http://www.epochtimes.com/b5/9/2/11/n2426320.htm

Fibonacci numbers: a number = sum of two previous numbers (eg. 13 = 5 + 8)

http://www.epochtimes.com/b5/9/2/11/n2426320.htm

Fibonacci numbers: a number = sum of two previous numbers (eg. 13 = 5 + 8)

Mathematics is divided into 2 major branches:

1. **Analysis** (Continuity, Calculus)

2. **Algebra** (Set, Discrete numbers, Structure)

In between the two branches, **Poincaré** invented in 1900s the **Topology (拓扑学)** – which studies the ‘holes’ (disconnected) in-between, or ‘neighborhood’.

Topology specialised in

– ‘local knowledge’ = **Point-Set Topology**.

– ”global knowledge’ = **Algebraic Topology**.

__Example:__

The local data of consumer behavior uses ‘Point-Set Topology'; the global one is ‘BIG Data’ using Algebraic Topology.

This blogger has a very valid point on Math Self-study Technique : Learning Math ‘Just-in-Time’ using the rich resources in Wikipedia:

http://steve-yegge.blogspot.in/2006/03/math-for-programmers.html

What are the differences of these strings of characters?

1111111111111…

010101………..01…

1001100100001….

The 1st string is all ‘1’

The 2nd string is all ’01’

The 3rd string is complex: random ‘0’, ‘1”

Kolmogrov complexity deals with randomness.

This Math technique is very often used by great mathematicians who have the multi-year patience in the laboriously proofs:

Chen Jingrun “1+2″ Goldbach Conjecture. (Terrence Tao’s notes)

Zhang Yitang on the “70 million Prime Gap.”

It said: “(The above) Prof Yang was a long time colleague of Chen Jingrun (陈景润). He revealed that Chen was, by nature, **not a Math genius**, his success in climbing the Math Summit was through sheer determined hardwork — especially during the decade long cruel Cultural Revolution when the intellectuals were persecuted — sustained by a very strong interest in Math.”

**“Math journey is not a short 100-meter sprint but a 20-year marathon run.”**

“He critised the crazy rush of Math Olympiad training in whole China, not only adding extra school burden on kids, it also kills their interest in Math.”

**Note:** Recently China government bans IMO training in schools.

Chen Jingrun (陈景润), a student of Hua Luogeng (华罗庚), proved in 196x during The Cultural Revolution: (1+2) Goldbach Conjecture.

**Goldbach Conjecture:**

Any Even Integer = 1 prime + 1 prime

eg. 12 = 5+7 = “1+1″

**Thinking in Philosophy:**

Any prime (odd numbers except 2) together with another prime make an Even number:

**Two single odd (prime) persons together make a couple (even).**

*二个单(odd)身人 结合成 偶 (even)。*

This is the biggest secret in Nature (Natural Number). To prove it is extremely impossible, unless guidance from God.

*这是自然数(Natural numbers) 的奥秘, 天意 ! 要证明它, 难若登天, 除非上帝给你指引。*

**Theorem Chen:**

Chen’s proof is the world’s best approximate one (so far):

Any Even Integer = 1 prime + (1 prime x 1 prime) = “1+2″

Note: (1 prime x 1 prime) = semi-prime

**陈景润证明:
1 单(男) + 2 单(妻x妾) = 对偶**。还是非天意 :)

**陈景润电影:**

The result is not surprising to China but to USA:

♢Recently China government bans IMO training in schools.

♢Obama was surprised that the USA IMO team consists of predominantly Chinese American students.

IMO Math is like ‘Acrobatics’ to real ‘Kung-fu’, it is not real Math education, but special ‘cute’ techniques to solve tough ‘known’ solution problems. Real Math is long R&D solving problems with UNKNOWN solution (eg. Fermat’s Last Theorem, Riemann Conjecture,…)

2 types of Math: **Algorithmic ** or **Deductive (演绎)**. Chinese long traditional ‘abacus’ mindset, procedural computational Math is Algorithmic, applied to special cases (eg. astronomy, calendar, agriculture, architecture, commerce,…). European Greek’s Euclid deductive, step-by-step axiom-based proofing, is theoretical, generalized in all cases (Geometry, Abstract Algebra,…)

Look at the Fields Medal (aka ‘Nobel Prize’ of Math) super-power – France – which has produced 1/3 of the Fields Medalists, but performing so-so in IMO. In contrast, China has **ZERO** Fields Medalists, albeit dominating IMO championship for more than 2 decades!

**IMO 2015:**

https://www.imo-official.org/results.aspx

**USA 1st,**

**China 2nd,**

South Korea 3th,

North Korea 4th,

Vietnam 5th,

Australia 6th

Iran 7th

Russia 8th

Canada 9th

**Singapore 10th ** [2012 Individual World’s Champion ]

Ukraine 11th

Thailand 12th

Romania 13th

**France 14th**

…

United Kingdom 22th