This book gives (for the first time in English) a detailed scientific biography of Gerhard Gentzen (1909-1945), a German mathematician who was one of the founders of modern structural proof theory and who is considered to be one of the greatest logicians from the first half of the 20th century. In six chapters, the author describes Gentzen's life and his scientific achievements from his youth, through his studies, works, teaching and scientific activities, and his military service as well as his political ideas, until his arrest and tragic death in Prague in 1945. The author also analyses Gentzen's conditions for scientific study and research in National Socialist Germany before and during World War II, his fights for “German logic”, and his battles with colleagues and the political system. The book is based on a study of unknown and unpublished sources, archive materials, private letters, family documents and memoirs.

The book ends with four interesting appendices. The first and second appendix (written by C. Smoryński - Gentzen and Geometry, Hilbert's Programme) contain a short essay on Gentzen's results in geometry and a deeper analysis of Hilbert’s programme showing relations to ideas and mathematical results of Hilbert, Brouwer, Weyl, Gödel and Gentzen. In the third appendix, there are (for the first time in English) three lectures by G. Gentzen (The Concept of Infinity in Mathematics, The Concept of Infinity and the Consistency of Mathematics, and The Current Situation in Research in the Foundation of Mathematics), which were presented by G. Gentzen to a wide mathematical public in Münster (1936), at the Descartes Congress in Paris (1937) and in Bad Kreuznach (1937). The fourth appendix (written by John von Plato) explains in detail the Gentzen mathematical program, his ordinal proof theory, his work on natural deduction and his calculus, and it gives a general survey of later developments in structural proof theory.

The book can be recommended to a wide audience; it is suitable for mathematicians, historians of science, students and teachers.

Reviewer:

mbec