"Computer Support for Inventing Groebner Bases Theory" Bruno Buchberger. RISC - Research Institute for Symbolic Computation, Johannes Kepler University Schloss Hagenberg A-4232 Hagenberg Austria E-mail:buchberg@risc.uni-linz.ac.at Abstract: We will speak about the Theorema project (based on Mathematica), which aims at supporting mathematicians in playing with new notions and studying their consequences. The main tools are various computer-supported provers that generate proofs in a style that imitates human proving. The project is motivated by the author's work on various variants and generalizations of the Groebner bases theory.