……20 世纪初的，所以稍微有点过时，但 Kline 的观点极具前瞻性。Courant 和 Robbins 的《What is Mathematics》，另一部经典。Hilbert 和 Cohn-Vossen 的《Geometry and the Imagination》，数学科普写作的黄金标杆。一本极美的书。
…beginning of the 20th century so are slightly outdated, but kline was extremely forward-looking in his point of view. Courant & Robbins - What is Mathemaics. Another classic. Hilbert & Cohn-Vossen - Geometry and the Imagination. The gold standard of popular mathematics writing. A beautiful book.
经典著作都很棒：* Hilbert 和 Cohn-Vossen 的《Geometry and the Imagination》 * Courant 和 Hilbert 的《Methods of Mathematical Physics》 * Spivak 的《A Comprehensive Introduction to Differential Geometry》（以及它的两本小老弟《Calculus》和《Calculus on…
The classical stuff is great: * Geometry and the imagination by Hilbert and Cohn-Vossen * Methods of mathematical physics by Courant and Hilbert * A comprehensive introduction to differential geometry by Spivak (and its little brothers Calculus and Calculus on…
……应该去读《Calculus on Manifolds》。如果你想向大师学习，而且你有自信、胆识和智商。我推荐 Andrew Gleason 的《Fundamentals of Abstract Analysis》和 David Hilbert 的《Geometry and the Imagination》。先提个醒：这些书是给精通数学、并且愿意为了一两页纸琢磨好几个小时的人准备的。如果你做不到，那就别碰这些书。
…should read Calculus on Manifolds. If you want to learn from the masters and you have the confidence, audacity and intelligence. I would suggest Fundamentals of Abstract Analysis by Andrew Gleason and Geometry and the Imagination by David Hilbert. Just a warning. These books are for people adept at mathematics and are willing to spend hours on a page or two. If you are not, then avoid these books.
这里列出的 Arnold、Spivak 和 Lanczos 的书都极其优秀。还没人提到 Hilbert 和 Cohn-Vossen 的《Geometry and the Imagination》。如果数学界有哪本书能媲美费曼，那绝对是这本。至于初等几何，能媲美费曼的可能要数 H.S.M. Coxeter 的《Introduction to Geometry》了。……
All the books cited here by Arnold, Spivak, and Lanczos are extraordinarily good. Nobody has mentioned yet "Geometry and the Imagination" by Hilbert and Cohn-Vossen. If there is a Feynman equivalent in math it is certainly this book. For elementary geometry, the Feynman equivalent is probably "Introduction to Geometry", by H.S.M.Coxeter.…
……放手边备查，但你不会真的从头读到尾。Spivak 的微积分则是你可以带去海滩，游完一圈上来读几页的那种。编辑补充：另外，Hilbert 的几本书简直美得令人屏息：《Geometry and the Imagination》（单是综合微分几何那一章，就比其他 10 本好书加起来还值），《Methods of Mathematical Physics》也非常棒。它一上来就给出了柯西-施瓦茨不等式的三种证明……
…to have around, but you do not really read it end to end. Spivak's calculus you bring to the beach and read it between swim and swim. EDIT: Also, some books by Hilbert are breathtakingly beautiful: Geometry and the Imagination (just the chapter on synthetic differential geometry is worth more than 10 other great books), and the Methods of Mathematical Physics is also great. It begins by giving three proofs of cauchy-schwartz…
……https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/... 帮我强化了那部分的理解。* 今年我正试着啃下 https://www.amazon.com/Methods-Mathematics-Calculus-Probabil... ，它主打的是如何“融会贯通”。* 我在读 Hilbert 的《Geometry and the Imagination》https://www.amazon.com/Geometry-Imagination-AMS-Chelsea-Publ... ，想借此“沉浸”在几何的世界里。我简直太爱这本书了。
…https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/... helped strengthen that understanding. * This year I am trying to master https://www.amazon.com/Methods-Mathematics-Calculus-Probabil... which focuses on how to "connect the dots". * I am using Geometry and the Imagination by Hilbert https://www.amazon.com/Geometry-Imagination-AMS-Chelsea-Publ... as an attempt to "immerse" myself in Geometry. I just love this book.
……20 世纪初的，所以稍微有点过时，但 Kline 的观点极具前瞻性。Courant 和 Robbins 的《What is Mathematics》，另一部经典。Hilbert 和 Cohn-Vossen 的《Geometry and the Imagination》，数学科普写作的黄金标杆。一本极美的书。
…beginning of the 20th century so are slightly outdated, but kline was extremely forward-looking in his point of view. Courant & Robbins - What is Mathemaics. Another classic. Hilbert & Cohn-Vossen - Geometry and the Imagination. The gold standard of popular mathematics writing. A beautiful book.
经典著作都很棒：* Hilbert 和 Cohn-Vossen 的《Geometry and the Imagination》 * Courant 和 Hilbert 的《Methods of Mathematical Physics》 * Spivak 的《A Comprehensive Introduction to Differential Geometry》（以及它的两本小老弟《Calculus》和《Calculus on…
The classical stuff is great: * Geometry and the imagination by Hilbert and Cohn-Vossen * Methods of mathematical physics by Courant and Hilbert * A comprehensive introduction to differential geometry by Spivak (and its little brothers Calculus and Calculus on…
……应该去读《Calculus on Manifolds》。如果你想向大师学习，而且你有自信、胆识和智商。我推荐 Andrew Gleason 的《Fundamentals of Abstract Analysis》和 David Hilbert 的《Geometry and the Imagination》。先提个醒：这些书是给精通数学、并且愿意为了一两页纸琢磨好几个小时的人准备的。如果你做不到，那就别碰这些书。
…should read Calculus on Manifolds. If you want to learn from the masters and you have the confidence, audacity and intelligence. I would suggest Fundamentals of Abstract Analysis by Andrew Gleason and Geometry and the Imagination by David Hilbert. Just a warning. These books are for people adept at mathematics and are willing to spend hours on a page or two. If you are not, then avoid these books.
这里列出的 Arnold、Spivak 和 Lanczos 的书都极其优秀。还没人提到 Hilbert 和 Cohn-Vossen 的《Geometry and the Imagination》。如果数学界有哪本书能媲美费曼，那绝对是这本。至于初等几何，能媲美费曼的可能要数 H.S.M. Coxeter 的《Introduction to Geometry》了。……
All the books cited here by Arnold, Spivak, and Lanczos are extraordinarily good. Nobody has mentioned yet "Geometry and the Imagination" by Hilbert and Cohn-Vossen. If there is a Feynman equivalent in math it is certainly this book. For elementary geometry, the Feynman equivalent is probably "Introduction to Geometry", by H.S.M.Coxeter.…
……放手边备查，但你不会真的从头读到尾。Spivak 的微积分则是你可以带去海滩，游完一圈上来读几页的那种。编辑补充：另外，Hilbert 的几本书简直美得令人屏息：《Geometry and the Imagination》（单是综合微分几何那一章，就比其他 10 本好书加起来还值），《Methods of Mathematical Physics》也非常棒。它一上来就给出了柯西-施瓦茨不等式的三种证明……
…to have around, but you do not really read it end to end. Spivak's calculus you bring to the beach and read it between swim and swim. EDIT: Also, some books by Hilbert are breathtakingly beautiful: Geometry and the Imagination (just the chapter on synthetic differential geometry is worth more than 10 other great books), and the Methods of Mathematical Physics is also great. It begins by giving three proofs of cauchy-schwartz…
……https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/... 帮我强化了那部分的理解。* 今年我正试着啃下 https://www.amazon.com/Methods-Mathematics-Calculus-Probabil... ，它主打的是如何“融会贯通”。* 我在读 Hilbert 的《Geometry and the Imagination》https://www.amazon.com/Geometry-Imagination-AMS-Chelsea-Publ... ，想借此“沉浸”在几何的世界里。我简直太爱这本书了。
…https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/... helped strengthen that understanding. * This year I am trying to master https://www.amazon.com/Methods-Mathematics-Calculus-Probabil... which focuses on how to "connect the dots". * I am using Geometry and the Imagination by Hilbert https://www.amazon.com/Geometry-Imagination-AMS-Chelsea-Publ... as an attempt to "immerse" myself in Geometry. I just love this book.