Twin Prime Gap : Zhang YiTang

Twin prime gap we know should be 2 in the infinity, so far Zhang proved the gap is bounded by 70,000,000 further reducing to 246… How to get to “2“ is a challenge which may take another 50 years.

2014 Lecture:

张益唐 天才的野心： 《朗道-西格尔零点》猜想

Dr. Zhang YiTang (1955 -) the “Subway Sandwich” mathematician who, before 50 was still a temporary hourly worker… until 2013 at 58 proved the “70-million Twin Prime Gap“.

He becomes overnight famous worldwide, now a tenure professor.

His next ambition is the “Landau-Siegel Zero Conjecture”, a weaker form of the Millenium Problem “Riemann Conjecture”.

Landau–Siegel zeros and zeros of the derivative of the Riemann zeta function

https://www.sciencedirect.com/science/article/pii/S0001870812001600

(想看更多合你口味的内容，马上下载 今日头条)

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:

不向命运低头的数学家: 张益唐

1. 文化大革命: 父母下乡劳改

2. 中学辍学, 自修数学 《十万个为什么》

3. 留美大学的博士导师为难

4. 博士毕业就失业7年, 当Subway 快餐职员, 学非所用, 身无分文, 家无定所。

张益唐：我的数学人生

[录音小声, 请用earphone耳机听更清楚。]

Key Points Take Away:

1. 身处逆境, 不是勇气, 是淡定。

2. 对目的要穷追不捨, 不要放弃。他从北大的Analytic Number Theory (解析数论)兴趣, 被”人为”的转道去搞博士论文Algebraic Geometry, 7年毕业却无业。从新回到” 解析数论”的跑道, 才得到大成就。

3. 如果2个不同领域的学问之间有些联系, 只要往里鑽, 必能发现新东西。

4. 人生低谷, 碰到3个贵人(2位北大校友, 一位美国系主任青睐)协助。

5. 太太不知他干何学问, 不给 他家庭经济压力, 才能安心于数学。

Q&A:
1. 对于天才儿童, 他劝家长不要 “压 “也不要”捧”, 只要多鼓励, 像Perleman 的(俄国数学家, 证明100年的Poincaré Conjecture)父母循循教导儿子

2. 希望能收PhD学生, 会对他们负责任, 不要有像他个人的悲剧发生 (指被教授利用做私人的项目, 误了学生的前途)。他手头有半’成品’和 3/4’成品’, 可让学生拿去参考, 继续完成当论文。

【台湾壹週刊】