=ADD= =author= Buchberger; Bruno =title= {\em Mathematica:} Doing Mathematics by Computer? =number= 93-50 =year= 1993 =url= ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1993/93-50.ps.gz =abstract= This paper is presented in the form of a {\em Mathematica} notebook. This fact should be conceived as a symbolic gesture that expresses my high appreciation and admiration for the wholistic oeuvre of Stephen Wolfram with its many facets: mathematics, language design, algorithms, software and system design, teaching and publication tools, applications, and -- yes -- business, marketing, popularization. I like his way of doing and succeeding in doing things many of us were only speaking or dreaming about. \xpar Hence if, in the present paper, I will criticize the basic tenet of {\em Mathematica} this is nit meant to decrease the invaluable merits of Stephen's work. Rather, it is my sincere hope and wish that my analysis might help to make soon further progress in achieving, asymptotically, 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 {\em Mathematica} and similar systems. \xpar (If the reader is not satisfied with typesetting of text in the following {\em Mathematica} notebook, he should be informed that, soon, a new version of {\em Mathematica} will be released that incorporates a fantastic pretty-print facility for mathematical text cells.) =howpublished= A. Miola, M. Temperini (eds), Advances in the Design of Symbolic Computation Systems, Springer Wien - New York, 1997, pp. 2-29. =note= Invited Talk at DISCO'93, Gmunden, Austria, Sept. 1993. =location= 2 =owner= 2 =source= 3 =reftype= 14