In this volume, Jan von Plato gives an overview of Gerhard Gentzen’s life and scientific achievements and examines his long-lost work on logic and foundations of mathematics. Attempts at locating Gentzen’s missing manuscripts had failed for many years, but after several decades, two slim folders of shorthand notes were found. This book is essential for placing the translations of those notes in their proper context, and the materials within are unique in the way they show the birth and development of Gentzen’s central ideas and results, sometimes in a well-developed form, at other times as flashes into the workings of a unique mind.
Gentzen is best known for his development of the proof systems of natural deduction and sequent calculus, central in many areas of logic and computer science today. Another noteworthy achievement was his resolution of the embarrassing situation created by Gödel's incompleteness results, in particular, the result surrounding the unprovability of consistency of elementary arithmetic. After his successes, Gentzen dedicated the remainder of his short life to the main problem of Hilbert's proof theory—the question of the consistency of analysis. He was arrested in the summer of 1945 with other professors of the German University in Prague and died soon afterward of starvation in a prison cell.
