|Headquarters||Providence, Rhode Island|
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
The AMS 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.
In 1891 Charlotte Scott became the first woman to join the society. The society reorganized under its present name and became a national society in 1894, and that year Scott served as the first woman on the first Council of the American Mathematical Society.
In 1951, the society's headquarters moved from New York City to Providence, Rhode Island. The society later added an office in Ann Arbor, Michigan in 1965  and an office in Washington, D.C. in 1992.
In 1954 the society called for the creation of a new teaching degree, a Doctor of Arts in Mathematics, similar to a PhD but without a research thesis.
In the 1970s, as reported in "A Brief History of the Association for Women in Mathematics: The Presidents' Perspectives", by Lenore Blum, "In those years the AMS [American Mathematical Society] was governed by what could only be called an 'old boys network,' closed to all but those in the inner circle." Mary W. Gray challenged that situation by "sitting in on the Council meeting in Atlantic City. When she was told she had to leave, she refused saying she would wait until the police came. (Mary relates the story somewhat differently: When she was told she had to leave, she responded she could find no rules in the by-laws restricting attendance at Council meetings. She was then told it was by 'gentlemen's agreement.' Naturally Mary replied 'Well, obviously I'm no gentleman.') After that time, Council meetings were open to observers and the process of democratization of the Society had begun." 
In 1988 the Journal of the American Mathematical Society was created, with the intent of being the flagship journal of the AMS.
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 2019 Joint Mathematics Meeting in Baltimore drew approximately 6,000 attendees. Each of the four regional sections of the AMS (Central, Eastern, Southeastern, and Western) holds meetings in the spring and fall of each year. The society also co-sponsors meetings with other international mathematical societies.
The AMS selects an annual class of Fellows who have made outstanding contributions to the advancement of mathematics.
The AMS publishes Mathematical Reviews, a database of reviews of mathematical publications, various journals, and books. In 1997 the AMS acquired the Chelsea Publishing Company, which it continues to use as an imprint. In 2017, the AMS acquired the MAA Press, the book publishing program of the Mathematical Association of America. The AMS will continue to publish books under the MAA Press imprint.
Some prizes are awarded jointly with other mathematical organizations. See specific articles for details.
The AMS was an early advocate of the typesetting program TeX, requiring that contributions be written in it and producing its own packages AMS-TeX and AMS-LaTeX. TeX and LaTeX are now ubiquitous in mathematical publishing.
The AMS is led by the President, who is elected for a two-year term, and cannot serve for two consecutive terms.