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This book presents four mathematical essays that explore the foundations of mathematics and related topics ranging from philosophy and logic to modern computer mathematics. It details the state of the art as well as new ideas and directions.

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This book presents four mathematical essays which explore the foundations of mathematics and related topics ranging from philosophy and logic to modern computer mathematics. While connected to the historical evolution of these concepts, the essays place strong emphasis on developments still to come.

The book originated in a 2002 symposium celebrating the work of Bruno Buchberger, Professor of Computer Mathematics at Johannes Kepler University, Linz, Austria, on the occasion of his 60th birthday. Among many other accomplishments, Professor Buchberger in 1985 was the founding editor of the Journal of Symbolic Computation; the founder of the Research Institute for Symbolic Computation (RISC) and its chairman from 1987-2000; the founder in 1990 of the Softwarepark Hagenberg, Austria, and since then its director.

More than a decade in the making, Mathematics, Computer Science and Logic - A Never Ending Story includes essays by leading authorities, on such topics as mathematical foundations from the perspective of computer verification; a symbolic-computational philosophy and methodology for mathematics; the role of logic and algebra in software engineering; and new directions in the foundations of mathematics. These inspiring essays invite general, mathematically interested readers to share state-of-the-art ideas which advance the never ending story of mathematics, computer science and logic.

Mathematics, Computer Science and Logic - A Never Ending Story is edited by Professor Peter Paule, Bruno Buchberger´s successor as director of the Research Institute for Symbolic Computation.

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Preface.- Henk Barendregt: Foundations of Mathematics from the Perspective of Computer Verification.- Manfred Broy: On the Role of Logic and Algebra in Software Engineering.- Stephen Wolfram: New Directions in the Foundations of Mathematics (2002).- Doron Zeilberger: Towards a Symbolic Computational Philosophy (and Methodology!) for Mathematics.

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From the reviews:

"This book contains the more philosophical papers common in festschriften ... . 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." (J. H. Davenport, Computing Reviews, January, 2014)

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