Challenges of Symbolic Computation: My Favorite Open Problems

The success of the symbolic mathematical computation discipline is striking. The theoretical advances have been continuous and significant: Gröbner bases, the Risch integration algorithm, integer lattice basis reduction, hypergeometric summation algorithms, etc. From the beginning in the early 60s, it has been the tradition of our discipline to create software that makes our ideas readily available to scientists, engineers, and educators: SAC-1, Reduce, Macsyma, etc. The commercial viability of our system products is proven by Maple and Mathematica. Today’s user communities of symbolic computation systems are diverse: educators, engineers, stock market analysts, etc. The mathematics and computer science in the design and implementation of our algorithms are sophisticated. The research challenges in symbolic computation at the close of the 20th century are formidable. I state my favorite eight open problems in symbolic computation. They range This material is based on work supported in part by the National Science Foundation under Grant No. CCR-9712267. †URL: http://www.kaltofen.netE-mail: [email protected]