My Modern Met: Geometry Lovers Will Enjoy This Interactive Version of Byrne’s Euclid.

https://mymodernmet.com/byrnes-euclid-nicholas-rougeux/

My Modern Met: Geometry Lovers Will Enjoy This Interactive Version of Byrne’s Euclid.

https://mymodernmet.com/byrnes-euclid-nicholas-rougeux/

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Lycée Louis-Le-Grand, founded since 1563, is the best high school (lycée, 高中 1~3) for Math in France – if not in the world – it produced many world-class mathematicians, among them “**The Father of Modern Math**” in 19th century the genius Evariste Galois, Charles Hermite, the 20th CE PolyMath Henri Poincaré, (See also: Unknown Math Teacher produced two World’s Math Grand Master Students ), Molière, Romaine Rolland (罗曼.罗兰), Jean-Paul Satre, Victor Hugo, 3 French Presidents, etc.

Its Baccalauréat (A-level) result is outstanding – 100% passed with 77% scoring distinctions. Each year 1/4 of Ecole Polytechnique (*) (France Top Engineering Grande Ecole ) students come from here.

More surprisingly, the “Seconde” (Secondary 4 ~ 中国/法国 “高一”) students learn Chinese Math since 6ème (Primary 6).

**Note **: Below is the little girl Heloïse (on blackboard in Chinese Math Class) whose admission application letter to the high school :

Translation– I practise Chinese since 6ème (Primary 6), 5 hours a week. I know that your school teaches 1 hour in Chinese Math, which very much interests me because Chinese and Mathematics are actually the 2 subjects I like most.

Interviewerasked Heloïse :Q: Why do you learn Chinese?

A: It is to prepare (myself) for working in China in the future, to immerse now in the language of environment. Anyway, the Chinese mode of operation is so different from ours.

**Note **: Louis Le Grand (= Louis 14th). He sent in 1687 AD the Jesuits (天主教的一支: 耶稣会传教士) as the “French King’s Mathematicians”(eg. Bouvet 白晋) to teach the 26-year-old Chinese Emperor (康熙) KangXi in Euclidean Geometry, etc.

**Note (*):** 5 Singaporeans (out of 300+ French Scholarship students) had entered Ecole Polytechnique through Classes Préparatoires / Concours aux Grandes Ecoles in native French language since 1980 to 2011. It is possible one day some of these elite French boys and girls could enter China top universities via “Gaokao” (高考 ~ “Concours”) in native Chinese language.

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 in Singapore) to be replaced by Vector Geometry (UK/USA) and Abstract Linear Algebra aka Vector Space / Affine Geometry (in France). It was a pedagogical mistake now these countries recognise – never “Throw the baby (Euclidean Geometry) together with the bath water (Old Maths )”.

IMO Competition usually has 2 out of 6 problems in Euclidean Geometry but no modern math or Calculus, reason being to cater for 100+ countries still with Classical Math. That’s why the Asian countries – South Korea (2017 IMO Champion), China (2nd IMO 2017), Vietnam (3rd IMO 2017) , HK, Taiwan, Thailand, – with old syllabus are top IMO but not the Advanced countries (France, UK, other European, Japan, USA, Singapore…).

**Historical Backgroud**:

Math evolves since antiquity, from Babylon, Egypt 5,000 years ago, through Greek, China, India 3,000 years ago, then the Arabs in the 10th century taught the Renaissance Europeans the Hindu-Arabic numerals and Algebra, Math progressed at a condensed rapid pace ever since: complex numbers to solve cubic equations in 16th century Italy, followed by the 17 CE French Cartersian Analytical Geometry, Fermat’s Number Theory,…, finally by the 19 CE to solve quintic equations of degree 5 and above, a new type of Abstract Math was created by a French genius 19-year-old Evariste Galois in “Group Theory”. The “Modern Math” was born since, it quickly develops into over 4,000 sub-branches of Math, but the origin of Math is still the __same__ eternal truth.

**Math Education Flaw: ** 本末倒置 *Put the cart before the horse.*

Math has been taught wrongly since young, either is boring, or scary, or mechanically (calculating).

This lecture by Queen Mary College (U. London) Prof Cameron is one of the rare Mathematician changing that pedagogy. Math is a “Universal Language of Truths” with unambiguous, logical syntax which transcends over eternity.

I like the brilliant idea of making the rigorous Math foundation compulsory for all S.T.E.M. (Science, Technology, Engineering, Math) undergraduate students. Prof S.S. Chern 陈省身 (Wolf Prize) after retirement in Nankai University (南开大学, 天津, China) also made basic “Abstract Algebra” course compulsory for all Chinese S.T.E.M. undergraduates in 2000s.

The foundations Prof Cameron teaches are centered around 4 Math Objects:

1. **SET 集合**

– Set is the founding block of the 20th century Modern Math, hitherto introduced into the world’s university textbooks by the French “Bourbaki” school (André Weil *et al*) after WW1.

Note: *The last “Bourbaki” grand master Grothendieck proposed to replace Set by Category. That will be the next century Math for future Artificial Intelligence Era, aka “The 4th Human Revolution”.*

2. **FUNCTION 函数 **

– A vision first proposed by the German Gottingen School’s greatest Math Educator Felix Klein, who said Functions can be visualised in graphs, so it is the best tool to learn mathematical abstractness.

3. **NUMBERS**

– The German mathematician Leopold Kronecker, who once wrote that “**God made the integers; all else is the work of man.”**

– The universe is composed of numbers in “NZQRC” (ie Natural numbers, Integers, Rationals, Reals, Complex numbers). After C (Complex), no more further split of new numbers. Why?

4. **Proofs**

– reading and debugging proofs.

**Example 1: Proof by Contradiction**, aka *Reductio ad Absurdum * (Euclid’s Proof on Infinitely Many Prime Numbers)

Challenge the proof: Why ?

Induction intuitively by:

**[Hint:] **

By Reasoning (which is unconscious), most would get “2 & A” (wrong answer)

By Logic (using consciousness), then you can proof …

**Correct Answer: 2 and B**

Test on all 3 Truth cases below in Truth Table:

p = front side

q = back side

Recommended The Best Book on Abstract Algebra by Prof. Peter J. Cameron

Matteo Ricci (利马窦) the Italian Jesuit Priest who came to China during the 16th Century Ming Dynasty of WanLi 万历 Emperor, tried to evangelise the Imperial Court Mandarins with his impressive western Science knowledge and Mathematics. In1607 Ricci translated Euclid’s Masterpiece “The Elements” in Chinese with the Prime Minister Xu GuangQi (徐光啓), the later named Geometry as “几何”, a Chinese term still being used today. Paul Xu and few Scientist Officers were baptised by Ricci as the first Catholics in Chinese history. Ricci stopped the Euclid translation at Book 6 of 15 (Euclid’s 13 books + 2 add-on books from Ricci’s Jesuit professor Clavius), albeit the earnest plea from Xu to translate the remaining 9 books (likely because Ricci himself was not taught in Rome before he left for China), which were later translated by a British Alexander Wylie and a Chinese mathematician 李善兰 in 1857 of Qing Dynasty.

Ricci spent his remaining life in China because the Catholic Pope in Rome, influenced by the Macau-based Franciscans (then the opponent of Jesuits), prosecuted him for being ‘compromised’ by Chinese rituals of Ancestor Worship.

Now the current Pope Francis wants to befriend China, which broke diplomatic tie with Vatican in 1950s, intents to beatify Matteo Ricci : The first Saint ‘Mathematician’ !

http://news.yahoo.com/vatican-asked-honour-jesuit-tried-evangelise-china-193740033.html

Prime Numbers

God multiplies Primes: Fundamental Law of Arithmetic (Euclid):

Any number (n) can be UNIQUELY Prime Factorized: n = P1 x P2 x …Pn

e.g. 12= 2 x 2 x 3,

28=2 x 2 x7

Men add Primes: Goldbach Conjecture.

2n = P1+P2

e.g. 12= 5 + 7, 28 = 17 + 11, 30 = 11+19