# The Laws of Mathematics Zermelo-Fraenkel Axioms Set Theory

The Foundation of Modern Math which is based on the “Set Theory”, hit a crisis due to Bertrand Russell “Barber’s Paradox”, until the Zermelo-Fraenkel Axioms came to its rescue.

Here is a humorous example of an ISP Internet Plan violating the 9 Z-F Axioms:

How ISPs Violate the Laws of Mathematics:

Video:

# 通俗群论

Challenge: Put ’15’ and ’14’ in the right sequence (Impossible! )

# 陈省身 SS Chern – “The 2nd Gauss”

http://www.bilibili.com/video/av5473133

Key Points:

1. SS Chern won the “Wolf Prize” in the same year with the Hungarian “Vagabond” 流浪汉 Mathematician Erdos Paul.
2. He was appointed the Scientific Advisor of President Reagan, during which Chern recommended to build the USA Center of Math in Berkeley University. After retirement, Chern built a similar center in China at his alma mater Nankai University 南开大学 where he graduated in 1930.
3. SS Chern was an assistant lecturer of Prof Yang WuZhi 杨武之, who liked to invite Chern to his house for dinners, where he saw his 8-year old son Yang ZhenNing 杨振宁 (Nobel Prize Physics 1958).
4. SS Chern has guided great PhD students eg. James Simons (Billionaire Financial Investor applying Math Modeling) , Prof ST Yau 丘成桐 (First Chinese to win the Fields Medal).
5. Russian Perelman solved The “Poincare Conjecture” usung Ricci Flow.
6. Chern won an overseas scholarship from QingHua Preparatory School (now 清华大学) which was built by americans with the money “refunded” from the “Boxer Indemnity” 庚子赔款 over-paid by the previous Manchurian dynasty to the 8 European invaders (USA, UK, France, Germany, Italy, Austria-Hungary, Russia, include Japan).
7. He went to Hamburg University in 1934 (Hiltler in power from 1933) for 2 years post-doc, during which he attended a seminar introducing the works of the French greatest Differential Geometry Mathematician Elie Cartan. It impressed Chern but all attendees left the lecture room except him.
8. Chern then moved to Paris University to study under the 69-year-old Prof Elie Cartan, who kindly invited Chern to his house for discussions fortnightly during 10 months.
9. [Video 57:20 mins] The great contributions of Elie Cartan: Lie Group Symmetry applied in Geometry (after Felix Klein, Sophus Lie “E8” ).
10. Simple Lie Group E8＂ is misleading not so “Simple” – Chern advised those curious minds to look into its potentials.
11. Cartan’s 2nd contribution is Exterior Differential 外微分:

# 70-million Bounded Gap Between Primes

Since Ancient Greek :

1. Euclid had proved there are infinite primes.
2. Sieve of Eratosthenes to enumerate the primes.
3. Recent time 3 Mathematicians GPY attempted another Sieve method to find the bounded gap (N) of primes in infinity, but stuck at one critical step.
4. Dr. YiTang Zhang 张益唐 (1955 -) spent 7 years in solitude after failure in academic career, in 2013 during a 10-min walk at the deer backyard of his friend’s house, he found an Eureka solution for the GPY’s critical step: $\boxed { \epsilon = \frac {1} {168}}$ which gave the first historical bounded Gap (N) from an infinity large number to a limit of 70 million.

Notes:

• Chinese love the number “8” \ba which sounds like the word prosperity 发 \fa (in Cantonese) . He could have instead used 160, so long as $\epsilon$ is small.
• The Ultimate Goal of the Bounded Gap (N) is 2 (Twin Primes Conjecture) .
• The latest bounded gap (N) is reduced from 70-million to 246 from The PolyMath Project led by Terence Tao using Zhang’s method by adjusting the various values of $\epsilon$ (analogous to choosing different sizes of the holes or ‘eyes’ of the Prime Sieve.)

A Graduate Level Talk by Dr. Zhang:

A Simpler Overview: