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Rating: 
Summary: A thoughtful, engaging discussion of a complex relationship
Review: I have read Rothstein's book several times since it was printed, and I have also used it as a text in several Honors College courses devoted to the the relationship between music and mathematics. One way of defining music is that it's a five letter word in the English language for a lot of different things that people do with patterns of sound and silence. And one way of defining mathematics is that it's an eleven letter word in the English language for a lot of different things that people do with pattern. By exploring the ways in which music and mathematics handle pattern, one is naturally pointed in other directions (weaving, art, science) that demonstrate how valuable it is to recognize and explore the inter-connectedness of apparently "different" fields. Rothstein's book is an elegant exploration of this kind of inter-connectedness. Although both musicians and mathematicians might find themselves alternately arguing with Rothstein about an issue in their own field, or befuddled because he is talking about something they do not understand, "Emblems of Mind" provides both with a thought-provoking and outstanding contribution to the literature on the topic. While other texts have tended to be so sophomoric as to be useless, Rothstein's book challenges the reader to explore more deeply a connection which seems so obvious yet amorphous when one looks at it more closely. It's unfortunate he doesn't write more about it.
Rating:
Summary: A thoughtful, engaging discussion of a complex relationship
Review: I have read Rothstein's book several times since it was printed, and I have also used it as a text in several Honors College courses devoted to the the relationship between music and mathematics. One way of defining music is that it's a five letter word in the English language for a lot of different things that people do with patterns of sound and silence. And one way of defining mathematics is that it's an eleven letter word in the English language for a lot of different things that people do with pattern. By exploring the ways in which music and mathematics handle pattern, one is naturally pointed in other directions (weaving, art, science) that demonstrate how valuable it is to recognize and explore the inter-connectedness of apparently "different" fields. Rothstein's book is an elegant exploration of this kind of inter-connectedness. Although both musicians and mathematicians might find themselves alternately arguing with Rothstein about an issue in their own field, or befuddled because he is talking about something they do not understand, "Emblems of Mind" provides both with a thought-provoking and outstanding contribution to the literature on the topic. While other texts have tended to be so sophomoric as to be useless, Rothstein's book challenges the reader to explore more deeply a connection which seems so obvious yet amorphous when one looks at it more closely. It's unfortunate he doesn't write more about it.
Rating: 
Summary: Tough reading
Review: The subject matter of this book should be a well known fact - that music and mathematics have much in common. The author's expertise in both subjects is presumably well developed and his experience as music critic of the New York Times should have endowed him with eloquence and clarity. Sadly, none of this comes through to me. The book is very heavy reading with many tortuous sentences and themes which wander all over the place. The approach taken to identifying the similarities between music and mathematics actually cause me to ask myself: "yes, but many of these characteristics could equally be applied to engineering, art, language, poetry - even crowd dynamics!" It is hard to see from his development of the subject why these factors apply exclusively to music and mathematics. Thus the esoteric similarity between musical notation and mathematical symbols is not exclusive to those disciplines. I think the author missed a wonderful opportunity to expand on a fascinating subject with insight and clarity.I found I was unable to finish reading the book. The writing style and theme development was too daunting.
Rating:
Summary: Tough reading
Review: The subject matter of this book should be a well known fact - that music and mathematics have much in common. The author's expertise in both subjects is presumably well developed and his experience as music critic of the New York Times should have endowed him with eloquence and clarity. Sadly, none of this comes through to me. The book is very heavy reading with many tortuous sentences and themes which wander all over the place. The approach taken to identifying the similarities between music and mathematics actually cause me to ask myself: "yes, but many of these characteristics could equally be applied to engineering, art, language, poetry - even crowd dynamics!" It is hard to see from his development of the subject why these factors apply exclusively to music and mathematics. Thus the esoteric similarity between musical notation and mathematical symbols is not exclusive to those disciplines. I think the author missed a wonderful opportunity to expand on a fascinating subject with insight and clarity. I found I was unable to finish reading the book. The writing style and theme development was too daunting.
Rating: 
Summary: Disparate but Interesting Ideas are Developed
Review: These reviews cast a poor light on this book. Although I read it some time ago (1999), the book seemed to be interesting because it tracked the development of mathematical thought and musical thought over several centuries. It might be poorly written, but what can one expect from a mathematician? Even if the links between math and music are not clearly developed, I found both topics interesting. This interest may be related to my ignorance of pure math and musical theory; nonetheless, it provides people like me with a port of entry into two topics that could easily be treated with too much complexity. Maybe this book is just a collection of very interesting and unrelated topics.
Rating:
Summary: Disparate but Interesting Ideas are Developed
Review: These reviews cast a poor light on this book. Although I read it some time ago (1999), the book seemed to be interesting because it tracked the development of mathematical thought and musical thought over several centuries. It might be poorly written, but what can one expect from a mathematician? Even if the links between math and music are not clearly developed, I found both topics interesting. This interest may be related to my ignorance of pure math and musical theory; nonetheless, it provides people like me with a port of entry into two topics that could easily be treated with too much complexity. Maybe this book is just a collection of very interesting and unrelated topics.
Rating: 
Summary: Good Food for thought
Review: This book has a lot of interesting information about both music and mathematics. But it seems to me to be two different books interleaved with each other in one volume. The mathematics covers factors and primes, the Golden Ratio, and infinity; none of these are related to music by the author. The music analyzes by what seems to be traditional methods musical compositions such as Beethoven's Appassionata Sonata and Chopin's Prelude in A minor Op 28 No. 2 (I call this one "The Monster"). The analysis of the latter is faulty in one respect: at the climax the author says that the chords can't be named; I can name the main chord: a D# diminished chord with a minor seventh on top; actually the piece reminds me of someone trying to be funny by ending a D major piece with a sour-note D# in the melody. There is relationship between music and mathematics; for example, the structure of the scale and that the A of G major differs from the A in C major in just intonation by the ratio of 81/80; or the relationship of rhythm styles with numbers in binary notation. But none of this is mentioned. To me this is two separate books; interesting to read (especially on Chopin's monstrous prelude above) but still with a split identity.
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