Foundations of Computational Mathematics

What is it all about?

The reaction to the Park City meeting on Mathematics of Numerical Analysis: Real Number Algorithms which was chaired by Steve Smale and which had around 275 participants was very enthusiastic. At the suggestion of Narendra Karmarkar we decided to try to hold an annual or perhaps biennial meeting entitled Foundations of Computational Mathematics and to form an organization with the same name whose primary purpose will be to hold the meeting. A lunch time meeting of Felipe Cucker, Arieh Iserles, Narendra Karmarkar, Jim Renegar, Mike Shub and Steve Smale asked Mike Shub to act on its behalf.

The first Foundations of Computational Mathematics meeting was held at the Instituto de Matemática Pura e Applicada in Rio de Janeiro during the week of 5-12 January, 1997. It consisted of twelve invited lectures and nine workshops.

The Rio de Janeiro meeting provided an opportunity to restructure FoCM in a more organized manner. Thus, the governing body is now the FoCM Council, while the day-to-day affairs of the organisation are managed by the FoCM Executive Committee.

The business of FoCM has expanded greatly since the lunch-time meeting at Park City in August 1995. Our primary aim is to further the understanding of the deep relationships between mathematical analysis, topology, geometry and algebra and the computational process as they are evolving together with the modern computer. Many of our intellectual stimuli have been found in numerical analysis and the complexity theory of computer science, but the current range of our interests is best represented by the workshops and speakers at our meetings. If there is a unifying theme it is that the mathematical algorithm itself is the object of study, either via the analysis of a particular algorithm, the comparison of classes of algorithms or the discovery of an appropriate class of algorithms for the solution of problems of practical or mathematical origin. We hope in this fashion to influence both mathematics and computation, especially as related to real number computations. Although we do not expect immediate practical results, it is our belief that, ultimately, the better understanding of its foundations will facilitate major new applications of mathematical computing.

Current FoCM activities include

According to a decision at an open meeting during the FoCM'97 conference, we have established a small committee to debate the future aims, structure and decision-making procedures of FoCM. The committee comprises of Lenore Blum (convener), Stefan Heinrich, Herb Keller, Mike Shub and Mike Todd.

In an advanced stage of its deliberations, the committee plans to consult widely with the broad FoCM community. This procedure will be advertised, when relevant, on the FoCM home page.

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