A computer aid for symbolic mathematics

Abstract

Long before it is solved, many a problem has been tossed aside by creative scientists simply because of the sheer tedium in carrying out repeated mathematical operations. In addition to being time consuming, this "clerical" activity is a frequent source of trivial errors which can invalidate the entire analysis. One approach toward solving this problem is the creation of computer aids that will assist the scientist as he develops a theory or tries to solve a mathematical problem. However, when a scientist is trying to develop a theory he does not only want numbers or graphs that satisfy a particular case. He is most happy when he can derive a general formula that not only describes a large number of cases, but also shows how the various cases are interrelated. The theoretician often starts with a set of postulates or some initial equations and manipulates them symbolically to get resulting equations and conditions. Occasionally the scientist has to develop his own mathematics as he works out a problem by creating new symbols, operators, and functions. A computer system that will aid the scientist in the creative process must be flexible enough to accept these new rules with a minimum of effort on the scientist's part. Our work in developing one experimental system of this nature (Magic Paper 1) will be described and several possible extensions to this program will be suggested.