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】

张益唐谈做数学

2013年7月13日 台大访问笔记摘要 Summary:

http://blog.sina.cn/dpool/blog/s/blog_c24597bf0101ctdp.html

Holistic Approach to Attack Math :

10岁的启蒙书:

Ref: 白居易写给元稹《与元九书》

Shimura Modular Form:

On Riemann Hypothesis:

Our Daily Story #6: A Subway Sandwich Mathematician Zhang Yitang 张益唐

Zhang is the typical demonstration of pure perseverance of traditional Chinese mathematicians: knock harder and harder until the truth is finally cracked.

His work is based on the prior half-way proof by 3 other mathematicians “GPY”:

Gap between Primes:

Let p1 and p2 be two adjacent primes separated by gaps of 2N:

p1 – p2 = 2 (twin primes)
eg. (3, 5), (5, 7)… (11, 13) and the highest twin primes found so far (the pair below: +1 and -1)

p1 – p2 = 4 (cousin primes)
eg. (7, 11)

p1 – p2 = 6 (sexy primes)
eg. (23, 29)

p1 – p2 = 2N

Euclid proved 2,500 years ago there are infinite many primes, but until today nobody knows are these primes bounded by a gap (2N) ?

Zhang, while working as a sandwich delivery man in a Subway shop, kept trying alone for 7 years with the GPY method, finally in 2013 he found the bounded gap: $\boxed {2N < 70,000,000,000}$

Recent mathematicians (Terrence Tao’s Polymath Project and others) follow his technique to narrow 2N down from 70 million to, hopefully, 16.

At age above 50, Zhang (1955 -) has shown that Mathematics is not limited to only young minds – as GH Hardy had set 35 the age limit for any great math achievements.

http://en.m.wikipedia.org/wiki/Yitang_Zhang

Part 1:

Part 2:

Ref:

3. Euclid’s Proof of Infinite Primes: