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195 of 204 people found the following review helpful
First of all, let's be honest and not mislead the general reader - this book covers a lot of highly advanced math. The author, Edward Frenkel, likely does as well as anyone could to outline the math in a way that a non-specialist audience can usefully grasp if they put in considerable effort and re-reading, but even then the reader needs to be comfortable with math at least at the undergrad level (calculus, differential equations, linear algebra, etc.). Don't expect to really 'understand' what Frenkel is talking about unless you have considerably greater math background, say grad school level and prior familiarity with the particular areas of math Frenkel covers.

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.
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193 of 208 people found the following review helpful
Edward Frenkel is one of the great mathematicians in the world, and in this book he voices an ancient complaint: "Intelligent people would never say, 'I don't care about art, or music. But it is totally okay to say, 'I hate math.'" The usual antidote is to show people that math can be fun and useful as in The Math Book: From Pythagoras to the 57th Dimension, or even exciting and sexy as in Numb3rs. Another species of popular math books and movies (such as Perfect Rigor,Pi,A Beautiful Mind and Good Will Hunting) imply (in Frenkel's words), "a mathematician is on the verge of a mental illness."

Love and Math takes a novel approach. The author loves math with a deep intensity that has animated an extraordinary life story, and he has the rare ability to explain why. The only comparable work I know is Stephen Hawking's A Brief History of Time. Both Frenkel and Hawking discuss work normally considered too advanced even for non-specialist professionals in their fields, in terms any serious reader can comprehend, without resorting to trite analogy or oversimplification. Love and Math does not teach you how to do advanced mathematics, but it can make you see what it is mathematicians are doing, why they do it, and why it matters.

The book proudly rejects defenses of mathematics as a useful applied field or as a mere adjunct to philosophic or scientific inquiry. The author holds himself out unapologetically as a pure mathematician, exploring abstract relationships for the love of it. He does make a few noises about the applicability of some mathematics, but it's always the same quantum physics and public key cryptography and he's half-hearted about that. He wants to tell us about the fierce emotions he feels: fear, doubt, disappointment, joy and triumph; and he's not ashamed to put mathematics up there with great art, or with concepts as fundamentally human as sex and death.

In a sense it is like a book on art or music appreciation that doesn't show you how to paint or play an instrument, but that delves deeply enough into those activities to allow a lay person to share some of the intense love felt by artists. But there is an important difference, at least in my opinion. All these books can claim to show you "The Heart of Hidden Reality," but I believe the "hidden reality" of art is basically subjective. Ultimately art tells us about ourselves, not about the universe. Mathematics is also revealing about the nature of the human mind, but amazingly it seems that God is a Mathematician as well. Mathematical truths that were discovered purely because they seemed logically appealing have often turned out to illuminate deep facts about the universe, many decades before we had empirical hints about those facts, or even before anyone thought to ask questions about them.

The first step in Frenkel's unorthodox strategy is to include brief but poignant autobiographical details. He skillfully sketches a character who is shy and brilliant, tough and sensitive. He has the great misfortune to be born under Communism, and in particular to be Jewish (according to USSR ethnicity rules, that is) in Russia in the 1980s. Yet he is extraordinarily fortunate in his mentors and colleagues, and in opportunities like being offered a visiting professorship to Harvard as a 21-year-old without a graduate degree (and in being allowed to accept it and emigrate to the West in 1990). He illustrates his personality through sharp portraits of incidents like disappointing his mentor by refusing the return to Russia or confronting a blustering apparatchik bigot, inexplicably invited to lecture at MIT.

Autobiography is interspersed with accounts of some of his mathematical researches. He explains the problems in simple terms, but he does not try to motivate them. Anyone can follow his definitions of braid groups and his discussion of his explorations. They take no mathematical interest or training, although a non-mathematical reader will have to plow through an unfamiliar amount of unmotivated details.

Why does he tackle these problems? Because it's fun and challenging. If that were the whole story he would be like an applied mathematician, or even a recreational one. He makes clear there is another factor. His problem choices are guided by professional mathematicians who feel the answers will open up new areas for exploration. He feels keenly the fear that he is working on an insoluble problem, or one with no elegant or useful answer, or one he is unequipped to solve. Yet that thrills him as much as daunts him. But when he finds the answers he treasures having discovered universal truth, unknown to any other human. Writing up formal proofs is a tedious ordeal.

This is a wonderful combination of autobiography, mathematics and, yes, love. Although it is easy and pleasant to read, it is a deep book that deserves careful contemplation and rereading. A few people can explain advanced mathematics, and fewer can explain love. Almost no one can explain both at once. This is an important book that everyone should read.
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61 of 70 people found the following review helpful
on September 30, 2013
Frenkel's book tackles a difficult challenge, that of writing a mathematics book for a popular audience while still actually writing about mathematics. In my mind Frenkel succeeds. He does so through unbridled passion and the telling of engaging autobiographical stories. Not all readers will be able to understand all of the mathematics on the first try but you will still come away with curiosity and excitement about mathematics. Aside from the popularization of mathematics, I found the book valuable because it describes in comprehensible terms Langlands program, a very exciting ongoing research effort. An understandable overview from an expert in a specialized field is a rare thing.

Anyone who reads Love and Math will be richer for it.
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22 of 23 people found the following review helpful
on November 27, 2013
Although much of the Mathematics (especially in the endnotes) is beyond my capability (even though I have a graduate degree in Math) the story of how this man fell in love with Math, overcame the anti-semitism in the Soviet educational system to become a Mathematician, and sought connections both within Mathematics and between Mathematics and Physics is fascinating and vividly told. My advice to the reader-- just skip what you don't understand. There is enough here without that to make for interesting reading.
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40 of 48 people found the following review helpful
on January 5, 2014
In the preface Frenkel hooks you by explaining that all the Math you ever learned in school was only a small part of the story and most of us have never been shown the masterpieces. He makes the analogy of learning about art without ever being shown a da Vinci or Picasso. There is truth to this. But as the book progresses Frenkel drags the reader through murkier and murkier waters until all but the most well schooled mathematician could hope to see but a fraction of what Frankel is trying to show.

It also does not help that Frankel writes badly. His prose is truly boring and uninspired. So even the autobiographical parts of the book, which the non-mathematician could easily follow, are tough to slog through.

I do give the author credit for the choice of subject matter. Group Theory, Topology, Reimann Surfaces and ties to Quantum Physics and String Theory are some of the jewels of Mathematics. However, Frenkel lacks what many genius mathematicians lack: empathy. He is unable to empathize with the plight of the mathematically unsophisticated reader and hence leave even the motivated lost, dazed and confused.
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23 of 27 people found the following review helpful
on December 22, 2013
A boy who grew up in a town closer to Moscow became interested in quantum physics. Plenty of popular science books were easy for him to find to read. His parents were engineers and were quick to recognize boy's talents. A mathematics professor of the only college in the town who is also a friend of the family took the boy under his wings. The professor asked him if he knew about the group SU(3). This conversation made the boy realize that he had to learn math to answer many questions he had by reading popular science books. Thus began the journey of this boy becoming one of the premier mathematicians of today. He was introduced to great mathemati- cians from the beginning. Mathematicians gave him problems to solve. He solved his first problem on Braid groups as a freshman. He attended Israel Gelfand’s legendary seminars at Moscow State University. He was offered a visiting professorship at Harvard even before he received his bachelor’s degree. To get a permanent job he needed a degree. He enrolled in the Harvard PhD program and received his PhD in one year. He first heard about the Langlands Program at Harvard. Since then until today he has been working on the Lang- lands Program. Langlands program is like a Rosetta stone revealing similarities in three apparently unrelated fields; namely, Number the- ory & curves/finite fields, Riemann surfaces and Quantum Physics. The book "Love and Math" is Edward Frenkel’s autobiography. He has done a masterful job of trying to bring hard mathematics that he has been working on to a level of an average reader by inter-vowing it with his fascinating life experiences. It is hard not to get excited about the math that you know practically nothing about. "Love and Math" makes you wanting to read more and get to know more about this fascinating mathematics. Frenkel has included many references for an interested reader to follow through as notes at the end of the book. "Love and Math" is a must read for young and old alike.
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18 of 21 people found the following review helpful
on January 11, 2014
The author says in the introduction that he wrote this book for non math people.

However, I am a high school math teacher and I would say the author missed his mark on his goal. The author discusses topics that he is really passionate about and that makes him really excited, but the topics (quarks, braids, etc) do not have very much pop appeal to the masses. He makes the mistake that just because he is excited about it, that other people will be as well.

Unfortunately, the author uses mathematical language and logic in his writing, which is difficult for non math people to follow. I wish he watered down the math a little bit and wrote more about the beauty of math in general, which he does an excellent job of doing in the 1st chapter.

The sections where the author speaks autobiographically about his life are interesting and are the more accessible parts of the book, but unfortunately between these sections the author dives into abstract concepts of math that are difficult to read through.
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32 of 40 people found the following review helpful
on July 14, 2014
This book should have been titled, "How I overcame anti-Semitism and a host of other problems to become the self-proclaimed greatest mathematician in the world."

I have a doctorate in mathematics from Oxford. I love mathematics as much as anyone I have ever known. I love mathematics because, to me, it epitomizes beauty, and truth, and grace. Mathematics, for example, forgives you completely when you make a mistake -- as soon as you admit it. :)

Frenkel appears to love mathematics for none of these reasons. Rather, he loves mathematics because mathematics makes him feel good about himself. (And he certainly feels awfully good about himself.) I found it incredibly distasteful.

Beyond that, the book is terribly written. The English is a bit choppy, and I didn't find it engaging at all. The mathematics will be completely inaccessible to a layman (and I mean *completely* inaccessible). In a good book of this sort, like Brian Greene's "The Elegant Universe," you wind up feeling like you understand what's being discussed (whether you really do or not is another matter, but you *feel* that you understand). Read this book, and all you'll feel is that Frenkel knows more mathematics than you do.

This is a book about Frenkel's love of Frenkel, nothing more.
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14 of 17 people found the following review helpful
on December 11, 2013
I loved math in high school and college (which is quite some time ago) enough to go to "math camp" two summers. This book looked great from the descriptions and the reviews but I found it quite frustrating.

It is a mixture of a memoir and a description of some cutting edge math that Edward Frenkel is working on. It doesn't really succeed as either a memoir or as an introduction to number theory for the layman.

As a memoir the early discussion of encountering antisemitism in Russia was interesting but then it became too much of "see how wonderful I am and how I am working with the best mathematicians in the world".

I call it a "description" of the cutting edge work rather than an "explanation" because I don't think he really explains much. He does try to describe the concepts but doesn't go far enough for the reader to see the beauty of it for themselves. I realize some of it is very advanced but I think some of it -- such as the connections between groups and quantum particles -- would be understandable to the general reader if he explained it better.

Ultimately, I struggled to get to the end because I kept hoping it would come together more clearly but ended up disappointed. Frenkel clearly is an excellent mathematician and apparently is a good teacher. I did learn some things from it but would not recommend it. I'd rather spend the time and considerable mental effort on a different book. I hope he has a co-author for his next book because I'd still like to understand the Langlands program.
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5 of 5 people found the following review helpful
on December 31, 2014
I expected this book to be yet another popular mathematics book explaining some fascinating mathematical subject at a level that most readers can partially understand. But this book is different. It does try to communicate the ideas in the Langlands Program, but for most readers, including me (a mathematically trained computer scientist), that material remains inaccessible. That is OK. The real subject of this book is the love and passion of mathematicians and the wonder of the profound connection between mathematics and the natural world. I appreciate the fact that the author does not strain to simplify the deepest material down to my level. I get great pleasure out of getting the flavor of material that is over my head, and understanding in that indirect way how vastly more mathematics is known to the specialists than I will ever know, and yet how much more there is that none of them even knows.
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