Vladimir Arnold 在 1960 年代曾用一种具体、门槛很低的方法，向莫斯科的高中生讲授了五次方程不可解性的证明，这事儿非常出名。他的讲义后来被整理成了 V.B. Alekseev 的一本书《阿贝尔定理的解题分析》（Abel's Theorem in Problems and Solutions），可以在网上免费看：https://webhomes.maths.ed.ac.uk/~v1ranick/papers/abel.pdf。他没有讨论最一般意义下的伽罗瓦理论，而是给出了一个更具体的拓扑/几何…
Vladimir Arnold famously taught a proof of the insolubility of the Quintic to Moscow Highschool students in the 1960s using a concrete, low-prerequisite approach. His lectures were turned into a book Abel’s Theorem in Problems and Solutions by V.B. Alekseev which is available online here: https://webhomes.maths.ed.ac.uk/~v1ranick/papers/abel.pdf. He doesn't consider Galois theory in full generality, but instead gives a more concrete topological/geometric…
有没有什么范畴论（Category Theory）教程能说明我们需要这一套工具来解决某个实际问题的？比如群论（Group Theory）方面就有一本绝妙的好书《阿贝尔定理的解题分析》（Abel's theorem in problems and solutions），它正是这么做的。
Is there any Category Theory tutorial that illustates that we need this apparatus to solve some real problem? For example, for Group Theory there is an excellent book 'Abel's theorem in problems and solutions' that does exactly that.
如果你有兴趣翻翻看的话，这本书出版时的书名叫：《阿贝尔定理的解题分析》（Abel's Theorem in Problems and Solutions），作者是 VB Alekseev。https://link.springer.com/book/10.1007/1-4020-2187-9
This was published as: Abel's Theorem in Problems and Solutions by VB Alekseev if you are interested in taking a look. https://link.springer.com/book/10.1007/1-4020-2187-9
Vladimir Arnold 在 1960 年代曾用一种具体、门槛很低的方法，向莫斯科的高中生讲授了五次方程不可解性的证明，这事儿非常出名。他的讲义后来被整理成了 V.B. Alekseev 的一本书《阿贝尔定理的解题分析》（Abel's Theorem in Problems and Solutions），可以在网上免费看：https://webhomes.maths.ed.ac.uk/~v1ranick/papers/abel.pdf。他没有讨论最一般意义下的伽罗瓦理论，而是给出了一个更具体的拓扑/几何…
Vladimir Arnold famously taught a proof of the insolubility of the Quintic to Moscow Highschool students in the 1960s using a concrete, low-prerequisite approach. His lectures were turned into a book Abel’s Theorem in Problems and Solutions by V.B. Alekseev which is available online here: https://webhomes.maths.ed.ac.uk/~v1ranick/papers/abel.pdf. He doesn't consider Galois theory in full generality, but instead gives a more concrete topological/geometric…
有没有什么范畴论（Category Theory）教程能说明我们需要这一套工具来解决某个实际问题的？比如群论（Group Theory）方面就有一本绝妙的好书《阿贝尔定理的解题分析》（Abel's theorem in problems and solutions），它正是这么做的。
Is there any Category Theory tutorial that illustates that we need this apparatus to solve some real problem? For example, for Group Theory there is an excellent book 'Abel's theorem in problems and solutions' that does exactly that.
如果你有兴趣翻翻看的话，这本书出版时的书名叫：《阿贝尔定理的解题分析》（Abel's Theorem in Problems and Solutions），作者是 VB Alekseev。https://link.springer.com/book/10.1007/1-4020-2187-9
This was published as: Abel's Theorem in Problems and Solutions by VB Alekseev if you are interested in taking a look. https://link.springer.com/book/10.1007/1-4020-2187-9