https://vt.tiktok.com/ZSQrMg4m4/
AI Hallucination Fixed By Physics
CODEX OpenAI
CODEX Plus recommended, Pro for company
Docker & Kubernetes
https://vt.tiktok.com/ZSxXHsqxy/
If you are looking at the modern tech tool, you are likely thinking of Kubernetes (commonly abbreviated as K8s), which is an open-source platform used to automate deploying, scaling, and managing containerized applications.
However, the name itself isn’t just random tech jargon—it has a classic origin.
The Greek Etymology
The word comes directly from the ancient Greek word κυβερνήτης (kubernētēs).
- Literal Meaning: It translates to “helmsman”, “pilot”, or “steersman”—the person who steers a ship through treacherous waters.
- Metaphorical Meaning: In ancient Greek philosophy (including the writings of Plato), it was often used metaphorically to mean a “governor” or “leader”—someone who guides the ship of state.
Why the Tech World Adopted It
When Google engineers built the platform in 2014, they chose the name as a perfect metaphor for what the software does.
If individual software containers (like Docker containers) are the physical cargo boxes on a merchant vessel, Kubernetes is the helmsman steering the entire ship, making sure every container gets to where it needs to go safely, adjusting to the wind and waves (traffic spikes, server failures), and keeping the system on course.
Fun Fact: The Connection to “Cybernetics”
The Greek root kubernētēs is also the direct ancestor of the English word cybernetics (the science of communications and automatic control systems) and, by extension, the prefix “cyber-“ that we use for everything related to computers today.
So when you work with Kubernetes, you are quite literally working with the original “cyber-pilot.”
https://vt.tiktok.com/ZSxXVgXAD/
纯粹数学三大结构
IDEAL Polynomials
In Sec 3/4 we learnt a technique by factorizing higher degree polynomial P(x) into 2 lower degree polynomials L1(x), L2(x)
eg P(x) = 0
L1(x).L2(x) = 0
then solve L1, L2
These L1, L2 are “IDEALS” of P(x).

IDEALs
Note: Affine Transformation
If you flatten the circle to an ellipse , the Butterfly Theorem still true (EO1 = FO1), BCOS preserved under Affine Transformation (flatten).
Vector Space 101

Physics In History on X: “The mathematical symbols “∫” for integration and “d” in derivatives were introduced by Leibniz — and the world still uses them today.
https://t.co/zBqERm9HK5″ / X https://share.google/ta79WilFZNkFs7O4v
Marden’s Theorem & Affine Geometry

Interesting Marden’s Theorem:
Physics <=> Affine Geometry
Chinese Remainder Theorem : ancient math to modern math

Entry From Classical Algebra to Abstract Algebra : Chinese Remainder Theorem
(九章算术) -> Ideal
Free Claude Code
PDF to Latex
Seadance2.0
Seadance2.0 is the engine available from many platform:
- jimeng 即梦 (*)
- Dola 豆包(*)
(*)Need 斗音 ton register Seadance, but 斗音 only in China.
Note : Seadance has an international version “Dreamina”. It is free from the portal:
dreamina.capcut.com


OO Python has no Encapsulation
Python has NO encapsulation although it has Modules.
Explain here by Grok:
Gradient, Divergence, Curl
Geometry Easu
AI / ML Maths
https://vt.tiktok.com/ZS9M7rbkF/
- Calculus: Gradient Discent
- Linear Algebra: SVD
- Probability: Bayesian
- Statistics
- Object Oriented / Functional Programming (Category, eg Monad)
数学≠计算
从小学到高中=12年,数学= 计算
大学后,数学≠ 计算
所以,很多高考状元,IMO 金牌, 进985/211 /北大/清华 后, 头脑思维转不过来,觉得数学 困难!
这位blog UP 主, 进清华 “姚班” ,就见过 许多 同学 数学“翻车”。他要帮忙改变,就从小学中学生开始 改变 数学 思维。。。例如: 魔方 => 群论
大学数学≠计算
Foundation of Abstract Algebra : Set Theory
Python “Pass”
Python function:
“pass” do nothing now (add later)
Wang Hong 王虹 Kakeya Conjecture
张益唐 (“Subway Sandwich Mathematician” who proved “Twine Prime Conjecture” after 7 years making sandwiches) praised Wang Hong 王虹 (née 1991-, 广西 客家村 ) as very 专注 (focused) , although she doesn’t have math talent like her 北大 cohort 韦神 (also né 1991-).
Fields Medalist 丘城桐 (Hakka, HK) gave her the top China Maths prize after she had already won few young mathematician prizes (Iranian “Maryam Mirzakhani” Prize) in USA.
A French scholar after her Bsc degree Maths from 北大 Maths.
While she is world-famous today as a master of Harmonic Analysis, her path through the French system involved exactly:
Academic Pivot at Ecole Polytechnique (X)
The Switch: Hong Wang (王虹) entered Ecole Polytechnique (X2010) and initially found the theoretical math classes exceptionally challenging. Feeling that pure math might be “too difficult” at that level, she chose to specialize in a more applied engineering track—specifically Civil Engineering and Architecture (often referred to in the French system as Génie Civil or Architecture/Urbanisme).
The Degree: She graduated from Polytechnique in 2014 with the standard Diplôme d’Ingénieur.
Return to Mathematics (MSc Maths)
*The Realization: Despite her engineering studies, her passion for mathematics remained. She decided to return to pure math for her graduate work.
She obtained her MSc in Mathematics in 2014 with Paris-Sud/Paris-Saclay.
*PhD: After rediscovering her footing in math, she moved to the US to complete her PhD at MIT under Larry Guth, eventually solving the long-standing Kakeya Conjecture in 3D.
Summary of her Path
Undergraduate: Math at Peking University (2007–2011).
“X”( Ecole Polytechnique) Specialization: Engineering & Architecture (2011–2014).
Master’s: MSc in Math at Paris-Sud / Paris-Saclay (2014).
Doctorate: PhD in Math at MIT (2019).
She is now a Permanent Professor at the IHES in France and a professor at NYU Courant, proving that her initial feeling that math was “too difficult” was just a temporary hurdle on her way to becoming one of the field’s top researchers.
Note: She obtained her MSc from Paris-Sud (Paris 11), which was the premier math school in the Orsay cluster.
During that exact period (2014), Paris-Saclay was being established as a “mega-university” to group Paris 11 with other schools like Ecole Polytechnique .
丘城桐 has been a vocal supporter of her career, especially as she solved the 3D Kakeya Conjecture, a problem that had stumped the math world for nearly a century. Her ability to pivot from architecture—which she found more “intuitive”—back into pure math to solve one of the most abstract problems in geometry is cited as a major reason for her receiving the ICCM Gold Medal ( equiv “China Fields Medal”).
Given her recent wins of the Salem Prize and the ICCM Gold Medal, she is currently a front-runner for the 2026 Fields Medal.
Python *args,**kwargs
Claude Shortcut Prompts
Python Data
Bayes’ Conditional Probability
Bayes’ Probability
Presbyterian Priest cum Mathematician Thomas Bayes (1701-1761) defended
Newton’s Calculus “Fluxions” , ie dy/dx in Leibniz notation.
How to remember Baey’s Probability Formula :
P(A|B) = Opposite * weightage of P( A) over Prob (B)
Opposite = P(B|A)
Weightage = P(A) / P(B)
P(A|B) = P(B|A) × P(A) / P(B)
The last AI Revolution in 1980s Rules-based Expert System *(“ES”)* is based on Bayes’ Probability, where each expert rule fired with probability calculated from other related rules (with own probability) by Bayes’ formula.
With more than 500 rules in each ES specialist domain (eg Weather, Geology, special disease, computer complex configuration,… ), ES re-used by Deepseek in 2025 as the “MoE” technique (Mixture of Experts) shocked the OpenAI ChatGPT / NVIDIA with cheaper GPUs and faster LLM at $50 million AI token training instead of the $ billions by americans.
Now MoE + Deeplearnig is the NORM in all LLMs.
AI Frameworks
康熙朝的数学家
AI Build Prep Documents
Fermat’s Last Theorem
LLM Comparison
Python UI builder
O not Natural
0 is not a Natural Number (Peano’s axiom)
To be clearer, we denote
N* = Natural Number N Set without 0.
Python Decorator
Naive Set Theory (pdf)

The pdf ebook:
[Author ] Prof Paul Halmos was well-known in teaching students how to learn “Abstract Math” by building a library of “concrete” examples.
Python Web Scrapping , Automation
Building Machine Learning Model
Tannery’s Theorem
Tannery’s Theorem condition: CONVERGENCE a must before swap of limit and Σ.

Algebra in 2026 PSLE
Finally Algebra allowed in PSLE taught to P6.

Free Maths eBooks
Free book: Analysis
Free book: Maths Logic
写数学书,不应该这样写, 读者看第一页 就睡觉/吓跑 :)
Matrix applied in Social Media
How matrix & cosine similarity (vector for 2orc3 dim data, or tensor for > 3 dim data, applied in social media apps (Netflix,TikTok, …) to recommend movies/videos
TikTok uses your personal ” interest” (from your past historical viwership record ), FB uses your friends’ interests… that’s why TikTok beats FB.
eLearning with LLM RAG from YouTube videos
AI Roadmap

Splitting Field
Claude MCP & Skills
Fermat’s Little Theorem
Fermat’s Little Theorem used in RSA Encryption.
This guy demo how modern math can link / prove from many angles : Euler Totient φ number, Group theory with Lagrange Theorem , using the Set function Surjective, Injective, Bijective fundamental concept technique …
Also can prove by ancient Chinese in 200 BCE from Chinese Remainder Theorem (CRT)…
条条大路通罗马。
Beauty of modern maths is the REAL Maths study, not the UK/China computational maths.
“Fermat” is my Alma mater lycée (Classe Prepa, University years 1&2 ) in France (Toulouse, AirBus HQ City). He was a 17CE judge cum amateur mathematician invented Number Theory, Probability (co- with Pascal), Analytic Geometry (co- with Descartes), and Physics (Refraction Law.)
Fibonacci in Complex Plane
Riemann Zeta Function
Great video, quite different from others on Riemann Zeta Function for non-trivial zero.
Must view at least 2 times to understand the final part with Cauchy Residual Theorem.
Iranian Math Tradition
Python GUI
Python GUI
Yann LeCun funded by Temasek




