Name: Elliptic tales
ISBN: 9780691151199

Elliptic tales

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 eye-opening examples, Ash and Gross make these ideas accessible to general readers, and, in the process, venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profound discoveries of the last three centuries in algebraic geometry, abstract algebra, and number theory. They demonstrate how mathematics grows more abstract to tackle ever more challenging problems, and how each new generation of mathematicians builds on the accomplishments of those who preceded them. Ash and Gross fully explain how the Birch and Swinnerton-Dyer Conjecture sheds light on the number theory of elliptic curves, and how it provides a beautiful and startling connection between two very different objects arising from an elliptic curve, one based on calculus, the other on algebra.

What Hacker News says

nhatcherFeb 2026

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)

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nhatcherFeb 2026

Elliptic Tales, but maybe it is because I read it first

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mkiddJan 2023

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 the field. I also recommend Jim Baggott's Perfect Symmetry: The Accidental Discovery of Buckminsterfullerene as another example at this rarely seen intermediate level. (Arguably all of Scientific American was at this level 50 years ago, but that era is long gone.)

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frutigerOct 2019

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 in Maths (the Birch-Swinnerton-Dyer conjecture).

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soVeryTiredFeb 2019

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.

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mrkgnaoAug 2017

For anyone looking to learn 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 elliptic curves:

https://www.amazon.com/Rational-Points-Elliptic-Undergraduat...

(Non-affiliate links, just so you know.)

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