数学武林的四大门派

数学武林的四大门派比喻:

[0. 希腊 = 达摩祖师]

  1. 法国 =少林派
  2. 德国 = 武当派(德国祖师 Lindemann 是法国宗师 Charles Hermite 的得意外国徒弟
  3. 俄国 = 峨眉派 (俄国祖师奶 Sofya Vasilyevna Kovalevskaya 是 德国大师 Karl Weierstrass 的得意女弟子)
  4. 中国 = 古墓派 (‘小龙女’ 的奇特功夫 自成一派:中国古代数学 + 融合 留 法/英/美/日 数学派 )

https://m.sohu.com/a/216801634_404328/

英/美/日 数学都是支派,非主流宗派 掌门:

英国 受法国影响 : Newton 说他是站在巨人 Descartes, Fermat 的肩膀. 近代 Bertrand Russell 也是读法国Camile Jordan 的 《Group Theory 》书。

美国 数学 : WW2 德国/东欧 犹太人移民: Noether, Godel, Courant, Artin,…

日本数学 : 唐朝留学 中国 (日本”和算” 鼻祖 关孝和 把中国 “行列式” 传给欧洲Leibniz : Determinant ) ,明治天皇 时期 日本留学欧洲。

Note:

1. 奇特数学: 东汉 3AD  Chinese Remainder Theorem (韩信点兵 Modular Arithmetics), Singapore Modelling Math (eg. 鸡兔问题) ,13CE 的 行列式 (Determinant, before “Matrix” was invented in 20th CE by JJ Sylvester )

2. Determinant was invented by the ancient Chinese Algebraists 李冶 / 朱世杰 /秦九韶 in 13th century (金 / 南宋 / 元) in《天元术》.The Japanese “和算” mathematician 关孝和 spread it further to Europe before the German mathematician Leibniz named it the “Determinant” in 18th century. The world, however, had to wait till the 19th century to discover the theory of Matrix 矩阵 by JJ Sylvester (Statistical Math private Tutor of Florence Nightingale, the world’s first nurse) closely linked to the application of Determinant.

Dr. Eugenia Cheng: “How to Bake Pi”

Key Points of the Talk:

1) Math is interesting but is only so after undergraduate school. Before that, Math is taught as computation subject from Elementary to High school.

2) Braid : Bach music, Juggling 3 balls

3) Platonic Icosahedral (20面体) Structure discovered by ancient Greek Plato 2000 years ago, but can’t find a real world Icosahedral object until in Viruses found by Louis Pasteur in 20th century – also now in Sars, Covid19.

4) Group Theory : Battenberg Cake, Bed Mattress Rotate/Flop/ Flipping

5) Mobius Strip & Donnut Cutting.

6) Fermat’s Last Theorem : Andrew Wiles in 1994 proved in 7 years still with a “hole”, but fixed a year later by himself & his student.

7) MacLane Pentagon : Higher-Dimension Categories (PhD Math)

The Black-Sholes Formula – 诺贝尔经济奖Scholes, Merton与LTCM S

Key Points:

1) From 1950 an unknown PhD Math Thesis by French Dr. Bachelier (a PhD student of the 20CE last Polymath Henri Poincaré, who was not impressed with the ‘gambling’ math, gave only an above-average marks to the thesis) – invention of “Options” Trading to eliminate risk in stock fluctuations.

2) The technique is called “Dynamic Hedging”…

3) …by applying the Japanese mathematician “Ito Math”.

4) Noble Prize Economics awarded to “ Black-Sholes Formula”

5). Sholes & Merton Company “LTCM” – making tons of money until… 1997 Asian Crisis, bailed out by USA government after loss of billions !

https://m.toutiaoimg.cn/a6906337056042156551/?app=news_article&is_hit_share_recommend=0&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share

CAS (Computer Algebra System)

CAS or YaCAS (free).

https://www.r-bloggers.com/doing-maths-symbolically-r-as-a-computer-algebra-system-cas/

[Manual Proof :]

[Notes]

1.

That’s why French Math insists must test rigorously the Integrand is CONTINOUS over interval [0,1], else integration is meaningless & wrong !

2. CAMBRIDGE GCE A-level Calculus still never insists the first Rigorous Test step : “Interval” (aka Domain of Definition) + Continuous

IMO 2019

【打破美国35年纪录的天才,与中国奥数、信息学双料冠军的巅峰对决】
https://m.toutiaocdn.com/group/6714952524924715531/?app=news_article_lite&timestamp=1563521442&req_id=20190719153042010152029169696E814&group_id=6714952524924715531&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share

USA Team (2016 & 2018 World Champion) :

China IMO Team :

【2019国际数学奥赛结果公布 中美两国并列团体冠军】
https://m.toutiaocdn.com/group/6715594110440309261/?app=news_article_lite&timestamp=1563682066&req_id=20190721120745010025067136905FD11&group_id=6715594110440309261&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share

Two observations:
1. Why almost all Chinese in top China, USA, Canada, NZ, Singapore teams?
Either Chinese chase the wrong Math (IMO) education, or the western Math Power countries (UK, France, Germany…) are RIGHT to ignore IMO education?
2. Singapore team skewed heavily in 2 schools: RI (5) + HCI (1). Also 0 girl.

【解读中美数学奥赛并列第一,敬请期待对话美国队总教练 | 袁岚峰】
https://m.toutiaocdn.com/group/6716112894641046024/?app=news_article_lite&timestamp=1563733425&req_id=20190722022345010152042134236B8C3&group_id=6716112894641046024&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share

(想看更多合你口味的内容,马上下载 今日头条)
http://app.toutiao.com/news_article/?utm_source=link

Alibaba “Damo” Global Math Competition

https://m.damo.alibaba.com/alibaba-global-mathematics-competition/

Jack Ma is a kongfu fan, his Alibaba offices all named under the Kongfu heroes, eg. Damo Academy.

Damo” 达摩 (Bodhidharma) was an indian Buddhist monk who came to China in 5th Century, established ShaoLin Monastery, also invented Chinese Kongfu.

Problem 1

Hint: Answers in the above link.

English Fun Math

Different Schools of Math:
1. English (UK/USA) Math is playfully tricky (Math Olympiad, Math Puzzles eg. this Numberpile video)

2. French Math is abstractly theoretical but VERY rigorous (Group theory explains Symmetry, Rubik’s cube game,… ). Its derived schools are German Math (via French Charles Hermite’s German student Lindermann to Felix Klein, Gauss, Riemann, Hilbert), Russian Math (via French Descartes) .

3. Chinese Math (Abacus, “Chicken-Rabbits Problem” 鸡兔问题, Singapore Modeling Math) is applied & algorithmic / procedural (明朝 13th CE invented “Determinant” 行列式 before the 19th CE “Matrix” by UK J. J. Sylvester,Chinese Remainder Theorem 韩信点兵).

4. Indian Math (Vedic Math , Factorization, Ramanujian-Style Math) is mythical spiritual.

Numberpile:

Mathematician Couple’s Wedding Math Questions

https://m.facebook.com/nikita.nikolaev.752/posts/2208321356091587

It is fun for the guests who are also mathematicians like the wedding couple…

Why don’t the IT couples do the same with computer questions (eg. private cloud, serverless, containers, DevOps,… ) , lawyers with legal cases, doctors with medical questions …

Example 1 is obvious to this guest whose PhD research topic is in Differential Geometry “Chern Class” invented by Prof S. S. Chern (陈省身) :

Example 2 is obvious to this guest unless he/she can’t count the number of sides (8):

Example 3 is to the guest with some background in secondary school organic chemistry but forgotten, definitely not linear…

Example 4 to the hobbyist of Rubik’s cube, but the answer can be guessed easily by elimination: definitely not 2019 (this year), or π.

Answer in multiple choices (Only 1 answer is correct, the other 2 answers are obviously wrong) :

Maths is a potential life changer — from wages to dating

https://www.ft.com/content/f039c3ca-d762-11e8-aa22-36538487e3d0

When you are stuck with too many choices in life, whether buying houses recommended by agents, finding schools for children, hiring staff among the hundreds of CVs…apply ‘e’ the number from nature (logarithm) to make smart and efficient decision under the constraints of time and resources.

Theory of Optimal Stopping” = 1/e ~ 37%

where

e = 2.7 18281828 45 90 45…

If you do a house search with 20 properties, then by the Theory of Optimal Stopping, pick the first property which is better than the first 7 properties you see (7. 4 = 20 x 37%).

[Note] Ponder over the hidden Philosophy behind – “Brilliant Limit” :

\displaystyle \boxed{ \lim_{n \to \infty}\left({\frac{n!}{n^n}}\right)^{\frac{1} {n}} = \frac{1} {e}}

My favorite Fermat Little Theorem with Pascal Triangle

Fermat Little Theorem: For any prime integer p, any integer m

\boxed {m^{p} \equiv m \mod p}

When m = 2,

\boxed{2^{p} \equiv 2 \mod p}

Note: 九章算数 Fermat Little Theorem (m=2)

Pascal Triangle (1653 AD France )= (杨辉三角 1238 AD – 1298 AD)

1 \: 1 \implies sum = 2 = 2^1 \equiv 2 \mod 1

1\: 2 \:1\implies sum = 4 = 2^2 \equiv 2 \mod 2 \;(\equiv 0 \mod 2)

1 \:3 \:3 \:1 \implies sum = 8= 2^3 \equiv 2 \mod 3

1 4 6 4 1 => sum = 16= 2^4 (4 is non-prime)

1 \:5 \:10\: 10\: 5\: 1 \implies sum = 32= 2^5 \equiv 2 \mod 5

[PODCAST]

https://kpknudson.com/my-favorite-theorem/2017/9/13/episode-4-jordan-ellenberg

Auspicious Year 2016

2016很神奇

2016=168+168+168+168+168+168+168+168+168+168+168+168

总共12个168,祝大家2016年每个月都一路发!

2016=666+666+666+6+6+6
祝大家2016年顺心隨意、顺风顺水、六六大顺!

2016=888+888+88+88+8+8+8+8+8+8+8+8,
祝大家2016年事业兴旺发达!发发发!

2016 = 999+999+9+9
祝大家在2016年幸福的日子长长久久!
恭祝2016年新年快乐,身体健康,阖家欢乐,实现梦想

Happy 2016 New Year !

来自数学迷的祝福:

2016=666+666+666+6+6+6

祝大家2016年顺心随意! 顺风顺水!六六大顺!

2016=888+888+88+88+8+8+8+8+8+8+8+8

祝大家2016年事业兴旺发达!一路发!

2016=999+999+9+9

祝幸福的日子长长久久!

2016=168+168+168+168+168+168+168+168+168+168+168+168
總共12個168,祝大家2016的每個月都一路發!