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。

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张益唐: 速食店员竟然是数学天才

【台湾壹週刊】

速食店员竟然是数学天才

张益唐 (1955 – ) : 北京大学 – 美国数学博士。因为执着数学理论的真理, 得罪美国大学台湾籍论文教授, 毕业后找不到大学教职, 在朋友的 Subway 速食店做会计8年, 潜心业余思考世界数学大难题: Twin Primes Gap, 终于攻破。

他的下一个目标是Riemann Hypothesis, 困扰数学家百年的难题: “素数 (Prime numbers)的分布”都集中在 Zeta function complex plane的 实轴(real = 1/2) 上。大数学家David Hilbert说如果五百年后复活, 第一件事会急着问 “Riemann Hypothesis” 证明了吗?

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

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突破瓶頸: “先上对车, 后补上票”

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Holistic Approach to Attack Math :

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新酒进旧瓶, 可以突破: 勤能补拙

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10岁的启蒙书:

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现代”科举”考场失意:

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文学与数学相通: Intuition

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Ref: 白居易写给元稹《与元九书》

如何教好数学?

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Shimura Modular Form:

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好书推荐: 华罗庚的《数论导引》 , 华的剑桥老师Hardy…

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解析数论 Analytic Number Theory:

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选对导师和有兴趣的题目
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On Riemann Hypothesis:

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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”:

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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)
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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:

1.
https://tomcircle.wordpress.com/2013/05/22/prime-gap-by-unknown-mathematician/

2. 张益唐(中文) 伯克利大学演讲记:
http://bluepanda5.wordpress.com/2014/02/17/%e5%bc%a0%e7%9b%8a%e5%94%90%e5%9c%a8%e4%bc%af%e5%85%8b%e5%88%a9%e7%9a%84%e6%bc%94%e8%ae%b2%e7%b5%ae%e8%ae%b0-%ef%bc%88%e8%bd%ac%e8%bd%bd%ef%bc%89/

3. Euclid’s Proof of Infinite Primes: