Abstract

The Theorema project aims at extending current computer algebra systems by facilities for supporting mathematical proving. The present earlyprototype version of the Theorema software system is implemented in Mathematica 4.0. The system consists of a general higherorder predicate logic prover and a collection of special provers that call each other depending on the particular proof situations. The individual provers imitate the proof style of human mathematicians and produce humanreadable proofs in natural language presented in nested cells. The special provers are intimately connected with the functors that build up the various mathematical domains.
The longterm goal of the project is to produce a complete system which supports the mathematician in creating interactive textbooks, i.e. books containing, besides the ordinary passive text, active text representing algorithms in executable format, as well as proofs which can be studied at various levels of detail, and whose routine parts can be automatically generated. This system will provide a uniform (logic and software) framework in which a working mathematician, without leaving the system, can get computersupport while looping through all phases of the mathematical problem solving cycle:
 the phase of specifying a problem including the compilation of relevant knowledge and the definition of new concepts(predicates, functions) and auxiliary algorithms;
 the phase of exploring a given problem and creating ideas and conjectures by studying examples using the available knowledge and algorithms;
 the phase of proving or disproving conjectures and thereby increasing the relevant knowledge base;
 the phase of programming, i.e. transforming useful new and provenly correct mathematical knowledge into algorithms for solving the initial problem;
 the phase of writing up one's finding in interactive mathematical documents.
People
Prof. Dr. Tudor Jebelean  9946 mail 
CoInvestigators
Prof. Dr. Bruno Buchberger  9941 mail 
Scientific Staff
Dr. Martin Giese  9969 mail  
DI Laura Kovacs  9939  
DI Nikolaj Popov  9926  
DI Camelia Rosenkranz  9969 
Publications
SpezialForschungsBereich SFB F013  Special Research Program of the FWF  Austrian Science Fund