既然你提到自己已经有了扎实的应用数学背景，不妨试试 Saunders MacLane 的《Mathematics: Form and Function》，它勾勒了一幅广阔的数学图景，或许能让你提起兴趣去更深入地研读某个子领域。注意，虽然这本书涵盖了极广的数学领域，但它需要……
Since you mentioned you already have a strong applied math background, try Mathematics: Form and Function by Saunders MacLane for a broad portrait of mathematics that might get you excited to read more deeply into a given subtopic. Note that while this book surveys a broad swathe of mathematics, it depends…
如果你能搞到手，Saunders MacLane 的《Mathematics: Form and Function》对于理解数学如何从现实世界中衍生并反映现实来说，是一本极好的书。当然，这里写的要比那具体得多，但如果你对这种图解感兴趣，那它可能会……
If you can find a way to get a hold of it, Saunders MacLane's Mathematics: Form and Function is a tremendous book for understanding how math arises from the world and reflects it. What's written here is a lot more specific than that, of course, but if this illustration interests you then it might…
鉴于大家都在为想了解数学“广度”的数学自学者推荐书籍，我必须强烈安利 Saunders MacLane 的《Mathematics, Form and Function》。读起来就像是一部高屋建瓴的假想历史，讲述了如果数学以最直接、最符合逻辑的方式，从我们共同的人类经验中展开，它会如何全盘发展出来（在……的引导下）
Given everyone recommending books for math autodidacts interested in learning the "breadth" of mathematics, I cannot recommend more highly Saunder's MacLane's "Mathematics, Form and Function". It reads as a high level false-historical account of how math might have been developed, in its entirety, if it unfolded in the most direct and logical way from the human experiences we all share (guided…
我非常喜欢 Saunders MacLane 的《Mathematics Form and Function》，它能让人窥见这篇文章所探寻的“答案”。MacLane 的论点是，数学源自相对少数几种有意义的力量，而当这些力量全部对齐时，“好”的数学就产生了……
I really enjoy Saunders MacLane's Mathematics Form and Function for sight at the "answers" this article seeks. MacLane's argument is that mathematics arises from a relatively small number of meaningful forces and "good" mathematics arises when those forces all align…
对高中生来说可能不是一本完美的书，但再往上一点，我强烈推荐 MacLane 的《Mathematics Form and Function》。这是一部修正主义的数学史，旨在展示思想如何从一个流向另一个。他删去了很多死胡同，并给出了一种关于人们“应该”如何从一个主题走向另一个主题的视角……
Probably not a perfect book for someone at the HS level, but just a bit past that I would HIGHLY recommend MacLane’s Mathematics Form and Function. It’s a revisionist history of mathematics aimed to demonstrate how ideas flow from one to another. He eliminates a lot of dead-ends and takes a perspective as to one “ought” to move from one subject…
……我知道的有趣条目：* George Lakoff 和 Rafael Nunez 的《Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being》* Jacques Hadamard 的《The Mathematician's Mind》* Saunders MacLane 的《Mathematics Form and Function》* Agustin Rayo 的《On the Brink of Paradox: Highlights from the Intersection of Philosophy and Mathematics》Charles C. Pinter 的《A Book of Abstract Algebra》的前言和第一章……
…interesting entries I know about: * Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being by George Lakoff and Rafael Nunez * The Mathematician's Mind by Jacques Hadamard * Mathematics Form and Function by Saunders MacLane * On the Brink of Paradox: Highlights from the Intersection of Philosophy and Mathematics by Agustin Rayo The preface and chapter 1 of A Book of Abstract Algebra by Charles C. Pinter…
既然你提到自己已经有了扎实的应用数学背景，不妨试试 Saunders MacLane 的《Mathematics: Form and Function》，它勾勒了一幅广阔的数学图景，或许能让你提起兴趣去更深入地研读某个子领域。注意，虽然这本书涵盖了极广的数学领域，但它需要……
Since you mentioned you already have a strong applied math background, try Mathematics: Form and Function by Saunders MacLane for a broad portrait of mathematics that might get you excited to read more deeply into a given subtopic. Note that while this book surveys a broad swathe of mathematics, it depends…
如果你能搞到手，Saunders MacLane 的《Mathematics: Form and Function》对于理解数学如何从现实世界中衍生并反映现实来说，是一本极好的书。当然，这里写的要比那具体得多，但如果你对这种图解感兴趣，那它可能会……
If you can find a way to get a hold of it, Saunders MacLane's Mathematics: Form and Function is a tremendous book for understanding how math arises from the world and reflects it. What's written here is a lot more specific than that, of course, but if this illustration interests you then it might…
鉴于大家都在为想了解数学“广度”的数学自学者推荐书籍，我必须强烈安利 Saunders MacLane 的《Mathematics, Form and Function》。读起来就像是一部高屋建瓴的假想历史，讲述了如果数学以最直接、最符合逻辑的方式，从我们共同的人类经验中展开，它会如何全盘发展出来（在……的引导下）
Given everyone recommending books for math autodidacts interested in learning the "breadth" of mathematics, I cannot recommend more highly Saunder's MacLane's "Mathematics, Form and Function". It reads as a high level false-historical account of how math might have been developed, in its entirety, if it unfolded in the most direct and logical way from the human experiences we all share (guided…
我非常喜欢 Saunders MacLane 的《Mathematics Form and Function》，它能让人窥见这篇文章所探寻的“答案”。MacLane 的论点是，数学源自相对少数几种有意义的力量，而当这些力量全部对齐时，“好”的数学就产生了……
I really enjoy Saunders MacLane's Mathematics Form and Function for sight at the "answers" this article seeks. MacLane's argument is that mathematics arises from a relatively small number of meaningful forces and "good" mathematics arises when those forces all align…
对高中生来说可能不是一本完美的书，但再往上一点，我强烈推荐 MacLane 的《Mathematics Form and Function》。这是一部修正主义的数学史，旨在展示思想如何从一个流向另一个。他删去了很多死胡同，并给出了一种关于人们“应该”如何从一个主题走向另一个主题的视角……
Probably not a perfect book for someone at the HS level, but just a bit past that I would HIGHLY recommend MacLane’s Mathematics Form and Function. It’s a revisionist history of mathematics aimed to demonstrate how ideas flow from one to another. He eliminates a lot of dead-ends and takes a perspective as to one “ought” to move from one subject…
……我知道的有趣条目：* George Lakoff 和 Rafael Nunez 的《Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being》* Jacques Hadamard 的《The Mathematician's Mind》* Saunders MacLane 的《Mathematics Form and Function》* Agustin Rayo 的《On the Brink of Paradox: Highlights from the Intersection of Philosophy and Mathematics》Charles C. Pinter 的《A Book of Abstract Algebra》的前言和第一章……
…interesting entries I know about: * Where Mathematics Comes From: How the Embodied Mind Brings Mathematics Into Being by George Lakoff and Rafael Nunez * The Mathematician's Mind by Jacques Hadamard * Mathematics Form and Function by Saunders MacLane * On the Brink of Paradox: Highlights from the Intersection of Philosophy and Mathematics by Agustin Rayo The preface and chapter 1 of A Book of Abstract Algebra by Charles C. Pinter…