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4.27 AVERAGE
4.27 AVERAGE
This is easily my best read this year! I was wowed by the story and it read like a modern day detective novel.
The author did an amazing job of outlining the problems and even the journey that Andrew Wiles took to solve Fermat's Theorem.
Elliptical curves, modular maths, riddles and problem solving approaches and so much more. This book was for a nerd who likes math, gripping reading.
The author did an amazing job of outlining the problems and even the journey that Andrew Wiles took to solve Fermat's Theorem.
Elliptical curves, modular maths, riddles and problem solving approaches and so much more. This book was for a nerd who likes math, gripping reading.
informative
medium-paced
adventurous
challenging
informative
inspiring
reflective
medium-paced
"My mind is at rest."
This book reignited my love for this particular problem.
This book reignited my love for this particular problem.
challenging
informative
inspiring
slow-paced
challenging
informative
inspiring
The author's ambition and aspiration to cover the vast journey from the discovery of Fermat's Last Theorem to its ultimate proof are certainly commendable. However, a great book is born only when the details support the ambition, and as a mathematics major, I can definitely say that there are too many disappointing parts in the details of this book.
First of all, Pythagoras is described in an overrated manner. Pythagoras was more of a cultist than a scholar, and it is not certain whether he actually proved the Pythagorean theorem (the author admits that Pythagoras did not 'discover' the Pythagorean theorem, but it is also difficult to guarantee that he 'proved' it). And the false anecdote about Euler is also regrettable: the anecdote that Euler proved the existence of God with a formula. Euler was a modern scholar enough to know that mathematics and religion are separate, and the person participating in the discussion was not Euler, but a Russian philosopher.
And Fermat's last theorem is a theorem that belongs to the field of algebraic number theory. Of course, I know that this choice was made to lower the difficulty of the book, but the fact that there is too little content about algebra is also a big drawback of this book(Although there is a brief mention of Galois' group theory in the latter part, it is far too insufficient.). It would have been much better if the history of the development of algebra had been told in line with the history of the development of number theory. Furthermore, Chapter 4 of this book has almost nothing to do with Fermat's last theorem. Only amateur math nerds would have been afraid that Fermat's last theorem would not be proven because of Gödel's incompleteness theorem. How much better if the pages allocated to that chapter had been filled with the history of algebra!
Also, some of the proofs in the book are so poorly explained that I sighed. In the process of proving that the number of primes is infinite, the proof was drawn out by adding unnecessary processes, and when explaining Gödel's incompleteness theorem, he made an absurd claim that "if Fermat's last theorem is unprovable, then Fermat's last theorem is true." Also, the proof of the three-point line inference (which is not in the book, but is now called the 'Sylvester-Gallay conjecture') in the appendix is so poorly explained that I feel like rewriting it all.
When explaining hyperbolic space, the author explained that our universe is a four-dimensional space, but I don't understand how an author who majored in physics could make such a wrong statement. The universe is a three-dimensional space, and when time is considered as one dimension, it can be called a 'four-dimensional space-time'. In the explanation of topology, the author also said that squares and crosses are topologically different, but this is also a completely wrong statement. Squares and crosses are topologically isomorphic because they have the same number of 'holes', 0.
Lastly, the content of the 'computer-based proof' at the end of the book seems to need to be revised significantly because times have changed a lot. The atmosphere in the current mathematics community is one where using computers for proofs is taken for granted much more than before. It is true that we cannot dissect the calculation process of a computer, but instead, we know how the computer works. And this is the same as mathematicians who do not memorize the proof process of every mathematical theorem, but at least know how mathematics works.
I think this book should be revised someday. And the biggest lesson I got from this book is that a mathematics book that is not written by a mathematician should be examined by a mathematician.
First of all, Pythagoras is described in an overrated manner. Pythagoras was more of a cultist than a scholar, and it is not certain whether he actually proved the Pythagorean theorem (the author admits that Pythagoras did not 'discover' the Pythagorean theorem, but it is also difficult to guarantee that he 'proved' it). And the false anecdote about Euler is also regrettable: the anecdote that Euler proved the existence of God with a formula. Euler was a modern scholar enough to know that mathematics and religion are separate, and the person participating in the discussion was not Euler, but a Russian philosopher.
And Fermat's last theorem is a theorem that belongs to the field of algebraic number theory. Of course, I know that this choice was made to lower the difficulty of the book, but the fact that there is too little content about algebra is also a big drawback of this book(Although there is a brief mention of Galois' group theory in the latter part, it is far too insufficient.). It would have been much better if the history of the development of algebra had been told in line with the history of the development of number theory. Furthermore, Chapter 4 of this book has almost nothing to do with Fermat's last theorem. Only amateur math nerds would have been afraid that Fermat's last theorem would not be proven because of Gödel's incompleteness theorem. How much better if the pages allocated to that chapter had been filled with the history of algebra!
Also, some of the proofs in the book are so poorly explained that I sighed. In the process of proving that the number of primes is infinite, the proof was drawn out by adding unnecessary processes, and when explaining Gödel's incompleteness theorem, he made an absurd claim that "if Fermat's last theorem is unprovable, then Fermat's last theorem is true." Also, the proof of the three-point line inference (which is not in the book, but is now called the 'Sylvester-Gallay conjecture') in the appendix is so poorly explained that I feel like rewriting it all.
When explaining hyperbolic space, the author explained that our universe is a four-dimensional space, but I don't understand how an author who majored in physics could make such a wrong statement. The universe is a three-dimensional space, and when time is considered as one dimension, it can be called a 'four-dimensional space-time'. In the explanation of topology, the author also said that squares and crosses are topologically different, but this is also a completely wrong statement. Squares and crosses are topologically isomorphic because they have the same number of 'holes', 0.
Lastly, the content of the 'computer-based proof' at the end of the book seems to need to be revised significantly because times have changed a lot. The atmosphere in the current mathematics community is one where using computers for proofs is taken for granted much more than before. It is true that we cannot dissect the calculation process of a computer, but instead, we know how the computer works. And this is the same as mathematicians who do not memorize the proof process of every mathematical theorem, but at least know how mathematics works.
I think this book should be revised someday. And the biggest lesson I got from this book is that a mathematics book that is not written by a mathematician should be examined by a mathematician.
challenging
informative
inspiring
medium-paced
For someone with a background in math (though by no means one deep enough to understand the proof that the book is about), the historical proofs involve too much hand waving, even the ones in the appendices. Also, the proof of the Pythagorean theorem is an algebraic proof, and not the proof by construction that the ancient Greeks used. While that is an easy proof to follow, presenting it in the context of the ancient Greeks is weird.
However, by the time we get to the elliptic equations and modular forms hand waving is OK with me. I liked that Singh presented the mathematics behind the proof so that I could at least get a vague idea of what it is about, and how the real significant math behind the proof is the proof of the Taniyam-Shimura conjecture. Also cool was seeing the psychological processes that Wiles went through in proving Fermat's last theorem.
However, by the time we get to the elliptic equations and modular forms hand waving is OK with me. I liked that Singh presented the mathematics behind the proof so that I could at least get a vague idea of what it is about, and how the real significant math behind the proof is the proof of the Taniyam-Shimura conjecture. Also cool was seeing the psychological processes that Wiles went through in proving Fermat's last theorem.
Gut recherchiert und sehr laienfreundlich verfasst (zum Leidwesen aller mathematisch Bewanderten... beispielsweise statt Induktionsbegriff praktisch immer Dominosteinallegorie) schildert Simon Singh in diesem Werk die historischen Hintergründe und den Werdegang des Beweises von Andrew Wiles in Bezug auf den wohl bekanntesten mathematischen Satz - Fermats letzter Satz.