Restoring the Link to Computer Science

This sketchy note tries to answer the question put forward "What is your view of the future of Computer Algebra". Part of the answer is to explore better the links with Computer Science. We stress the fact that a question raised by John Mc Carthy in 1963 on the interaction between Algebra and Logic can set partly an agenda for future research. To foresee the future of a scientiic eld is a hazardous game. Trend iden-tiication depends in particular on the present state of the art, on the past history of the eld, on the research interests of the assessor and on the available technology. 1 A brief history Computer Algebra (CA) started as a discipline of Computer Science 1]. The rst conferences were divided into three sections: systems, algorithms and applications. These sections had almost equal weight. This is best illustrated by the Los Angeles conference in 1971. The application section was very important since it was a way to validate the systems and algorithms being designed. At that time, Mathematics was part of the agenda set up by the founder's of Artiicial Intelligence in the late 1950's 2]. Along the years, the application component became weaker. Today, authors of papers on systems have diiculty to get them accepted at ISSAC. Indeed, algebraic algorithms dominate the eld now. This may look surprising since the outside world knows CA best from the several successful systems such as Maple or Mathematica. In fact, research on algebraic algorithms has been both successful and ourishing along the years. The thesis in this short note is that the applications have now found their optimal setting, that research on algebraic algorithms faces some challenging problems and that the decline of the "system" part is due to severed links to Computer Science and needs to be restored.