In the speaker’s Theorema Project, computer-support for the exploration of mathematical theories is provided. In the frame of Theorema, the speaker's "Lazy Thinking" approach is a general heuristic method for inventing (and proving) theorems and inventing (and proving) algorithms.
In the first part of the talk, the Lazy Thinking approach is illustrated by the standard example of synthesizing sorting algorithms. It will then be shown that an algorithm for a problem as difficult as Groebner bases construction can be synthesized completely automatically by Lazy Thinking. Groebner bases are sets of multivariate polynomials with certain properties that allow to solve fundamental problems of algebraic geometry (commutative algebra) algorithmically. The theory of Gröbner bases was introduced by the speaker in his PhD thesis many years ago.
Thus, in a way, in this talk the speaker reports on how, in his mature age, he was able to automate his mathematical inventive power of his young age.
Bruno Buchberger is professor of computer mathematics at the Johannes Kepler University (JKU) Linz since 1974 and is founding editor of the Journal of Symbolic Computation (1985). In 1987 he founded the RISC (Research Institute for Symbolic Computation) at JKU and two years later the JKU Softwarepark, which he is still heading.
Bruno Buchberger’s main contribution is the theory of Gröbner bases for non-linear systems. For his theory, he became Member of the Academy of Europe (1992), earned six honorary doctorates, and the ACM Award for Theory and Practice (2007). Furthermore, in 2010, he was awarded Austrian of the Year in the category research. He is also a honorary professor of the Vienna University of Technology.
This talk is organized by the Vienna PhD School of Informatics.