Mathematica: doing mathematics by computer?

Abstract

When, in the present paper, I will criticize the basic tenet of Mathematica this is not meant to detract anything from the invaluable merits of Stephen Wolfram’s wholistic oeuvre with its many facets: mathematics, language design, algorithms, software and system design, teaching and publication tools, applications, and — yes — business, marketing, popularization. Rather, it is my sincere hope and wish that my analysis might help to make soon further progress in achieving, gradually, the goal of “doing mathematics by computer”. Also, my proposal will show that this goal may well be achieved by suitable modifications and extensions of Mathematica and similar systems. Of course, I take Mathematica only as a paradigm for symbolic computation software systems and my analysis applies to all current systems in this category.