Elliptic tales
by Avner Ash, Robert Gross · first published 2012
83% recommend17% neutral
Why HN recommends it
Accessible, non-textbook tour of elliptic curves that covers their motivations, group law, Bézout's theorem and open problems; suits readers with calculus or an undergraduate maths background.
Summarised by Claude from recommending comments
Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous ey
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…more about elliptic curves, which are astoundingly "well-connected" as math topics go, here's a good book that should be accessible to anyone with some calculus under their belt: https://www.amazon.com/Elliptic-Tales-Curves-Counting-Number... It's not a textbook, which is both good and bad. In my case, it did a good job whetting my appetite for more! A really well-written and not-extremely-difficult undergrad textbook…
on “How do you find integer solutions to x/(y + z) + y/(x + z) + z/(x + y) = 4?” ↗I can recommend https://www.amazon.com/Elliptic-Tales-Curves-Counting-Number.... It goes in-depth into the motivating use cases for elliptic curves (as well as their group law) and explains some very elegant theorems (Bézout's theorem) as well as open problems…
on “Elliptic Curve Cryptography Explained” ↗I'm sure it's a great book :). I find good popular books on higher mathematics difficult to come by. A nice exception is the trilogy written by Avner Ash and Robert Groß: Elliptic Tales, Fearless Symmetry and Summing it up (in my order of preference)
on “Six Math Essentials” ↗For anyone with an undergrad maths background, I'd recommend 'Fearless Symmetry' and 'Elliptic Tales'. They would be tough going for someone without a maths background, but they give a view to the forefront of some active areas of research in maths.
on “Classic Mathematics Books for Lifelong Learners” ↗I second frutiger's recommendation of Elliptic Tales: Curves, Counting, and Number Theory. There should be more science and math books at this level but it's rare—either you're assumed to be starting from scratch or to be at least a graduate student in…
on “Elliptic Curves: The Great Mystery” ↗Elliptic Tales, but maybe it is because I read it first
on “Six Math Essentials” ↗Yup! Making my way through Zero: The Biography of a Dangerous Idea right now. It's a little more "pop math" than Fermat's Enigma or The Code Book. I also have The Man Who Loved Only Numbers and Elliptic Tales on my to-read list once I wrap up Zero.
on “Ask HN: Books you read in 2017?” ↗