Welcome to FoCM!
The computer has profoundly changed the relationship between mathematics and computation. Besides its invaluable role in numeric, symbolic, and experimental applications, computation is an important object of mathematical study in its own right and a fundamental theoretical tool. It is a source of new and exciting problems for mathematics.
Foundations of Computational Mathematics (FoCM) is an international nonprofit organization that supports and promotes research at the interface of mathematics and computation. It fosters interaction among mathematics, computer science, and other areas of computational science through conferences, events and publications. FoCM traces its beginnings to the Park City AMSSIAM seminar in 1995 and its first conference has been held in Rio de Janeiro in 1997.
The FoCM journal, produced by SpringerVerlag, publishes highestquality research articles treating various aspects of computational mathematics.
The FoCM conference, held every three years, covers the entire spectrum of mathematical computation.
Specialized events are held from time to time, and focus on timely research topics.
Membership in FoCM is free and available through this website.
FoCM'14 Conference
 Carlos Beltrán and Mark Braverman win the Smale Prize 2014

Next FoCM Conference:
Montevideo, Uruguay
December 11 to 20, 2014.
Click to visit web site

The Prize is awarded by the Society for the Foundations of Computational Mathematics to young researchers in recognition of major achievements in furthering the understanding of the connections between mathematics and computation, including the interfaces between pure and applied mathematics, numerical analysis and computer science.
The award will be made on December 13, 2014, at the FoCM’14 conference.
Carlos Beltrán,
University of Cantabria, is one of the two recipients of the Smale Prize 2014 for his brilliant contributions to fundamental problems in the foundations of computational mathematics. Beltrán’s work embodies original approaches that combine the use of complex geometric structure and analytic power to make important progress on problems which have been the focus of intense research efforts by others. An important part of his work has been devoted to polynomial system solving, producing with Luis M. Pardo a Las Vegas algorithm for Smale's 17th problem, and studying the underlying geometry with Mike Shub and others. His work on producing equidistributed points on the sphere defines the state of the art on Smale's 7th problem. With Anton Leykin he has provided tools to adapt numerical methods to supply proofs in algebraic geometry. In addition, his work with Oscar González and Ignacio Santamaría on interference alignment (solving a problem in information theory, open for more than 10 years) is also a milestone. 

Mark Braverman,
Princeton University, is one of the two recipients of the Smale Prize 2014 for his pioneering work on the foundations of computational mathematics. Braverman has made fundamental contributions to our understanding of computability and complexity questions involving both continuous and discrete systems. In particular, his joint work with Michael Yampolsky showed how to apply deep and modern techniques of complex analysis and dynamics to classify Julia sets according to their computability and complexity. Concerning discrete problems, in a series of papers Braverman and his collaborators have shown how to apply Shannon's information theory to settle central open questions in communication complexity, including proving lower bounds on the ability of linear programs to approximate NP complete problems. He also developed surprising techniques from harmonic analysis to finally prove the LinialNisan Conjecture, and disproved, with collaborators, an old conjecture of Krivine. 



