A writer in the journal Nature once said that “festschriften are for men who have put their stamp on some branch of enquiry during a certain period of time” [1]. Bruno Buchberger, the honoree of this festschrift, more than meets that description. He founded the theory of Gröbner bases (which, with characteristic modesty, he named after his supervisor), a field that today is responsible for several textbooks, sessions in most computer algebra conferences, and implementations in any reasonable general-purpose computer algebra system (as well as several specialist ones, including CoCoA, Macaulay, and Singular, to name but three). The field even has its own mathematics subject classification: “13P10 Polynomial ideals, Groebner bases.” While this volume does not say much about Buchberger himself, the curious reader can consult a 2006 paper [2] for more on his life and work. In fact, it is the lead paper in the festschrift special (double) issue of the Journal of Symbolic Computation, which Buchberger founded over 20 years before.

This book contains the more philosophical papers common in festschriften, which would have been out of place in the previous publication:

In “Foundations of Mathematics from the Perspective of Computer Verification,” author Henk Barendregt presents a powerful piece arguing for the unity of mathematics and the importance of computer verification.

In “On the Role of Logic and Algebra in Software Engineering,” Manfred Broy has written a powerful essay precisely described by its title, and one that I shall be bringing to my own department during our next curriculum review.

Stephen Wolfram’s “New Directions in the Foundations of Mathematics (2002)” is a talk written in 2002, predating his later work, Wolfram Alpha.

In “Towards a Symbolic Computation Philosophy (and Methodology!) for Mathematics,” Doron Zeilberger makes the strong point that recent developments mean that many identities that used to have to be proved, or even discovered and proved, can now be computed.

All in all, I found this a useful set of papers using the umbrella of the festschrift to talk about what we are building, rather than just adding more bricks.