The History of the American Mathematical Society

It appears that the idea for a mathematical society in the United States came from a visit T S Fiske made to England where he visited Cambridge. He arrived with letters of introduction to Cayley, Glaisher, Forsyth and Darwin. Fiske writes:-
Scientifically I benefited most from my contacts with Forsyth and from my reading with Dr H W Richmond, who consented to give me private lessons. However, from Dr Glaisher, who made me an intimate friend, who spent many an evening with me in heart to heard talks, who took me to meetings of the London Mathematical Society and the Royal Astronomical Society, and entertained me with gossip about scores of contemporary and earlier mathematicians, I gained more in a general way than from anyone else.
Back in New York Fiske organised a meeting on 24 November 1888 to discuss creating the New York Mathematical Society. He invited to the meeting his fellow students Jacoby and Stabler, his professor from Columbia University J H Van Amringe, Professor Rees and a graduate student Maclay.

The Society was set up and had only 11 members in its first year with J H Van Amringe as President. J E McClintock joined the Society in December 1889 and was to become its second President. Only these two were Presidents of the New York Mathematical Society for, in 1894, the Society decided to become a national organisation and change its name accordingly to the American Mathematical Society.

The Bulletin was modelled on other journals. Fiske write:-
The external appearance of the Bulletin, the size of its page, and the color of its cover were copied from Glaisher's The Messenger of Mathematics ... The Bulletin's character, however, was influenced chiefly by Darboux's Bulletin des Sciences Mathématique and the Zeitschrift für Mathematik ...
The decision 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.

MacTutor links:

History of the AMS
Presidents of the AMS
AMS Colloquium Lecturers
AMS Gibbs Lecturers
AMS/SIAM Birkhoff Prize
AMS Bôcher Prize
AMS Cole Prize in Algebra
AMS Cole Prize in Number Theory
AMS Conant Prize
AMS Fulkerson Prize
AMS Satter Prize
AMS Steele Prize
AMS Veblen Prize
AMS Wiener Prize

Other Web site:

AMS Web site