Author Archives: tomcircle

About tomcircle

Math amateur

Visionary mathematician Vladimir Voevodsky

Originally posted on Math Online Tom Circle:
A self-study Russian mathematician, kicked out 3 times in high schools, expelled from Moscow University, all because he did not attend classes, preferred to self-study in a broader scope for his curiosity, at…

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Univalent Foundation – Computer Proof of All Maths

Originally posted on Math Online Tom Circle:
The scary complex field of Math worried the mathematicians who would prove a theorem relying on the previous theorems assumed proven correct by other mathematicians. A sad example was Zhang YiTang (1955 –…

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Motif (Motive 目的)

Originally posted on Math Online Tom Circle:
Below is an excellent intuitive explanation (in Chinese) of the abstract concept Motif by Grothendieck: Brief summary – Motif is the source of all “beautiful things” expressed in different forms. Example : God…

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Song of Simple Group

Originally posted on Math Online Tom Circle:
The lyrics to the song can be found in “Contemporary Abstract Algebra” (Seventh Edition) by Joseph A. Gallian (ISBN 978-0-547-16509-7) pages 422 & 423.

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10招教你用Google搜技巧

Originally posted on Math Online Tom Circle:
https://youtu.be/9PNf_u9adZs

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One of the world’s most influential math texts is getting a beautiful, minimalist edition – The Verge

Originally posted on Math Online Tom Circle:
https://www.theverge.com/2017/9/2/16247282/euclids-elements-kroncker-wallis-math-text-beautiful-minimalist-kickstarter Little print-edition of Math Classics: Euclidean 《The Elements》(几何原理) – the second printing by volume after 《The Bible》. The Euclidean Geometry was less emphasised in Secondary school from 1970s in the world (80s…

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The Evolution of Software

Originally posted on Math Online Tom Circle:
https://medium.com/@cscalfani/so-you-want-to-be-a-functional-programmer-part-1-1f15e387e536

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Zhihu 知乎: 环Ring, 域Field, (半Semi-)群Group, 幺半群 MonoId

Originally posted on Math Online Tom Circle:
数学中代数的有两个名词:环,半群,请问环为什么叫做环,它和汉字里的环(字典中的意思)有什么相同之处;同样,半群为什么叫做半群,这个”半“字是怎么解释呢? [葛利流,数学科技] (I) 环和域 环 (Ring) 是德文, 这名词是David Hilbert发明的。 “环”最好的例子: 整数(Integer) 记作 Z (德文Zahl) 是个环。 他研究 Clock Arithmetic 时钟 是个 Modular Arithmetic (Mod 12)运算, 比如 15 = 3 mod 12 … 钟表上的整数 Z…

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2017 PSLE Math Question

Originally posted on Math Online Tom Circle:
Answer: 10 (Yes!) but why ? …(see explanation here )

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ZAPZAP : Math + Game

Originally posted on Math Online Tom Circle:
https://vulcanpost.com/613827/zapzap-math-malaysia-education-app/

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Mathematical Functions vs Programming Functions

Originally posted on Math Online Tom Circle:
Key Points: Pure Function Partial Function Total Function https://medium.com/the-accepted-forest/mathematical-functions-vs-programming-functions-cf4c7e6f9f4b

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Symmetry, Algebra and the “Monster”

Originally posted on Math Online Tom Circle:
Very good introduction of Modern Math concept “Group” to secondary school math students by an American high school teacher. https://www.quantamagazine.org/symmetry-algebra-and-the-monster-20170817/ Summary: Symmetry of a Square Isometry (*) or Rigid Motion (刚体运动) = no…

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Math Problem Solver – SymboLab

Originally posted on Math Online Tom Circle:
A new alternative to the UK Mathematica’s “Wolfram Alpha” online tool: http://www.makeuseof.com/tag/not-wolfram-alpha-solve-math-equation-symbolab/ https://m.youtube.com/watch?v=Dinl6I77AoU

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UK Textbooks à la Chinese / Singapore Math Style

Originally posted on Math Online Tom Circle:
[Original Financial Times Article] Google: UK maths books fail DfE test UK, USA, France are copying Chinese Math (from which the “Singapore Modeling Math” derived) in Primary schools, this proves my above-mentioned “Ideal…

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How (not) to memorise mathematics

Originally posted on Math Online Tom Circle:
Many excellent Math students after leaving universities more than 10 years forget 90% of math they learned, save some primary school arithmetics – few could do Singapore PSLE Modelling Math or solve quadratic…

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Math drives Biology

Originally posted on Math Online Tom Circle:
https://youtu.be/X-8MP7g8XOE https://futurism.com/math-help-treat-diseases-develop-better-vaccines/

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The Ring Z/nZ, Fermat Little Theorem, Chinese Theorem (French)

Originally posted on Math Online Tom Circle:
Revision: Modulus Arithmetics (1/2) Fermat Little Theorem https://youtu.be/UaF-piufq84 (1/2) Chinese Theorem (Note: This is the “RING” foundation of “The Chinese Remainder Theorem” which deals with remainders ) https://youtu.be/_xTSQu8Ft5I

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Ideal Math Education

Originally posted on Math Online Tom Circle:
C = Chinese 中文 = Primary school Arithematics sans “Algebra” (= Singapore Modeling Math). Abacus-Algorithmic thinking. E = English = Secondary School Math=> Applied, Tricky, Math Olympiad-style=> Engineering, Business, Applied Science. F =…

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Math Olympiad (Primary Schools) 一筐鸡蛋

Originally posted on Math Online Tom Circle:
One basket of eggs.1粒1粒拿,正好拿完。Remove 1 by 1, nothing left in basket. 2粒2粒拿,还剩1粒。Remove 2 by 2, one left in basket. 3粒3粒拿,正好拿完。Remove 3 by 3, nothing left in basket. 4粒4粒拿,还剩1粒。Remove 4 by 4, one left…

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Les Categories Pour Les Nuls

Originally posted on Math Online Tom Circle:
“Categories for Dummies” (French) https://youtu.be/LVHoROSF3KA Example 1: Paris (P) -> Rome (R) -> Amsterdam (A) Objects: cities {P, R , A} Morphism (Arrow): railway? Identity: railway within the city Associative: (P -> R)…

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Debate (French): Set Theory vs Category Theory

Originally posted on Math Online Tom Circle:
https://sites.google.com/site/logiquecategorique/dcm 4. Category, Logic and IT https://youtu.be/Shk3TNagC-4

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An Introduction to N-Categories

Originally posted on Math Online Tom Circle:
Tom Leinster N = 0 : 0-Cat? => Set, 0-morphism = function N= 1: 1-Cat? => Cat, 1-morphism = functor N= 2: 2-Cat? => 2-morphism = Natural Transformation ? ? Definition of n-Category:?…

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Category Theory : “How to Make Pi”

Originally posted on Math Online Tom Circle:
Dr. Eugenia Cheng – Professor of Category Theory (Chicago University) Author of the Best Selling Category Book Book : (for readers from 7-year-old to high school and undergraduate students) “How to Bake Pi…

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Program = Category 

Originally posted on Math Online Tom Circle:
2017 Keywords:? Category? Monad = Monoid + Endofunctor Category Theory is replacing Set Theory as the foundation of Math. Nowadays, ?few Advanced Math papers are written without using Category to explain, and this…

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Integral Domains 整环 (Abstract Algebra)

Originally posted on Math Online Tom Circle:
Remember when you cancel a common factor at both sides of an equation, you must check if the factor is non-zero, otherwise you would miss some answers. This is about Cancellation Law, related…

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South Korean Young Mathematician June Huh

Originally posted on Math Online Tom Circle:
A weak South Korean Math student?June Huh?becomes a top Mathematician in the Princeton Institute for Advanced Study by proving the Read’s Conjecture and Rota Conjecture. “A path less taken to the peak of…

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Is There a Multi-dimensional Mathematical World Hidden in the Brain’s Computation?

Originally posted on Math Online Tom Circle:
“Algebraic Topology” can detect the Multi-dimensional neural network in our brain – by studying the Homology (同调) and co-Homology (上同调) with the help of Linear Algebra (multi-dim Matrix) & ?Computers. Homology = compute…

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What is math? 

Originally posted on Math Online Tom Circle:
What is Math ? https://infinityplusonemath.wordpress.com/2017/06/17/what-is-math/ Mathematics?= “that which is learned“ –(Pythagoras) Math is not about calculation, it is understanding the nature, the universe, the philosophy (logic, intelligence – both “human” and “artificial”)… What…

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Singapore Math for  Primary School Kids

Originally posted on Math Online Tom Circle:
Singapore scores the 2017 PISA Test World’s First in Math. Below is the “Singapore Math” shown by an USA School adopting the pedagogy. https://youtu.be/SlAEvaxMzXQ I had the opportunity to meet the inventor of…

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Pi hiding in prime regularities

Originally posted on Math Online Tom Circle:
Three mysterious Math Objects: Pi,? Complex Numbers,? Prime Numbers are hiding in circle. https://youtu.be/NaL_Cb42WyY

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AI “AlphaGo” beats World’s Best Go Player Ke Jie in 1st Match

Originally posted on Math Online Tom Circle:
After the defeat in 1st match, Ke Jie said “AlphaGo is approaching God!”.? This version of AlphaGo is 10x more powerful than last year’s version which has beateb the South-korean Go player Lee.…

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Google officially supports Kotlin from May 2017

Originally posted on Math Online Tom Circle:
Kotlin is the “New Java” officially supported by Google from May 2017! It is less verbose (罗唆) than Java which is clumsy with boilerplates (样板), ?interoperates with Java on JVM, with modern functional…

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French youngest President Emmanuel Macron and his Education 

Originally posted on Math Online Tom Circle:
Emmanuel Macron is the youngest French President (39) since Napoleon Bonaparte (40). A brilliant student since young, he impressed his secondary school Drama teacher 24 years older, finally married her. Like any genius…

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BM Category Theory II 8: F-Algebra, Lambek’s Lemma , Catamorphism, Coalgebra, Anamorphism

Originally posted on Math Online Tom Circle:
[Continued from previous BM Category Theory …] Intuition: [Artificial Intelligence] You teach the computer, like a Primary 6 kid, that Algebra is a?type of expression (f) which, after evaluation, ?returns a value. If…

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What is a Module (模)? 

Originally posted on Math Online Tom Circle:
Replace Field scalar as in a Vector Space to Ring scalar in a Module. https://youtu.be/IvukAijXgLE Module is more powerful than Vector Space – because Ring has an “Ideal” (理想) which can partition it…

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American Genius Series 1 1of8 Jobs vs Gates (2015)

Originally posted on Math Online Tom Circle:
https://youtu.be/prstbP2cG6M

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Structure Preserving

Originally posted on Math Online Tom Circle:
Abstract Algebra studies all kinds of?mathematical structures?(Group, Ring, Vector Space, Category, …) , and relationship between them if the structures are preserved after mapping.

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Mathematics: Beauty vs Utility – Numberphile

Originally posted on Math Online Tom Circle:
https://youtu.be/xopM9BFjcNo

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2 minutes pour le théorème de Bézout

Originally posted on Math Online Tom Circle:
https://youtu.be/0_ZzZzvxnP0

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Maths -Topologie

Originally posted on Math Online Tom Circle:
https://youtu.be/L3HXZfLsuXU

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中国初中生集体挑战美国高考数学SAT题

Originally posted on Math Online Tom Circle:
[Hint]:? https://youtu.be/mllw55JQy7Y

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The World’s Best Mathematician (*)

Originally posted on Math Online Tom Circle:
Terence Tao:? Weakness in Math: Algebraic Topology Collaborative & “Lone Wolf” Not attempting the Riemann Hypothese: tools not there yet. https://youtu.be/MXJ-zpJeY3E 3 Phases of Math Training: Pre-rigourous: intuition Rigorous: formal prove Post-rigourous: 1…

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The Legend of Question Six (IMO 1988)

Originally posted on Math Online Tom Circle:
This question was submitted ?by West Germany to the IMO Committee, the examiners could not solve it in 6 hours.? In the IMO (1988) only 11 contestants solved it, ?one of them proved…

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The Shortest Ever Papers 

Originally posted on Math Online Tom Circle:
https://youtu.be/QvvkJT8myeI

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Unknown German Retiree Proved The “Gaussian Correlation Inequality” Conjecture

Originally posted on Math Online Tom Circle:
https://www.wired.com/2017/04/elusive-math-proof-found-almost-lost Case “=” : if (a, b) independent? Case “>” : if (a, b) dependent Thomas Royen used only high-school math (function, derivative) in his proof in 2014. He then published it in…

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Tough Math : Diophantine Equation

Originally posted on Math Online Tom Circle:
Math Online Tom Circle View original post

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Fun Math

Originally posted on Math Online Tom Circle:
Answer : (scroll below) . . . . . . . . . . . . . . . . . . . . Answer = 3 mins See clearer if change person…

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Category Adjunctions 伴随函子

Originally posted on Math Online Tom Circle:
Adjunction is the “weakening?of Equality” in Category Theory. Equivalence of 2 Categories if: 5.2 ?Adjunction definition: such that the 2 triangle identities below ( red and blue) exist. 6.1?Prove: Let C any category,…

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Category Theory (Stanford Encyclopedia of Philosophy)

Originally posted on Math Online Tom Circle:
https://plato.stanford.edu/entries/category-theory/

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Beautiful Math Olympiad Problem

Originally posted on Math Online Tom Circle:
[INMO 1993]

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