Modern Algebra and the Rise of Mathematical Structures

by Leo Corry

A historical presentation of the two stages of development in the idea of mathematical structure. Corry traces the structural approach from the mid 19th century to its consolidation in the 1930s into "algebraic structures." On the other hand, the more elusive attempt to address the meaning of structure from a mathematical perspective begins in 1930 and is defined by Oystein Ore's lattice-theoretical theory of structures, Nicolas Bourbaki's theory of structures, and the theory of categories and functors. Annotation c. by Book News, Inc., Portland, Or.

Genres: Mathematics, History

Paperback

First published February 28, 1996

Reviews

[Arthur Ryman · Rating 3 out of 5]

This book is a very scholarly discussion of the historical evolution of algebra, starting from the introduction of ideals by Dedekind and Noether and finishing with the emergence of category theory by Eilenberg and Mac Lane. In fact, I was motivated to read it when it was cited in a recent YouTube lecture on category theory. However, I found the going tough. The book reads more like a dissertation than a book aimed at a general mathematically literate audience. The author has the pedantic habit of footnoting his citations with verbatim quotations of the original papers in their native French or German. I guess his intended auditence is fellow historians who are fluent in multiple foreign languages. Unfortunately, the book is also severely marred by a higher than normal frequency of both mathematical and grammatical typos. For example, even the cover diagram has a typo (the arrow from F(A) to F(B) should be labelled by F(f), not G(f)). Fortunately, the correct diagram appears on page 342. Do not expect to learn mathematics from this book. On the plus side, the book does give a very detailed historical account of the evolution of the concept of mathematical structure. I especially enjoyed the discussion of Bourbaki's influence. In summary, I found the historical content interesting but the way it was presented less so. One positive side-effect of reading this book was that it inspired me to acquire a copy of van der Waerden's classic textbook on Algebra, which inspired the title of the present book.