Winn Math Journey

Shepherd Self-Learning System, abbreviated as SSS. SSS Maxim 001: For Nothing is Everything — Learning without utilitarian purposes is precisely what leads to gaining everything.

SSS Maxim 002: A view of mathematics shapes one's values, which in turn determines mathematical thinking.

@naki2012 尤其是已经对一种语言有深刻洞见的人，特别有必要对多门外语突破到L6以上。

AI 时代，还要不要学语言？ 很多人觉得：翻译已经这么好，何必再刻苦背单词？ 答案其实分两层： 为了生存，不必了。 为了文明，依然必要。 1/ AI 已经彻底消灭了“生存型语言学习”： 看论文、读新闻、旅游交流 → 全部翻译瞬间解决。 如果你只是想“看懂内容”，AI 足够。 2/ 但学语言的真正价值，从来不仅是“看懂”。 进入另一种思维模式（德语的结构感，法语的修辞感，日语的含蓄…） 在跨文化关系中建立身份与信任 用原生语言创造、写作、演讲、影响他人 这些，AI 依然做不到。 3/ 所以，在AI时代，语言学习不再是“必需品”， 而是一种 认知升级的投资品。 4/ 我把它分成六个层级： L0：全靠AI翻译 L1：日常生活交互 L2：阅读理解无障碍 L3：用外语思考 L4：身份嵌入，跨文化关系 L5：创造与说服 L6：文明桥梁，创造协议语言 5/ AI 可以帮你覆盖 L0～L2， 但 L3 以上是人类的独特价值。 这就是为什么—— AI越强，越凸显学语言的意义。 💡问题： 如果AI能帮你看懂所有资料，你还会愿意学语言吗？ 还是你想站到 L3以上的文明层级？

The greatest love for a child is seeing their excellence from your heart. Use Math Academy together: push knowledge limits, laugh, strive, even cry—no shame, but a lifelong treasure. Happiness and worth flow like a warm stream.Diamond League’s first place. It’s a champion’s proof

@espressocoder Your words have given me much food for thought. Thank you.

Almost didn't notice this 😄 Been slow lately, but cool to hit 25k

With simple words comes profound wisdom: it would be wonderful if children could learn independently from an early age, focus more on accumulating little by little every day, and compare themselves less with their peers.

@renfanzi @garrulous_abyss 数学教育还没包产到户，理性和逻辑还在构建的路上。

今早听播客，说中国和美国年轻人成长环境的最大不同，是： 美国人敢闯敢冒险，因为从小被鼓励“做你自己”，失败了或做错了家人和社会给予的是「forgiveness」； 中国人则畏手畏脚，因为从小到大无论做什么事儿之前都要得到家长、长辈、权威和社会的「permission」。 很有感触，甚至觉得这个比较基本上可以扩大到东亚 VS 美国/英语国家。

Comparing the paths of "cumbersome methods" at different levels can bring unexpected value.

In math self-study, the value of multiple solutions for one problem is often ignored. People prefer finding the optimal solution—the simplest way—quickly. Just as a big house feels like a prison without outdoor space, a "shortcut" may harm without comparing "cumbersome methods".

@feltanimalworld 我就很喜欢这样，我觉得这是秩序的体现

我发现我有个毛病： 我说话，写东西，必须要从头说起。 就好像故事一定要有： 很久很久以前…. Long long ago…. 这个毛病可能是从很小的时候看《列那狐的故事》就开始了。 有时候说话，对方很急： “说重点！” 我还是“long long ago…” 仔细检讨🤔🤔🤔

@justinskycak This is probably the greatest truth, yet many people realize it too late. People often talk about swimming theoretically while standing on the shore, reluctant to actually get in the water and practice. Perhaps an evasive personality is the root cause.

🎯 "I didn’t yet know how thoroughly schools were willing to lie about the capabilities of the students they’ve failed to educate." If a student’s school says that they’re doing fine in subject XYZ, then it does not automatically follow that the student is keeping college and career doors open that depend on XYZ proficiency. Academically oriented parents with means recognize this and are already taking action. For instance, my dentist and his hygienist both recognized that their kids weren't learning math at school, and put their kids in supplementary math education outside of school to fix the problem. (They came to this conclusion on their own -- they told me about this the very first time we met.) "My kid's school said she was doing fine at math, but they always tell you that so you don't really know. She didn't do well on state testing, so we had her do some workbooks at home, and now she's ACTUALLY doing well." -- the hygienist Their kids are lucky that their parents are clued in enough to diagnose the problem and intervene before it gets too bad. Countless other kids are in the same situation and most of them aren't so lucky.

@feltanimalworld 对比不同文明的迭代和建构，昙花式的消耗不值得称道，耀眼光辉后留下的是涂炭灰烬和一片漆黑。审慎式的积累恪守边界，百年无战事实属可贵，留下了穿越千年的星火。返穷群体指向消耗，长青意味着秩序，群体的路径积分带来了文明的收敛或发散，大幕落下时，没有一片雪花是无辜的，恪守边界远重于攻城略地

巴菲特有一句极其简单却足以改变命运的话：“对一个已有些积累的人来说，最重要的事就是——别再穷回去。” 这句话我从来不只从金钱的角度去理解。在我眼中，它是一整套人生策略的总纲。 所谓“别再穷回去”，不仅是资产不归零，更是家庭关系别破裂、孩子别失教，别出意外，健康别垮掉、认知别退化。你已经拥有的，才是你真正的资本。守住它们，比什么都重要。 很多人的人生，就是不停地捡芝麻、丢西瓜。一边贪图眼前的效率，一边让系统性资源持续流失。比如几年前一位女同学说：“就算我上班的全部收入都拿来送幼儿园，也值得。”当时我就劝她，这种逻辑根本不成立。孩子的教育不仅是花钱，更是陪伴。而且幼儿园也不是一天24小时，尤其是见识过所谓的私立办学之后，我对花钱找人带孩子这件事情完全不信任。公立学校至少和老师的退休pension和教师资格挂钩，反而是品质最高的。分析完以后才理解为啥有钱人都支持高学历的全职妈妈。 人生不是只拼进攻，还要守住阵地。你有的东西，必须守住；你爱的人，不能放手；你建的系统，别轻易拆掉。这才是“别再穷回去”的真正含义。

The value of the first step is deeply underestimated, as few can internalize mathematical logic and apply it to life. Many act promptly but quit due to greed and impatience. The key is to treat every present action as the first step. So start now—immediately!

@feltanimalworld 这个过程既是解码，也是在重新编码，总之，一切都开始变得不一样了。

请数学化解释以下机制 我最近最喜欢用的一个 Prompt，就是“请数学化解释以下机制”。这个简单的请求，已经成为我在研究大模型底层机制时最常用、也最容易触发顿悟的认知工具。几乎所有的“aha moment”都源于某个抽象机制背后被成功数学化的那一瞬间。 你完全不需要成为数学家，只要掌握一些基本的线性代数，就能解锁一整套隐藏在模型背后的认知地图。 为什么“数学化解释”如此强大？因为它不仅压缩了语言，把看似复杂的概念还原为最小机制单元，更为理解建立了结构化的思维骨架。 像词向量的“语义相似性”，本质上是向量夹角的余弦距离，所谓的Cosine Similarity；Attention 权重，其实是归一化后的点积函数；Loss Function 的优化目标，从“更准确”转变为“最小化交叉熵”这一信息论意义下的精确表达。当你第一次真正看懂 Softmax(q·kᵗ / √d) 是如何通过向量投影聚焦相关信息时，或者理解 y = Wx + b 是如何控制 token 的语义偏移方向时，你就会体会到数学语言带来的“机制压缩感”。这类“顿悟”，正是构建认知闭环、理解模型黑箱的关键钥匙。 事实上，你只需要掌握少量认知压缩工具：向量空间、矩阵乘法、点积注意力、Softmax、交叉熵、奇异值分解甚至傅里叶变换，它们分别在词嵌入、Transformer层、Attention机制、Loss设计和语义压缩中反复出现。 我提供一个标准化的结构型Prompt模板： 输入结构是什么？ 中间过程如何公式化？ 输出结构代表什么机制？ 是否存在数学等价？ 这个框架不只是用来提问，也能反向训练你对语言模型的机制洞察力。说到底，“数学化”不仅仅是解释，它是认知迁移的最小通用语言。任何机制，只要能被数学语言表达出来，就具备了被压缩、调用、迁移的可能性——也就具备了被我们真正理解和激活的可能性。 对于前面所有的数学型aha moment， 你把这个帖子不停的往前翻，总能翻到的。 (2.2/n)

I’d like to share a tip for getting more practice building with AI — that is, either using AI building blocks to build applications or using AI coding assistance to create powerful applications quickly: If you find yourself with only limited time to build, reduce the scope of your project until you can build something in whatever time you do have. If you have only an hour, find a small component of an idea that you're excited about that you can build in an hour. With modern coding assistants like Anthropic’s Claude Code (my favorite dev tool right now), you might be surprised at how much you can do even in short periods of time! This gets you going, and you can always continue the project later. To become good at building with AI, most people must (i) learn relevant techniques, for example by taking online AI courses, and (ii) practice building. I know developers who noodle on ideas for months without actually building anything — I’ve done this too! — because we feel we don’t have time to get started. If you find yourself in this position, I encourage you to keep cutting the initial project scope until you identify a small component you can build right away. Let me illustrate with an example — one of my many small, fun weekend projects that might never go anywhere, but that I’m glad I did. Here’s the idea: Many people fear public speaking. And public speaking is challenging to practice, because it's hard to organize an audience. So I thought it would be interesting to build an audience simulator to provide a digital audience of dozens to hundreds of virtual people on a computer monitor and let a user practice by speaking to them. One Saturday afternoon, I found myself in a coffee shop with a couple of hours to spare and decided to give the audience simulator a shot. My familiarity with graphics coding is limited, so instead of building a complex simulator of a large audience and writing AI software to simulate appropriate audience responses, I decided to cut scope significantly to (a) simulating an audience of one person (which I could replicate later to simulate N persons), (b) omitting AI and letting a human operator manually select the reaction of the simulated audience (similar to Wizard of Oz prototyping), and (c) implementing the graphics using a simple 2D avatar. Using a mix of several coding assistants, I built a basic version in the time I had. The avatar could move subtly and blink, but otherwise it used basic graphics. Even though it fell far short of a sophisticated audience simulator, I am glad I built this. In addition to moving the project forward and letting me explore different designs, it advanced my knowledge of basic graphics. Further, having this crude prototype to show friends helped me get user feedback that shaped my views on the product idea. I have on my laptop a list of ideas of things that I think would be interesting to build. Most of them would take much longer than the handful of hours I might have to try something on a given day, but by cutting their scope, I can get going, and the initial progress on a project helps me decide if it’s worth further investment. As a bonus, hacking on a wide variety of applications helps me practice a wide range of skills. But most importantly, this gets an idea out of my head and potentially in front of prospective users for feedback that lets the project move faster. [Original text: deeplearning.ai/the-batch/issu… ]

@AndrewYNg This article deserves to be a classic textbook; many should study it and act promptly. Those who do may find pleasant surprises. Its value lies not in the action itself, but in the isomorphic connections among all things. A small step could unexpectedly open up a whole new world.

@feltanimalworld 我始终认为天人合一的农业文明被低估了，处处留有余地相比竭泽而渔，绝不仅仅是积累，更是一种孕育，人们往往惊喜于诞生时的伟大和不可思议，却忽视了最初的种子和土壤，以及必要的环境。鸡能生蛋的决定因素从来不是卧姿。中文世界总有民间高手和世外高人，绝非偶然。引领下个时代，华人不可或缺。

没错，绝大多数人根本不会察觉技术革命的到来。 就像荷兰乡村的少女，在风车下听到远方蒸汽机的轰鸣时，只会以为那是雷声或者怪物——她不会意识到，那是工业时代的心跳开始在跳动。 再往前看，当黄河流域的农业文明第一次定居播种、建立城邦，那一刻，草原上的游牧者还在追逐季风与猎物。他们不会知道，几千年后，自己仍站在历史结构的错位带上，被另一个系统定义。 结构跃迁从来不是全民共识的结果，而是认知差与路径选择共同挖出的时代裂谷。多数人不是拒绝改变，而是从未意识到“改变正在发生”。

@lapislagoons The feeling of anticipation is wonderful, and this is where another meaning of life lies. So instead of worrying about when to actually read a book, the first step should be to buy it decisively.

sometimes when an album comes out for an artist I love I have no motivation to listen to it , I look on lovingly toward and discourse online about how incredible it is and wait my turn , and then I think of it one day months later and it is speaking to my Exact Moment Right Here

@ach2678 You're absolutely right. I encounter a new lesson, instead of immediately checking the instructions, I try to deduce new theorems to solve problems. The process can be arduous, the success of deduction is extremely valuable—it almost always builds a permanent memory at once.

is there a better feeling than getting a review of fading material with problems for which you can no longer remember the formula/rule/most efficient way to solve, but due to improved intuition, you can reason/experiment your way to the correct solution anyway? when i can simply remember the optimal method, i am pleased about my recall ability, but when i can derive slow and cumbersome method myself, i feel closer to understanding the underlying nature of mathematical reality.

@justinskycak Inherent connections between different skill systems emerge. This realization spurs the initiative to explore related skills, facilitating horizontal expansion and deep integration of knowledge. Moreover, it serves as a litmus test for the mastery of underlying logic.

The higher you climb up a skill tree, the more you realize it actually intertwines with other skill trees you previously thought you didn't care about, and suddenly you're motivated to climb those as well.