This book is an excellent autobiography written by the one of the greatest 20th century mathematician Saunders Mac Lane (1909-2005). The book is an account of his personal and scientific life. In fifteen parts subdivided into 64 chapters, the author describes his life from his youth and studies in the USA, through his studies in Göttingen (where he was close to D. Hilbert) up to his stays at many important universities (including Yale, Harvard and Chicago). He explains the academic, cultural and political atmosphere and traditions in the USA, Europe and China in the 20th century. His memoirs contain many interesting reflections on his scientific work and teaching concepts, relations between the political situations and scientific activities in the USA and Europe, and the relationship between his professional and personal lives.

He presents his inspiring style of teaching, which influenced many leading mathematicians of our time in the USA. He explains his scientific activities and ideas (research in modern algebra, category theory, homological algebra, algebraic functions, geometric mechanics and the philosophy of mathematics). He also describes his work on the monographs ‘A Survey of Modern Algebra’ (with G. Birkhoff) and ‘Homology’, which influenced the development of modern mathematical research. Some chapters are devoted to his activities as part of the American Mathematical Society (he was its influential president) and the National Academy of Science. He mixes professional observations with deeply personal commentaries. Many photographs of Mac Lane, his family and friends are included. The book was written not only for mathematicians but also for laymen interested in mathematics, mathematicians and their lives.

Reviewer:

mbec