欢迎来到我的知识库。 > Welcome to My Knowledge Repository Base. 原本是想用英文写的，但是我意识到英文的输入效率其实不如中文，所以还是用中文算了。虽然英文不算差，到不了母语水平但是也接近，但是毕竟中文还是母语，用起来方便。为了英文读者方便，这篇 Welcome 我提供了一个 GPT 给的英文翻译。其他的文档如果英文读者想读，可以自己丢进 GPT 里。 > I initially intended to write in English, but I realized that inputting in English isn’t as efficient as Chinese, so I decided to stick with Chinese. Although my English isn’t bad and almost reaches native level, Chinese is my first language, so it’s more convenient to use. For the convenience of English readers, I've provided a English translation of this Welcome document by GPT. For the other documents that were written in Chinese, feel free to use GPT for translation. # 我是谁 Who Am I 新加坡国立的一名大四学生，专业是计算机和数学。现在在休学创业，创了一半决定跑路：我意识到我知道的东西还太少了，太浅薄了，缺乏很多经验，也缺乏很多认知。所以，还需要积累。但是休学已经在休了，所以最近就在认真看书，兼职赚点钱，以及去做一做科研，了解一下学术界大家都在想什么。 > I’m a fourth-year student at the National University of Singapore, majoring in Computer Science and Mathematics. I’m currently on a leave of absence to pursue entrepreneurship, though halfway through, I decided to pause and reflect: I realized I still know too little, my understanding is shallow, and I lack a lot of experience and insight. So, I need to keep building up. Since I’ve already taken the leave, I’m now focusing on reading, earning some money through part-time work, and diving into some research to see what people in academia are thinking about. # 你能看到什么 What You Can See 这是一个非常松散的博客，有一些想法，哪怕是零散的笔记，我也会公开出来。我并不太在意很多想法写没写完——因为本身就不指望能有什么人读。所以，很多时候一时兴起开了一个文档，顺手点一下 publish 就被发布了，但是里面什么东西也没写。这大概意味着我开了一个坑，等到我想起来的时候我会把它填上。 > This is a very loosely structured blog where I share some ideas—even scattered notes—and publish them openly. I don’t really mind if many ideas aren’t fully developed—I don’t expect anyone to read them anyway. Often, I start a document on a whim, casually click “publish,” and it goes live without much content. This probably means I’ve left a topic incomplete, and I’ll fill it in whenever I get around to it. 在这个博客中，我大概会分享一些数学、技术、商业上、人文上的学习内容与见解。 > In this blog, I’ll mostly share insights and learning content on mathematics, technology, business, and humanities. # 注意事项 Notes 我认为 AI 是一个具有变革意义的技术，所以在做笔记的过程中，我大量使用了 AI。这在数学的笔记中尤为常见。所以，如果没有特别说明的话，数学的笔记是通过 AI 生成的，看的时候请自己甄别对错（take it with a grain of salt）。我对数学的学习并不是很严谨，只是想要了解一下大的 idea 以及 intuition 是什么，等有空了我可能会慢慢更正并试图去校对一些 AI 生成的概念和笔记。但是就目前而言，这些笔记对给我提供一个 intuition 来说已经足够了。 > I believe AI is a transformative technology, so I heavily use AI in my note-taking process, especially for mathematics. So, unless otherwise noted, the math notes are AI-generated; please assess their accuracy on your own (take it with a grain of salt). My approach to learning math isn’t very rigorous—I’m more interested in understanding the big ideas and intuition. When I have time, I may slowly correct and verify some of the AI-generated concepts and notes. But for now, these notes are sufficient for providing an intuition. # 我的目标是什么 What Are My Goals 我希望尽可能地读书，在未来的几年内，我希望能对下面的几个领域有一些系统化的了解。大概就是：脑海中有一个框架。具体的知识倒是不用抓的很细，但是有了框架之后就可以往里填东西。 > I hope to read as much as possible and, in the coming years, gain a systematic understanding of the following fields. My goal is to have a framework in mind. The specific knowledge doesn’t need to be very detailed, but with a framework, I can fill in the details. ## 人文社科 Humanities and Social Sciences ### 宗教 Religion 之前在瑞典海外实习的时候，去欧洲顺便玩了一趟。我很懊悔不理解基督教，所以我很希望能读一遍圣经，明白基督教到底大概是个什么东西。我认为，这个也有助于对于西方社会的了解。同时，我也很好奇《古兰经》，我觉得主流西方国家对伊斯兰教其实是有一定的偏见的，或者至少说是有一定的刻板印象的。我希望能找到机会进去看看。 > During an internship abroad in Sweden, I traveled around Europe. I regretted not understanding Christianity, so I hope to read the Bible and gain a basic understanding of what Christianity is. I believe this will also help me understand Western society better. I’m also curious about the Quran; I feel that mainstream Western countries have some biases, or at least stereotypes, against Islam. I hope to find an opportunity to explore it further. ### 中西方哲学史，以西方哲学史为主 History of Eastern and Western Philosophy, Mainly Western Philosophy 很多的困惑其实在哲学中已经有所解答，所以希望能认真学习。 > Many questions already have answers in philosophy, so I hope to study it seriously. ### 中西方艺术史，以西方艺术史为主 History of Eastern and Western Art, Mainly Western Art 在欧洲旅游的时候，感觉狠狠学习了一下西方的艺术史。我觉得这真的非常有趣，很希望能有机会去进一步探索。 > When traveling in Europe, I had a deep dive into Western art history. I found it really fascinating and hope to have a chance to explore it further. ## 自然科学 Natural Sciences ### 物理学 Physics 朋友和我说，物理学有两种思维方式，一种是数学家的思维方式，另一种是物理学家的思维方式。比如，如果你想要理解广义相对论，你需要先理解[[Introduction to Topological Manifolds|拓扑]]，之后理解 Smooth Manifolds，而后黎曼几何，最后才能理解广义相对论——这是数学家的思维模式；另一方面，也有物理学家的思维模式，相对来说会更加的哲学化。我在听完了这样的描述后，对这两种思维方式都产生了很浓的兴趣。 > A friend told me that there are two ways of thinking in physics: one is the mathematician’s way, and the other is the physicist’s way. For example, if you want to understand general relativity, you first need to understand topology, then smooth manifolds, followed by Riemannian geometry, and finally general relativity—this is the mathematician’s way of thinking. On the other hand, there’s also the physicist’s way, which is relatively more philosophical. After hearing this description, I became very interested in both approaches. ### 数学 Mathematics 我一直觉得我的数学的第二专业是一个笑话。虽然很认真地学了，但是我学的课并不多，而且应用数学方面的东西我实在玩不来；但是作为一个计算机学生，纯数的东西对我来说其实并没有什么用——我觉得我也不太能做的了纯属。虽然如此，但是我觉得还是可以以一种兴趣的态度去认真学习一下纯数和应用数学相关的内容，更多地是去了解这些东西所对应的思维方式。 > I’ve always felt that my second major in mathematics is a bit of a joke. Although I studied seriously, I didn’t take many courses, and I struggle with applied mathematics; as a computer science student, pure math doesn’t have much practical use for me—I don’t think I’m cut out for pure math. Nevertheless, I think I can approach pure and applied mathematics with interest, mainly to understand the ways of thinking that they represent. 我的计划是先从分析开始看，把四本分析看完（傅立叶分析、复分析、实分析、泛函分析），之后再去探索一下其他的领域，比如：[[Introduction to Topological Manifolds|拓扑]]、集合论。 > My plan is to start with analysis, reading through four books (Fourier Analysis, Complex Analysis, Real Analysis, and Functional Analysis). After that, I’ll explore other areas, such as topology and set theory. ## 计算机科学 Computer Science 本职工作，大学的早几年玩的比较多，还是有不少看法的。经验相较于其他本科生来说，我觉得还是比较多的，基本上能玩的框架都玩过了一圈——但是主要缺对后端的一些常见工具的经验（Kafka、Redis 等）。我对前端最为熟悉，但是并不想做前端；对 Infra 的兴趣最大，但是这个好像不太容易找到好的岗位去做。 > My main field of work. I spent the earlier years of college experimenting a lot and have quite a few opinions on it. Compared to other undergraduates, I feel I have relatively more experience, having tried out most frameworks. However, I lack experience with some common backend tools (e.g., Kafka, Redis). I’m most familiar with front-end development, but I don’t want to do front-end work; I’m most interested in infrastructure, but it seems hard to find good positions in that area. ## 商科 Business 我其实从小到大对商业的兴趣大于对其他学科的兴趣。这样的兴趣来源于什么地方我并不知道，大概是在很小的一个年龄就去度过《乔布斯传》吧——虽然《乔布斯传》的内容我已经不太记得了（最近打算有空去重新读一下），但是它在我心中种下了一颗想要改变世界的种子。 > I’ve actually had a stronger interest in business than in any other field since I was young. I’m not exactly sure where this interest comes from; perhaps it started when I read the _Biography of Steve Jobs_ at a young age. Although I don’t remember much of the book’s content (I plan to reread it sometime soon), it planted a seed in me—a desire to change the world. 之后对商业有过各种各样的探索，包括初中的时候，作为一个重度的乐高玩家，写邮件给了一堆仿制乐高的厂商，希望他们能不要完全抄袭，而是去生产一些乐高已经绝版了、买不到的零件——当然，没有人理我就是了。高中的时候也做过一些尝试，比如忽悠了一个朋友去写代码，说我们要一起做一个 “线上教育平台”，我答应说我去写对应的内容。结果朋友写好了代码，我自己却一行字的内容也没写。 > Since then, I’ve explored various aspects of business. In middle school, as a heavy LEGO enthusiast, I emailed several knockoff LEGO manufacturers, hoping they’d stop copying LEGO directly and instead produce rare, discontinued pieces that were no longer available. Naturally, no one responded. In high school, I made other attempts, like convincing a friend to code for an “online education platform” we planned to build. I promised to write the content, but while my friend completed the coding, I didn’t write a single word. 上了大学之后，和这个朋友一起搞过一个手写笔记软件，拿了学校一万新币的 Grant，可惜最后发现没有人想用我们的软件——于是转行去把这个软件底层用于同步的数据库开源了，期望有人用，可惜这样的 2B 生意在当时还没有任何的经验，自然也做不成就丢在了一边。 > Once I got to university, this friend and I worked on a handwriting note-taking app, securing a 10,000 SGD grant from the school. Unfortunately, we found that no one wanted to use our app, so we repurposed its backend database as an open-source project, hoping it would find users in the B2B space. Without any experience in that area, it naturally didn’t go anywhere, and we left it behind. 这个时候我碰到了一个朋友并一起创办了 HesyraAI，一个用 AI 来帮癌症医生写病历的 App，并一起把它送进了 NUS Graduate Research Innovation Program（GRIP），一个投资 25W 新币的 Deep Tech 基金。可是很快我意识到，其实在折腾了这么久的创业中，我是学到了很多东西——但是通过试错学习其实是一种很慢的学习方式，而看书、积累其实更快。我也开始怀疑 HesyraAI 是否存在如张一鸣所说的，”摆脱平庸的加速度“。我觉得我们缺技术缺经验缺人才，同时对于做很多事情很傲慢。在想清楚很多东西之后，我在 HesyraAI 要拿到钱的前夕，果断离开了它，选择去进行更多的探索。 > At this point, I teamed up with a friend to co-found _HesyraAI_, an app using AI to help cancer doctors write medical reports. We got accepted into the NUS Graduate Research Innovation Program (GRIP), a Deep Tech fund with a 250,000 SGD investment. However, I soon realized that, although I had learned a lot from all my entrepreneurial trials, learning through trial and error is a slow process. Reading and accumulating knowledge, in contrast, is much faster. I also started to question whether _HesyraAI_ could truly achieve the kind of “escape velocity” from mediocrity that Zhang Yiming talks about. We lacked technology, experience, and talent, and our approach to many things felt arrogant. With these reflections in mind, I decisively left _HesyraAI_ right before it was about to receive funding, choosing instead to continue exploring new paths. ### Books Read #### Sales - [[Mastering the Complex Sale]] - [[SPIN Selling]] - [[The Mom Test]] - [[MEDDICC]] #### Management - [[一分钟管理]] - [[谁动了我的奶酪]] - [[干法]] - [[Measure What Matters]] #### Biographies - [[超越好奇]] - [[褚时健传]] - [[大力出奇迹 - 张一鸣创业心路与算法思维]] - [[小米创业思考]]