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 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 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 became the first president while Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance over 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 the launches of the Transactions of the American Mathematical Society and Proceedings of the American Mathematical Society, which were also de facto journals.

In 1891, Charlotte Scott of Britain became the first woman to join the AMS, then called the New York Mathematical Society. The society reorganized under its present name (American Mathematical Society) and became a national society in 1894, and that year Scott became the first woman on the first Council of the society. In 1927 Anna Pell-Wheeler became the first woman to present a lecture at the society's Colloquium.

In 1951 there was a southeastern sectional meeting of the Mathematical Association of America in Nashville. The citation delivered at the 2007 MAA awards presentation, where Lee Lorch received a standing ovation, recorded that:

Also in 1951, the American Mathematical 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 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." Also, in 1971 the AMS established its Joint Committee on Women in the Mathematical Sciences (JCW), which later became a joint committee of multiple scholarly societies.