Selected Works (Springer Collected Works in Mathematics)

Luis Antonio Santaló (Spain 1911 - Argentina 2001) contributed to several branches of Geometry, perhaps his most outstanding achievement being his having laid the mathematical foundations of Stereology and its applications. Considerable power of abstraction, a brilliant geometric intuition and his outstanding gifts as a disseminator of science were among his virtues. The present volume contains a selection of his best papers. 

Part I consists of a short biography and some photographs along with a complete list of his publications, classified into research papers, books, and articles on education and the popularization of mathematics, as well as a comprehensive analysis of his contribution to science.

Part II, the main part of the book, includes the selected papers, arranged in five sections, according to the nature of their contents: Differential Geometry, Integral Geometry, Convex Geometry, Affine Geometry, and Statistics and Stereology. Each section is preceded by a comment by a renowned specialist: Teufel, Langevin, Schneider, Leichtweiss, and Cruz-Orive respectively.

Finally, Part III emphasizes the influence of his work. It contains comments by several specialists about modern results based on, or closely related to, those of Santaló, some book reviews written by Santaló, as well as some reviews of his books. As a curious addendum, a ranking of his own articles, given by Santaló himself, is included.

Luis Antonio Santaló (Spain 1911 - Argentina 2001) contributed to several branches of Geometry, perhaps his most outstanding achievement being his having laid the mathematical foundations of Stereology and its applications. Considerable power of abstraction, a brilliant geometric intuition and his outstanding gifts as a disseminator of science were among his virtues. The present volume contains a selection of his best papers.

Part I consists of a short biography and some photographs along with a complete list of his publications, classified into research papers, books, and articles on education and the popularization of mathematics, as well as a comprehensive analysis of his contribution to science.

Part II, the main part of the book, includes the selected papers, arranged in five sections, according to the nature of their contents: Differential Geometry, Integral Geometry, Convex Geometry, Affine Geometry, and Statistics and Stereology. Each section is preceded by a comment by a renowned specialist: Teufel, Langevin, Schneider, Leichtweiss, and Cruz-Orive respectively.

Finally, Part III emphasizes the influence of his work. It contains comments by several specialists about modern results based on, or closely related to, those of Santaló, some book reviews written by Santaló, as well as some reviews of his books. As a curious addendum, a ranking of his own articles, given by Santaló himself, is included.

From the Preface written by Simon Donaldson:

"The word geometry can cover many different things. The paths that can be traced from the most ancient concepts to sophisticated modern abstractions form one of the charms of the subject. We can all agree that the study of lines in three dimensional Euclidean space is a part of geometry. It is a wonderful idea that the set of all lines can itself be considered as a space, which has in turn its own geometry. Of course this leap into abstraction may seem commonplace now... Modern differential geometry provides the language and tools for doing calculus on such spaces and in particular for integration. Then we can talk about the volume of a set of lines, the mean value of a function on the space of lines and so on. This is the beginning of Integral Geometry, to which Luis Santaló contributed so much."