During the final week at Michael Shub's behest an informal lunch was arranged where Felipe Cucker, Arieh Iserles, Narendra Karmarkar, James Renegar, Michael Shub and Stephen Smale decided to go ahead and create a permanent entity that would organize periodic conferences covering subjects in the interplay between these two areas.

After a discussion, the name Foundations of Computational Mathematics was settled, and Michael Shub was chosen to lead the initiative with a little team formed by himself, Arieh Iserles and James Renegar.

Ever since, its main activities are its triennial meetings, special semesters and the support of the FoCM journal, as well as general advocacy of the mathematical areas underlying computation.

In addition to that, specialized events focusing on particular research topics are organized by the society, including: Since January 2001, FoCM supports the journal Foundations of Computational Mathematics.

FoCM awards the Stephen Smale Prize [fr], whose objective is to recognize the work of a young mathematician in the areas at the heart of the society's interests and to help to promote his or her integration among the leaders of the scientific community.