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4.27 AVERAGE
4.27 AVERAGE
hopeful
informative
inspiring
reflective
medium-paced
Brilliant journey through the history of Mathematics culminating with one of the most remarkable intellectual achievements of the 20th century. Anyone who thinks math isn’t exciting should give this a read.
My brain doesn't do numbers good but I enjoyed this book.
Fascinating and compelling tour through some of the history of mathematics and some of the significant developments from the eighteenth century to the publication at the last gasp of the twentieth of something very remarkable indeed: an advanced mathematical proof that captured the public imagination and made a hero of a shy and rather gawky man with a predilection for bad sweaters.
What Andrew Wiles set out in his 1997 paper was not, it turns out, a direct proof of Fermat's Last Theorem but a proof of the Modularity Theorem, a much more abstruse idea with little obvious connection to Fermat's algebraic conundrum, which somebody else had earlier shown to imply Fermat's theorem if true. Such is the interconnectedness of modern mathematics. Such, too, is the interdependency of developments on the work of many individuals. It's long been a contention of mine that great breakthroughs are never the work of individual geniuses working on their own, but the culmination of a process where many minds gradually build up the conditions that make the breakthrough possible. As Isaac Newton (whose role in this story is only a minor cameo) once remarked, "If I have seen further it was only by standing on the shoulders of giants". All credit to Wiles though for his single-minded persistence over many years, during which his work produced spinoffs that were significant developments in themselves and helped to fire the work of others in the mathematical community. Perhaps slightly less creditworthy (because it involved holding back work that would have helped others) but entirely understandable is the way Wiles kept information to himself because he didn't want anybody else building on his work and stealing that ultimate triumph.
It's brave of Simon Singh to put forward a book about maths that is neither out of the reach of a general readership nor too simple to satisfy the more mathematically-minded, but he's done a reasonably good job. He's framed it in such a way as to build suspense, not an easy thing to do with this material and I suspect that the reality was much more mundane. I can live with that. It's in the nature of the subject matter, though, that it's going to be a frustrating experience for the curious. Singh mentions Modular Forms, not unreasonably as they turn out to hold the key to the mystery, and they sounded fascinating involving complex numbers as they do, but he doesn't go into much detail. So I turned to Wikipedia. BIG mistake! My head all but exploded. Hey ho, I was always much too impatient to make much of a mathematician.
What Andrew Wiles set out in his 1997 paper was not, it turns out, a direct proof of Fermat's Last Theorem but a proof of the Modularity Theorem, a much more abstruse idea with little obvious connection to Fermat's algebraic conundrum, which somebody else had earlier shown to imply Fermat's theorem if true. Such is the interconnectedness of modern mathematics. Such, too, is the interdependency of developments on the work of many individuals. It's long been a contention of mine that great breakthroughs are never the work of individual geniuses working on their own, but the culmination of a process where many minds gradually build up the conditions that make the breakthrough possible. As Isaac Newton (whose role in this story is only a minor cameo) once remarked, "If I have seen further it was only by standing on the shoulders of giants". All credit to Wiles though for his single-minded persistence over many years, during which his work produced spinoffs that were significant developments in themselves and helped to fire the work of others in the mathematical community. Perhaps slightly less creditworthy (because it involved holding back work that would have helped others) but entirely understandable is the way Wiles kept information to himself because he didn't want anybody else building on his work and stealing that ultimate triumph.
It's brave of Simon Singh to put forward a book about maths that is neither out of the reach of a general readership nor too simple to satisfy the more mathematically-minded, but he's done a reasonably good job. He's framed it in such a way as to build suspense, not an easy thing to do with this material and I suspect that the reality was much more mundane. I can live with that. It's in the nature of the subject matter, though, that it's going to be a frustrating experience for the curious. Singh mentions Modular Forms, not unreasonably as they turn out to hold the key to the mystery, and they sounded fascinating involving complex numbers as they do, but he doesn't go into much detail. So I turned to Wikipedia. BIG mistake! My head all but exploded. Hey ho, I was always much too impatient to make much of a mathematician.
This is my second straight Simon Singh book, and one that is quite difficult to completely understand (I had to wiki the Taniyama-Shimura conjecture, the Euler equations, and the Kolvagyn-Flach method to get things right). However, despite the difficulty, I can say that this book aroused my interest in one subject that I have not been to well with, namely mathematics. I liked Singh's method of explaining a lot of obvious stuff for us over and over again just so we can finally understand, if not the content, the logic of the arguments that lead to Andrew Wiles. This book inspired me to write something about my thinker Blaise Pascal and how mathematics influenced him to come up with his argument for belief.
That's an excellent history of mathematics from antiquity to the present day. The author skillfully captures the pedagogical trick of the Last Theorem. This "mathematical siren, ..., which attracted geniuses to destroy their hopes" better is a common thread that compellingly guides us through anecdotes, concepts very well explained in the maze of mathematics. The author gives both a technical and societal dimension to his story, thereby maintaining the reader's attention from start to finish.
Very successful. Good reading.
Very successful. Good reading.
informative
inspiring
fast-paced
Incredibly engaging writing style, somehow this maths book had a plot twist.
informative
medium-paced
informative
inspiring
fast-paced
Everything that a popular science book should be. It’s actually fast paced. I’m not even particularly interested in maths and it had me hooked. It tells the story of the theorem through a history of the mathematics that relate to it and there’s the inside story of the final proof and Wiles’ year of hell.
What particularly impressed me was how Singh explained the maths. He keeps the notation to a minimum and has a particular way of introducing news ideas (you’ll see what I mean if you read it) so that even someone like me whose brain just doesn’t work that way can follow it. Quick to read, but must have taken ages to get right on the page.
*4.3
Great pop math book! Uses the story of the solving of Fermat's last to delve into the history of many (but not all) parts of math, from the Greeks and the birth of mathematics to bits of number theorist's (sad) biographies to this stuff on elliptic curves and modular forms that I didn't know about previously (and had always assumed was too hard for me to grasp) - but Singh introduces them in a pretty nice (and admittedly probably oversimplified?) way; I at least feel like I have some intuition for what it is. Of course, the proof itself ends up being a little handwavy, since it's hard math that goes into it, but at least I understood the logic/the steps involved. It made me want to understand some of that math, or at least look into it a bit more, and appreciate the many struggles this historic problem generated and the many lives that it touched. Would recommend to anyone with a passing/amateur interest in/tolerance for math
Great pop math book! Uses the story of the solving of Fermat's last to delve into the history of many (but not all) parts of math, from the Greeks and the birth of mathematics to bits of number theorist's (sad) biographies to this stuff on elliptic curves and modular forms that I didn't know about previously (and had always assumed was too hard for me to grasp) - but Singh introduces them in a pretty nice (and admittedly probably oversimplified?) way; I at least feel like I have some intuition for what it is. Of course, the proof itself ends up being a little handwavy, since it's hard math that goes into it, but at least I understood the logic/the steps involved. It made me want to understand some of that math, or at least look into it a bit more, and appreciate the many struggles this historic problem generated and the many lives that it touched. Would recommend to anyone with a passing/amateur interest in/tolerance for math