From Publishers Weekly
It's a rare person who describes negative numbers (or any numbers) as "unassuming but fun," and he is likely the same person who would notice that negative numbers "stand as just about the only kind of numbers about which a book has not been written." That man is Martinez, and in this book, he touches on mathematics history and great mathematical squabbles about the "evident meaning" of negative numbers, all with the goal of sexing up negative numbers and proposing a "meaningful math" that could rekindle the "connection between mathematical truth and physical experience." No small feat, and the outcome is a qualified success: he writes with clarity and provides context (French novelist Henri Beyle resented the notion that two negatives make a positive) that helps layreaders to deal with abstruse subject matter, but many of his canny re-interpretations of mathematical laws depend on questionable means, such as rejiggering "the definition that we choose to give to the = sign." English majors who never understood why they were required to take math classes may enjoy Martinez's blend of humanism and philosophy, and number-people will certainly want to give this a look.
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It is fair to say that Negative Math completely blew my mind. . . . Martínez's superb writing makes even the most subtle arguments and paradoxes seem obvious, but don't expect this short book to be easy sailing. It will set your mind racing, although every page is absolutely worth the effort. -- Plus Magazine, University of Cambridge
this is a serious-minded and interesting book. . . . The first part of the book, which I enjoyed immensely, is a history of the struggles of mathematicians to cope with the idea of negative numbers. It is enormously encouraging . . . intriguing and provocative. . . -- The Mathematical Intelligencer
The author has committed himself to having this writing and this subject matter accessible to the general reader, and he has succeeded to a remarkable degree . . . For the teacher currently involved with these concepts, this innovative work should provide useful background and prove to be an outstanding read. -- The Mathematics Teacher
a book that is at once scholarly and readable . . . anyone with an interest in intellectual history would benefit . . . Martínez's book has the potential to cause the generation of many golden fibers that can be used in weaving the fabric of mathematics. -- Books & Culture
It is interesting and to a certain extent inspiring to look at this fundamental transformation of mathematics with the eyes of algebra and not as usual from the point of view of non-Euclidean geometry . . . whoever follows author will be inspired and forced to think about problems which he never put himself before. -- Zentralblatt MATH
"Alberto A. Martínez . . . shows that the concept of negative numbers has perplexed not just young students but also quite a few notable mathematicians. . . . The rule that minus times minus makes plus is not in fact grounded in some deep and immutable law of nature. Martínez shows that it's possible to construct a fully consistent system of arithmetic in which minus times minus makes minus. It's a wonderful vindication for the obstinate smart-aleck kid in the back of the class."--Greg Ross, American Scientist
"Alberto Martinez . . . has written an entire book about the fact that the product of two negative numbers is considered positive. He begins by reminding his readers that it need not be so. . . . The book is written in a relaxed, conversational manner. . . . It can be recommended to anyone with an interest in the way algebra was developed behind the scenes, at a time when calculus and analytic geometry were the main focus of mathematical interest."--James Case, SIAM News
] is very readable and the style is entertaining. Much is done through examples rather than formal proofs. The writer avoids formal mathematical logic and the more esoteric abstract algebras such as group theory."--Mathematics Magazine