The American Mathematical Society started its existence as the New York Mathematical Society which was founded in 1888. The history of that Society, prior to becoming the American Mathematical Society, is related in the article on the New York Mathematical Society.
A major motivation for the New York Mathematical Society to become a national mathematical society came about through the International Mathematical Congress held in Chicago in August 1893 in conjunction with the World's Columbian Exposition. The main international speaker was Klein who delivered the Evanston Colloquium lectures over a period of six days. After this Klein toured the United States and visited the New York Mathematical Society where J E McClintock, the President of the Society, introduced him as an:-
... apostle, prophet, evangelist, and teacher of mathematics - excelling in each office ...
Klein lectured to the New York Mathematical Society and engaged in an open discussion session.
Now Eliakim Moore was the chairman of the organising committee for the International Mathematical Congress which had been held in Chicago and the committee had received 39 papers for publication in a Conference Proceedings. After unsuccessfully attempting to find financial backing for the publication, he approached the New York Mathematical Society and, by June 1894, they had guaranteed up to $1000 to have Macmillan and Co publish the Proceedings. Archibald writes :-
This major publication enterprise, transcending local considerations and sentiment, quickened the desire of the Society for a name indicative of its national and continental character.
The New York Mathematical Society certainly become a national society in name on 1 July 1894 when it renamed itself the American Mathematical Society. At first, of course, little changed as the Society was firmly based in New York and it held its first meeting as the American Mathematical Society in Brooklyn in 1894. At this meeting G W Hill was elected President. Fiske continued to serve the Society as Secretary until 1895, and as editor-in-chief of the Bulletin of the American Mathematical Society from until 1897. He was vice-president of the Society from 1898 to 1901, an editor of the Transactions of the American Mathematical Society from 1899 to 1905, and President of the Society from 1903 to 1904.
Cole succeed Fiske in a number of these roles. He was appointed professor at Columbia University in 1895, and in the following year he was appointed as Secretary of the American Mathematical Society, a post he held until 1920. This was not his only work for the American Mathematical Society for in 1897 he was appointed as editor-in-chief of the Bulletin of the American Mathematical Society, holding this position until just before his death in 1926.
Two summer meetings were held while Hill was President, but both in conjunction with the American Association for the Advancement of Science. The first was held in Springfield, Massachusetts in the summer of 1895, the second at Buffalo, New York in the summer of 1896. Fiske writes:-
The summer meeting at Buffalo in 1896 is memorable for the first colloquium of the Society. The colloquium was the idea of Professor H S White, then at Northwestern University, who had been one of the leading spirits in the organisation of the colloquium held at Evanston in connection with the World's Fair at Chicago.
Indeed White had written to Fiske on 23 February 1896 making the following suggestions:-
Our summer meeting last year was profitable in various ways; but specifically, perhaps, as a stimulus to mathematical thought. One would likely derive more direct advantage from an hour in any one of several lecture rooms in this country. Yet each one found two or three papers out of the whole program of high interest. Now, why would it not be possible to combine with this miscellaneous program (which ought by all means to be kept up), something more akin to university models? Would not a series of three to six lectures on nearly related topics, if well chosen, prove attractive and useful to larger numbers?
White's suggestion was supported by the Society and the first Colloquium speaker was James Pierpont of Yale who lectured at the summer meeting at Buffalo in 1896. The Colloquium of the American Mathematical Society was born and continues to this day.
Despite changing its name to the American Mathematical Society, regular meetings were still held in New York City. The summer meetings were held out of New York, but still in the north east of the country. Members in Chicago proposed setting up sections of the American Mathematical Society in other parts of the country. They called a meeting of local members on 31 December 1896 with the following suggestion by Eliakim Moore:-
Our Society represents the organised mathematical interests of this country. Its function is to promote those interests in all possible ways.
Do we not need most of all frequent meetings? Those who have attended the summer meetings know the keen stimulus and inspiration resulting from personal contact - inside and outside the stated meeting - with colleagues from other institutions. The regular monthly meetings of the Society afford similar opportunities to those who live in the vicinity of New York.
By the organisation of sections of the Society can similar advantages be secured for other parts of the country? Shall, for instance, a Chicago section be organised? ...
The meeting approved the idea and the bylaws of the American Mathematical Society were amended to allow sections to be set up. The Chicago section first officially met on 24 April 1897. Further sections were set up once the success of the Chicago section became clear. The San Francisco West Coast section was set up in May 1902, and the South West section was up and running in Columbia, Missouri by December 1906.
The decision, in February 1899, to publish the Transactions of the American Mathematical Society was taken by Fiske, Eliakim Moore, McClintock, Bôcher, Osgood and Pierpont (the first Colloquium lecturer). The name was suggested by Bôcher and the idea of the journal was to accept only articles arising from contributions to a meeting of the Society or one of its sections. The idea was quite deliberately to give American authors a source to publish where they would have less competition from overseas authors. Eliakim Moore was elected editor-in chief and made sure that the quality of the journal was consistently high. Ernest Brown described :-
... the immense amount of trouble we all took - and especially Moore - to get the best information, the best printing, the best editing and the best papers before the first number appeared. And the work did not stop there. we wrestled with our younger contributors to try to get them to put their ideas into good form. The refereeing was a very serious business --. Most of it in those days was, I believe, done by Moore himself though he sought outside assistance whenever possible.
By 1901 the American Mathematical Society had 357 members and in the previous year 112 papers were read at Society meetings. By 1902 156 papers were read and the Society had elected its first President who was not from the North East, namely Eliakim Moore. However, the Society was still not truly national in its structure despite the introduction of sections. The problem was that the sections were still seen as holding less important meetings and the main meetings of the Society were still being organised in the north east. Matters came to a head in 1911 when the Chicago section complained bitterly about the place of the meeting at which Bôcher would give his Presidential address. Cole, as Secretary of the Society, allowed the decision to be put in Bôcher's hands and he made it clear that he wished to give his Presidential address in Chicago.
Although Bôcher's decision saved the American Mathematical Society from breaking apart, the Society still retained the idea of sections (and their meetings being of less standing) until 1929 when sectional meetings were recognised for the first time as regular meetings of the Society.
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