椭圆曲线的故事
Elliptic tales
Avner Ash、Robert Gross · 初版 2012 年
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Elliptic Tales 通过探讨当代数学中最令人兴奋的未解难题之一——Birch and Swinnerton-Dyer Conjecture，展现了数论的最新进展。Clay Mathematics Institute 悬赏 100 万美元，奖励任何能够找到该问题通解的人。该猜想的关键在于 elliptic curves，即二元三次方程。这些方程看似简单，却源自一些极其深奥——且往往非常神秘——的数学思想。全书仅使用初等代数和微积分，同时呈现了大量引人注目
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…想更多地了解椭圆曲线（在数学领域里它算得上是‘四通八达’的枢纽课题了），这里有一本好书，只要学过一点微积分的人应该都能看懂：https://www.amazon.com/Elliptic-Tales-Curves-Counting-Number... 它不是教科书，这既是好事也是坏事。就我而言，它非常成功地勾起了我的求知欲！一本写得极好且难度适中的本科教材…
…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…
我推荐这本：https://www.amazon.com/Elliptic-Tales-Curves-Counting-Number.... 它深入探讨了椭圆曲线的应用动机（以及它们的群定律），并解释了一些非常优美的定理（比如贝祖定理/Bézout's theorem）以及一些开放问题…
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…
我敢肯定这是本好书 :)。我觉得优秀的搞高等数学科普的书很难找。不过 Avner Ash 和 Robert Groß 写的三部曲算是个很棒的例外：《Elliptic Tales》、《Fearless Symmetry》以及《Summing it up》（按我个人的喜好排序）
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)
对于有本科数学背景的人，我推荐《Fearless Symmetry》和《Elliptic Tales》。没有数学背景的人读起来会很吃力，但它们能带你领略数学界一些活跃研究领域的最前沿。
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.
我也附议 frutiger 对《Elliptic Tales: Curves, Counting, and Number Theory》的推荐。这个水平档次的科普和数学书应该再多一些，但实在太少见了——通常要么假设你是零基础小白，要么就得默认你至少是个研究生…
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…
《Elliptic Tales》，不过可能是因为我最先读的就是它。
Elliptic Tales, but maybe it is because I read it first