege from Prussian and Russian forces. The population of the city suffered terrible hardships over the winter as the French held out against the surrounding armies. Only in May 1814 did the French surrender to the Russians. These events had an impact on the Society for the Propagation of Mathematical Sciences of Hamburg which became somewhat influenced by the mathematical developments in France, particularly at the École Polytechnique. From 1815 onwards, the Society gained members from the military and it added military books to its library while engineers, architects and mechanics began to join. For example in 1819 the Society published a famous handbook of navigation by Reinhard Woltman (1757-1837), the *Handbuch der Schiffahrtskunde*.

The move of the Mathematical Society into these areas of application did not succeed in attracting members in the long term since specialist societies for engineers and for architects began to be set up. The Mathematical Society again was reduced to a small membership, often not more than 20 members. The Society changed its focus and by the middle of the 19th century it was moving more towards being a pure mathematics society. One important person in the development of the Society was Hermann Schubert who moved to Hamburg in 1876 to take up an appointments as a teacher at the Johanneum, the renowned humanistic school. Four years earlier the Society had begun sending out to its members copies of talks given to the Society. This turned into the publication of its journal, the *Mitteilungen der Mathematischen Gesellschaft in Hamburg*, with volume 1 being published in 1881. The first volume contained papers by Hermann Schubert. The Society began an exchange with foreign societies, libraries and other institutions.

The University of Hamburg was founded on 28 March 1919. Plans to found the university had been made much earlier but had to be shelved when World War I broke out in 1914. Only after the war ended in 1918 was it possible to continue with the plan. With the opening of the university in 1919, Wilhelm Blaschke was appointed to the chair in the University of Hamburg. In Hamburg Blaschke built up an impressive school, managing to appoint mathematicians of the quality of Erich Hecke (appointed 1919), Johann Radon (appointed 1919), and Emil Artin (appointed 1922). These leading mathematicians attracted highly talented lecturers, assistants and doctoral students. Almost all of these became members of the Hamburg Mathematical Society which flourished until the end of the 1920s when the number of members began to reduce significantly. The disastrous economic situation caused the Society problems, then the rise of the Nazis in the 1930s saw several prominent members dismissed from the university and exiled by the Nazi regime. Hamburg suffered badly during World War II and in July 1943 much of the Society's library with its fine collection of books was destroyed. For four years the Society was unable to operate but from around 1950, under the leadership of Werner Burau (1906-1994), the Society was rebuilt and by 1963 it had returned to have as many members as there had been in the 1920s.

**List of References**(5 books/articles)

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