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3.48 AVERAGE
3.48 AVERAGE
Idea of math Platonism is mind bending. Infinite donuts is transcendent.
I wish there were way more pictures though.
Also, I was a little disappointed that the he drew analogy between the study of mathematics and the experience of love and then backed away from asserting that there is a “formula that describes or explains love”. Up until then his book was a compelling argument that there likely is a mathematical expression for love, though perhaps only contemplated at a god level. Or several nebula sized computers.
I guess that fits with his puzzling practice of simultaneously speaking of perception, love, beauty and objective “Truth”. Again, these broke from my Subjective apprehension of the beautiful concepts he described.
“The fact that b1, the first Betti number, is equal to 1 reflects the presence of a non-trivial one-dimensional piece.” p. 25
“It turns out that this is in fact the Lie algebra of the Lie group SO(3). So the esoteric-looking operation of cross-product is inherited from the rule of composition of rotations of the sphere.” p. 121
“a rule that assigns a point in the target manifold to each point in the Riemann surface.” p. 208
“The base of the fibration is a vector space, and the fibers are tori. That is, the whole space is a collection of tori, one for each point of the base.” p. 219
I wish there were way more pictures though.
Also, I was a little disappointed that the he drew analogy between the study of mathematics and the experience of love and then backed away from asserting that there is a “formula that describes or explains love”. Up until then his book was a compelling argument that there likely is a mathematical expression for love, though perhaps only contemplated at a god level. Or several nebula sized computers.
I guess that fits with his puzzling practice of simultaneously speaking of perception, love, beauty and objective “Truth”. Again, these broke from my Subjective apprehension of the beautiful concepts he described.
“The fact that b1, the first Betti number, is equal to 1 reflects the presence of a non-trivial one-dimensional piece.” p. 25
“It turns out that this is in fact the Lie algebra of the Lie group SO(3). So the esoteric-looking operation of cross-product is inherited from the rule of composition of rotations of the sphere.” p. 121
“a rule that assigns a point in the target manifold to each point in the Riemann surface.” p. 208
“The base of the fibration is a vector space, and the fibers are tori. That is, the whole space is a collection of tori, one for each point of the base.” p. 219
challenging
informative
inspiring
relaxing
medium-paced
challenging
hopeful
informative
inspiring
reflective
medium-paced
Frenkel does delve into heavy mathematics, but that's not really the point of the book. Frenkel uses math to show real universal truth, and how that can cut through any political or religious barriers. Along the way, he shows the connections between our physical world and its underlying mathematical constructs.
informative
inspiring
lighthearted
fast-paced
I struggled with whether to give this book three or four stars - I definitely enjoyed it, and Frenkel writes with a conversational, easy-to-read style. But, although it's billed as for non-mathematicians, without already having a reasonable understanding of certain basic ideas of abstract algebra, geometry, analysis and topology (and modern physics!), the math gets pretty hard to follow. The ideas he's communicating, especially towards the end of the book, simply don't have an easy-to-understand explanation. Analogies can only get you so far.
I get the impression Frenkel is writing to, essentially, himself as a teenager. So if you're someone naturally gifted and fascinated by maths, whose never had access to the so-called real stuff before, you'll eat it up. If you're an average person, looking to gain some idea of what the field of mathematics actually looks like, not so much. You'll get a glimpse, but a lot of the math in this book will go over your head.
That said, it was an interesting read, both as an autobiographical account of his struggles growing up in Soviet Russia, and as a survey of the Langlands Program. It both confirmed my belief that I'm not cut out to be a mathematician and made me wish I were.
I get the impression Frenkel is writing to, essentially, himself as a teenager. So if you're someone naturally gifted and fascinated by maths, whose never had access to the so-called real stuff before, you'll eat it up. If you're an average person, looking to gain some idea of what the field of mathematics actually looks like, not so much. You'll get a glimpse, but a lot of the math in this book will go over your head.
That said, it was an interesting read, both as an autobiographical account of his struggles growing up in Soviet Russia, and as a survey of the Langlands Program. It both confirmed my belief that I'm not cut out to be a mathematician and made me wish I were.
This author was a guest on the Colbert Report, which is when I first learned of his book. He described the concept so passionately, and he argued that mathematics has been so misunderstood because it isn't given its fair due in K-12 school curricula. Frenkel is disillusioned that the general masses don't appreciate math, and he set out to conquer our hearts with this book. He stated that this book was written specifically for people like me, laypeople who have never had the opportunity to give math a fair shake because all they learn are boring basic concepts in school and they never see the true beauty of it. He compared it to taking an art class in which you only get to paint a fence and are never actually shown the works of great artists. Fair enough, I thought. I'll give it a try.
By chapter three, I realized that Edward Frenkel is a misguided genius who truly believes that laypeople could possibly understand what he is talking about. I don't sense that he is a self-righteous individual who wants to come across as ridiculously smart (he is, in fact, ridiculously smart). I think he really just doesn't get that trying to relate these concepts to people like me, who only made it through Calc A, cannot be done. Hence, large parts of the book left me absolutely lost. Even BJ, who was a math minor, said he wasn't keeping up and so he quit reading it. Consider this sentence: "The idea of string theory is that by doing calculations in these sigma models and summing up the results over all possible Riemann surfaces E (that is, over all possible paths of the strings propagating in a fixed space-time S) we can reproduce the physics that we observe in space-time S." Honestly, I wish this particular sentence, which I chose at random, was a stand-apart in terms of its difficulty, but the truth is that much of this book is written in this language with ten unfamiliar concepts thrown together in the same sentence, all with the assumption that we must understand what the heck he is talking about.
The redeeming points of the book were the interspersed memoir portions, which were extremely interesting. Frenkel was born in the Soviet Union and endured intense antisemitism at practically every turn in his education, but still prevailed and eventually traveled to Harvard and then to UC-Berkeley with professorships. I very much loved hearing about his experiences growing up, in college, working with colleagues, and his personal excitement about solving mathematical problems. It was only that he felt the need to then delve INTO those problems with technical language that made this book a disappointment--along with the fact that I didn't feel it delivered what it originally promised.
In the end, I walked away appreciating Edward Frenkel's personal story. However, I did NOT end up appreciating math anymore than I ever did before, which was precisely why I decided to read the book in the first place. Unless you're ready to skip some major portions or else you're a mathematician, I don't recommend this book to you. This book is truly written for mathematicians, not laypeople, as it was so described.
By chapter three, I realized that Edward Frenkel is a misguided genius who truly believes that laypeople could possibly understand what he is talking about. I don't sense that he is a self-righteous individual who wants to come across as ridiculously smart (he is, in fact, ridiculously smart). I think he really just doesn't get that trying to relate these concepts to people like me, who only made it through Calc A, cannot be done. Hence, large parts of the book left me absolutely lost. Even BJ, who was a math minor, said he wasn't keeping up and so he quit reading it. Consider this sentence: "The idea of string theory is that by doing calculations in these sigma models and summing up the results over all possible Riemann surfaces E (that is, over all possible paths of the strings propagating in a fixed space-time S) we can reproduce the physics that we observe in space-time S." Honestly, I wish this particular sentence, which I chose at random, was a stand-apart in terms of its difficulty, but the truth is that much of this book is written in this language with ten unfamiliar concepts thrown together in the same sentence, all with the assumption that we must understand what the heck he is talking about.
The redeeming points of the book were the interspersed memoir portions, which were extremely interesting. Frenkel was born in the Soviet Union and endured intense antisemitism at practically every turn in his education, but still prevailed and eventually traveled to Harvard and then to UC-Berkeley with professorships. I very much loved hearing about his experiences growing up, in college, working with colleagues, and his personal excitement about solving mathematical problems. It was only that he felt the need to then delve INTO those problems with technical language that made this book a disappointment--along with the fact that I didn't feel it delivered what it originally promised.
In the end, I walked away appreciating Edward Frenkel's personal story. However, I did NOT end up appreciating math anymore than I ever did before, which was precisely why I decided to read the book in the first place. Unless you're ready to skip some major portions or else you're a mathematician, I don't recommend this book to you. This book is truly written for mathematicians, not laypeople, as it was so described.
Won't bother to finish this. Tedious, preachy, uninsightful.
This book gives a comprehensive look at the most recent mathematics. It is also a nice biography of Edward Frenkel. I'll quote the author a few times and give my comments.
What if at school you had to take an "art class" in which you were only taught how to paint a fence? Hits the nail squarely on the head - loving math starts with seeing beauty in math, not in rote work. The first several chapters of the book effectively use the concept of symmetry as a gateway to the Langlands Program.
My goal is to explain this stuff to you in terms that you will understand. I have a bachelors in math and followed most of it. I am not sure others would have as much ease, especially in the later sections of the book. The importance was conveyed, if not the full meaning.
As a whole, the book conveys the author's love for mathematics. A more casual reader should definitely skip the heavier math chapters suggested in the preface.
What if at school you had to take an "art class" in which you were only taught how to paint a fence? Hits the nail squarely on the head - loving math starts with seeing beauty in math, not in rote work. The first several chapters of the book effectively use the concept of symmetry as a gateway to the Langlands Program.
My goal is to explain this stuff to you in terms that you will understand. I have a bachelors in math and followed most of it. I am not sure others would have as much ease, especially in the later sections of the book. The importance was conveyed, if not the full meaning.
As a whole, the book conveys the author's love for mathematics. A more casual reader should definitely skip the heavier math chapters suggested in the preface.