It was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the Bulletin of the American Mathematical Society, with Fiske as editor-in-chief. The de facto journal, as intended, was influential in increasing membership. The popularity of the Bulletin soon led to Transactions of the American Mathematical Society and Proceedings of the American Mathematical Society, which were also de facto journals.

The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. The AMS, along with the Mathematical Association of America and other organizations, holds the largest annual research mathematics meeting in the world, the Joint Mathematics Meeting held in early January. The 2013 Joint Mathematics Meeting in San Diego drew over 6,600 attendees.

Each of the four regional sections of the AMS (Central, Eastern, Southeastern and Western) hold meetings in the spring and fall of each year. The society also co-sponsors meetings with other international mathematical societies.