As indicated by the title, the book consists of the collected papers that were written by a prominent German mathematician, Hellmuth Kneser, one of few mathematicians who were able to keep pace with the fast development of science and to retain a global view of mathematics at the beginning of the last century. His influence and role were significant and there is a stunning variety of topics to which he has contributed, including theoretical physics, topology, the theory of functions, Lie groups, ordinary differential equations and partial differential equations. He also had a great part to play in helping German mathematics catch up with the more mathematically developed countries by filling the gap created after the Second World War in some fields, e.g. in mathematical economy. He did a lot to show to the general public how important mathematics is for modern society and he contributed substantially in improving teaching.

The first chapter (576 pp.), containing Kneser’s mathematical articles, is followed by a chapter of review articles (20 pp.). The next chapter (with the title Wissenschaftliche Grundlagen der Schulmathematik, 185 pp.) is devoted to arithmetic, algebra, analysis and geometry. These three chapters are written in German. The rest of the book contains chapters with commentaries on H. Kneser‘s papers on topology and complex function theory, and on his contributions to convexity, foundations and education, and miscellaneous topics by D. Gabai, W. H. Kazez, C. McA. Gordon, K. H. Hoffman, G. Betsch, A. Huckleberry, R. Remmert, M. Range, I. N. Baker, G. Thorbergsson, J. Kindler and G. Pickert.

Reviewer:

jdr