Customer Reviews

Proofs and Confirmations: The Story of the Alternating-Sign Matrix Conjecture (Spectrum)

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This book tells the story of one of the more important areas of research in algebraic combinatorics in the last few years. Not only does it tell the story of how the relevant conjectures were proposed, and how they were eventually proved (including some of the blind alleys and several cases where surprising connections were discovered), but it also contains a beautiful exposition of the relevant mathematics, at a level which a reader with no more than a reasonable background in linear algebra can follow. The history is fascinating and the mathematics is beautiful. If you want to know what research in mathematics is really like, this is the book to read.

Everyone wants to know what mathematicians do should read this book. Yes, only very few among people can get familiar or endure gorgeous complicated formulas here, But even scan or skim this book one will learn much more than he predicted. The goal of this book is simple enough: To prove a conjecture (surely when proved, it becomes a theorem) But the structure and details are well selected and carefully designed. First it introduces and explains the original problem, than talk about it's history, how it does connect with other branches of math, what these branches is about, and what the other mathematicians do on this conjecture, and at last the most exciting: how these results all bringed together and then solve this 20-year-long famous conjecture in combinatorics. There are exercises after every chapter. so this is NOT merely a history survey (as most books do). Indeed it is a textbook and contains some very excellent introductions to some branches(for example, plane partition). And I think this is THE correct style to populating mathematics--- Do not afraid of formulas, just show readers the signs, the terrible formulas, show them how and what mathematicians study and think! Every student major in mathematics should read it, and it surely is a must-have for reseachers in combinatorics.

Dave Bressoud tells, in his wonderful gripping style, the fascinating recent history of the proof of the alternating sign matrix conjecture, and the not-so-recent background that lead to it. The book can be read on many levels, and is full of fascinating historical tidbits. This book is a must to anyone who wants to know how math is actually done, and who wants to share in the excitement of discovery.