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Love and Math: The Heart of Hidden Reality Hardcover – October 1, 2013
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From Publishers Weekly
U.C. Berkley mathematician Frenkel reveals the joy of pure intellectual discovery in this autobiographical story of determination, passion, and the Langlands program—a sort of Grand Unified Field Theory of mathematics. As a teenager Frenkel was converted from math hater to eager theorist by a mathematical friend of the family, enough to pursue it despite his struggles against an unapologetically anti-Semitic Soviet educational system. Frenkel writes casually of climbing over the fence to sit in on advanced classes at Moscow State University, a top school that didn&'t accept Jews. With the help of mentors, he worked hard and eventually found his way to Harvard and the freedom to focus on his research. Frenkel balances autobiographical narrative with enthusiastic discussions of his own work on the Langlands program, a web of algebraic conjectures named after a Canadian mathematician that is noted for its usefulness in organizing seemingly chaotic data into regular patterns full of symmetry and harmony, and its applications to quantum theory. While the math can be heavy going, Frenkel&'s gusto will draw readers into his own quest, pursuing the deepest realities of mathematics as if it were a giant jigsaw puzzle, in which no one knows what the final image is going to look like. B&w illus. (Oct.)
After Rick and Isla meet at a dinner party and fall in love, what’s next? For Frenkel, it is the mathematical charting of the Rick-Isla relationship as a trajectory on the x-y plane. The surprising notion of a “formula of love” fits into the remarkable understanding of math Frankel unfolds as he recounts his labors on conceptual frontiers where an audacious new master theory, the Langlands Program, is linking geometry, number theory, and algebra. To qualify for a role in those labors, Frenkel defied the anti-Semitism pervading the Soviet academic world in which he came of age and then won appointment to a Harvard professorship. Aware that few of his readers share his academic training, Frenkel pares the technical details to a minimum as he reflects on the platonic transcendence of mathematical concepts and marvels at their mysterious utility in explaining physical phenomena. Not merely dry formulas in textbooks, the math Frenkel celebrates fosters freedom and, yes, even distills the essence of love. A breathtaking personal and intellectual odyssey. --Bryce Christensen
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Being an engineer, I fall into the former category and came to this book already loving math, and I found the math in this book to often be quite tough going (especially in the second half of the book), though I did get a rough sense of what he was talking about (and I followed the advice to keep going in the tougher parts rather than getting bogged down). True, I could re-read the whole book to get a better understanding, but realistically it would make more sense to bone up on the prerequisite math using other books and then return to this book in a few years (yes, that long). Because I feel that the accessibility of this book for the general reader has been overstated by the book's endorsers and overestimated by the author, I'm deducting a star.
That said, I did enjoy this book greatly and am glad that I read it. Besides the exposure to high-level math and the associated research and discovery process (at both the individual and collaborative levels), I found this window into Russian culture fascinating, and frankly I was rather surprised to see that the culture matches many of the stereotypes quite well (Frenkel relates many memorable stories in this regard). I was also inspired to see Frenkel's passion for math, his perseverance against serious adversity, and his resulting remarkable achievements, which he describes with considerable humility, all things considered. In that regard, I was also awed, yet again, to see the reach of some human minds (alas, not mine!) into the wondrous parallel universe of Platonic objective truth which we call 'mathematics' (or more precisely, perhaps we should give a different name to that universe, since 'mathematics' only reflects what we've discovered and mapped so far).
Summing up, I can definitely recommend this book to anyone who already loves math and has decent mathematical 'maturity' in the sense of being able to handle math at a relatively abstract level. Those who don't have at least that background could mostly skip the math in the book and instead focus on the memoir aspect. Whether that would be worthwhile depends on the specific interests of the reader, and I only can say that I and apparently many other readers greatly enjoyed that aspect.
I've attended his course at UC Berkeley (2015 Spring- Linear Algebra). He is amazing at illustrating relations between quantum mechanics and mathematics. You know, it's rare that people on earth learn both math and physics thoroughly and I think he is definitely one of them.
This book tells a legend and I think few of us can experience such amazing moments.
The autobiographical part of the book is moving, and details Frenkel's travails in the declining days of the Soviet empire when open antisemitism caused some of the Soviet Union's most talented young people to be denied entry to the best graduate schools solely because of their Jewish origin. Fortunately Frenkel managed to overcome this, begin his career and eventually make his way out. The most heartrending part of this story is that Frenkel in fact grew up with little knowledge or experience of Jewish tradition or practice in any positive way; for him it was simply a millstone around his neck.
The second part of the writing, about Frenkel's main interest in mathematics, the so called Langland's program, is less successful. He jumps from elementary concepts to advanced language in a way that few non-experts will follow. Recently Frenkel has posted a series of YouTube videos on this which give a much more gradual exposition is about six hours of video; I recommend those.