h*h
发帖数: 27852 | 1 Zhang, Yitang’s life at Purdue
(Jan. 1985-Dec, 1991)
T.T.Moh1
Dr. Zhang Yitang made a major advancement to the twin prime conjecture
as verified by Prof. H. Iwaniec, a famous number theorist. This is a
historic result. I congratulate Dr. Zhang, Yitang.
The concept of prime nummbers started with Greek mathematics. Euclid
shown that there were infinitly many primes. We may view the integers as
houses built on the integer spots on the real line, and put a light in every
prime number houses. Then infinitely many houses are lighted (Euclidean
theorem). What are the relations of all lighted houses? The most nature
conjecture is that the prime numbers appear randomly. There is a surprising
conjecture (The twin prime conjecture) states that there are infinitly many
pairs (p, p+2) of houses are lighted. We can not find any trace of it in
Euclidean books. Any way the conjecture might be thousand years old. If
the twin prime conjecture is correct, then we may conclude that the integers
are not constructed randomly. How strange. What Dr Zhang proved is that
there is an n less than or equal to 70,000,000 such that p, p+n are lighted
as primes.
Some people are curious about Yitang’s life as a graduate student at
Purdue University. As the thesis adviser of Dr. Zhang, I will share my
memories of him.
1 China to USA
In the year 1984, a famous mathematician Prof S.S.Chern called Prof W.Y.
Hsiang,
Prof H.H.Wu of Berkeley, Prof Y.T.Siu of Harvard, Prof J.Morgan of Columbia
and me to go to Beijing, China to teach a special summer school with
graduate
students the very best all over China. I was greatly honored by Prof
Chern’s call and worked a whole summer for Prof Chern’s pet project and
met several important young futere mathematicians as Dr S.W. Zhang, Dr
Yitang Zhang, Dr. M.Chen etc.
1Mathematics Department, Purdue University
1
Certainly, we tried to move those talente graduate students to USA.
People outside China knew nothing about their qualities. At that time, I
was in the graduate committe of Math Department. I use my credit to
convince my collegues to admit 10 of them to Purdue. Once they shown up
and did excellent in the qualifying exams, and all doubts dispersed. After
they shown up I adviced them to various professors at Purdue, then there
is only one left with name Zhang, Yitang.
By the recommendations of Prof. Ding, Shihsun (an algebraist, President
of Peking University) and Prof. Deng, D.G. (Chairman of Department
of Mathematics, Peking University), Mr. Zhang was admitted to Purdue
University as a graduate student in Jan, 1985. Prof. Ding, Shihsun
specifically
requested me to take care of Mr. Zhang. When he arrived, we had
a cordial talk. Yitang expressed his desire to work in the field of
Algebraic
Geometry. I nodded while remembering the call of French mathematician
Jean Dieudonn′e in the international conference at Purdue (it was to
celebrate
Louis de Brangles’ result on Bieberbach’s conjecture). Dieudonn′e said
“ You should go to the field of algebraic geometry − that is the
future of
mathematics” to several hundred analysts. Yitang also mentioned that he
wanted to study under my guidance. Knowing that he had one published
paper, and some training in the field of Analytic Number Theory under
Prof. Pan (especially in the additive branch, where the central problem is
the Goldbach conjecture), I was happy to have a talented student. I was
surprised by Yitang’s next request of working on the Jacobian conjecture as
his thesis topic. I felt it was odd to select such a difficult task. After
seeing
his enthusiasm, I settled on it and did my best to guide him.
I thought Yitang as an ambitious, intelligent, and hard-working young
man.
2 Education at Purdue
After we settled on his thesis topic, we met almost daily for a whole
semester. Our discussions centered on my published paper
On the Jacobian conjecture and the configuration of roots. J. fur die Reine
and angewandte Mathematik, 340, 1983, pp. 140-212
Sometimes, they lasted into the dawn. That was the essential part of Yitang
’s
first semester at Purdue.
For the next two semesters, I organized a seminar with five graduate
students (including Yitang) on Prof. Hironaka’s monumental papers on
2
the theory of resolutions of singularities. I believed that we doubled the
world population of those who had studied the papers after we finished two
semesters. Prof. Grothendick once described those papers as among the
most complicated thesises in the human history.
Upon completing three semesters of intensive work, I felt that I might
not have done the right thing (I behaved too much like a modern day “tiger
mother”); I should give him the space to grow. I then laid back and did not
do any pushing. He would come to me once a week to talk, and I listened
carefully. I told him my philosophy of Mathematics. I think that there are
only good Mathematics and bad Mathematics. To find an original proof in a
good Mathematics, one must use computatins to do experiments, then you
need an insight. It is not wise to totally believe in the partial results of
the
past. For instance, if you want to work on the grand unification theory of
Physics and totally trust Einstein’s thesis on unified fields, then you are
a
fool. You have to look at the new evidents. For instance, my work on the
Jacobian Conjecture is beautiful while a generalization to a pair of degrees
less taht or equal to 1000 will require a lot more computations, hence will
not work by itself. We need more experiments and insight. What I want you
to learn from that paper is the methods of computations and the methods
of doing experiments. Yitang spent all of his free time thinking of
mathematics.
After years, Yitang started to believe that he might have gotten
a solution, one independent of my paper, to the Jacobian conjecture. As a
gatekeeper of the palace of the Jacobian conjecture, I did my duty of
examining
every claim presented to me and denied the entrance of anybody (even if
the claim has nothing to do with my work) if the proof was invalid. “Maybe
the Jacobian conjecture is a problem for the future”, I thought. In the
year
of 1991, his 7-th year at Purduei (which was the last year for Yitang at
Purdue.
according to school rules), I asked Yitang ito compose his Ph. D. thesis
Jacobian Conjecture and the Degree of Field Extension(click to view) (
Anybody’s
thesis is in the public domain. This thesis in in the Purdue Library).
He presented it to the committee which consisted of myself as the chair, L.
de Brangles, J. Lipman and W. Heinzer. His thesis passed the committee
with flying colors.
3 Daily life
Some people believe that mathematicians are weird. I think differently.
All the mathematicians I know are quite normal. Yitang was a normal
person for those seven years at Purdue. He was elected the President of
3
the Chinese Student Club at Purdue University, and he discharged his duty
responsibly and served his community well.
Yitang had some background in classical Chinese literature. Sometimes
we talked about them. I mentioned to him a phrase of Confucius: “A person
who knows a job is no match to a person who likes the job. A person who
likes the job is no match to a person who enjoys the job. ” I thought that
applied to research very well. He agreed.
Sometimes I regreted not fixing him a job. But really, who could tell
whether it was a good decision or not? Maybe it was his destiny to endure
and turn out to be great. I indeed got a job for my first student at the end
of 70’s. Later when I my thoughts to my colleagues, they all laughed and
told me that it was only normal of one who had taught in the long-gone 60’s.
The times changed at the late 70’s when there was a new term and trend.
It was the “tenure track” and that the students should look for jobs on
their own. So after Yitang graduated, I told him the normal way of seeking
jobs. When I looked into his eyes, I found a disturbing soul, a burning
bush, an explorer who wanted to reach the north pole, a mountaineer who
determined to scale Mt. Everest, and a traveler who would brave thunders
and lightnings to reach his destination. Yitang never came back to me
requesting recommendation letters. Apparently, he did not seek a job. Even
to the date Yitang announced his monumental result I did not know what
was the best for him. Though I was sure of one thing, − he could not
survive
the life of “tenure-track,” “tenure,” and “promotions”. It was not his
type.
I regarded him as a free spirit, and I should let him fly. Yitang flew away
after he told me that he was going to Rutgers University to talk to Prof.
Iwaniec. I bade him good luck. That was almost 22 years ago.
4 Epilogue
There are some questions as to if my paper on the Jacobian Conjecture
is correct. I will state reasons why that the paper is correct. In the year
1984, Prof. M. Miyanishi (the Provost of Osaka Universaity) and Prof.
S.S.S.Wang (Oakland University) visited Purdue University for one semester
for the purpose of studying this paper on the Jacobian conjecture. After
one semester seminar, they comfirmed the paper. About 10 years after the
publication of my paper, another mathematician published a paper that
obtained the same results as mine using a completely different method. In
fact, anybody who thinks that there is an error in my paper is welcomed to
publish a paper to point it out.
4
One should not overlook the tenure system in the USA. It might not be
suitable for some participants, but it fits most situations.
The year 1985 was extremely difficult for the students from mainland
China, they were unknown and without credits. I was the few professors
who had personal contacts with them, I had taught the previous summer in
the Peking University and had a vivid inpression of them. The mission of
education is to spread the knowledge everywhere. It is the noble American
spirit. For some 10 years, I had recommended 100 mainland Chinese students
to the department and all accepted by the department. I am always
indebt to the trust of my judgements by the department. Only very few
of them misbehaved, bit the hands which fed them, none of them
murdered their parents/friends, almost all of them performed well
and became well-liked. I was happy that my recommendations brought
fruits. Since than, due to the good office of Purdue administration, my
friend Mr Lam donated a fund to a fellowship ”T.T.Moh fellowship” in my
name, I was greatly honored, for the students from mainland China. So far
we only used the interests of it, and Mr Lam promised to continue donations
until 2020.
Reference;
Prime time, Insight, the official magazine of the Science College of Purdue
University(click
to view)
5 | m******t
发帖数: 1171 | 2 不着老莫，这本身就说明了问题。
every
【在 h*h 的大作中提到】
: Zhang, Yitang’s life at Purdue
: (Jan. 1985-Dec, 1991)
: T.T.Moh1
: Dr. Zhang Yitang made a major advancement to the twin prime conjecture
: as verified by Prof. H. Iwaniec, a famous number theorist. This is a
: historic result. I congratulate Dr. Zhang, Yitang.
: The concept of prime nummbers started with Greek mathematics. Euclid
: shown that there were infinitly many primes. We may view the integers as
: houses built on the integer spots on the real line, and put a light in every
: prime number houses. Then infinitely many houses are lighted (Euclidean
| h*h
发帖数: 27852 | 3 至少不是莫故意给张下绊子
张自己选错了学校
【在 m******t 的大作中提到】
: 不着老莫，这本身就说明了问题。
:
: every
| d******r
发帖数: 16947 | 4 It was the “tenure track” and that the students should look for jobs on
their own. So after Yitang graduated, I told him the normal way of
seekingjobs. When I looked into his eyes, I found a disturbing soul, a
burningbush, an explorer who wanted to reach the north pole, a mountaineer
who determined to scale Mt. Everest, and a traveler who would brave thunders
and lightnings to reach his destination. Yitang never came back to me
requesting recommendation letters. Apparently, he did not seek a job.
根据莫宗坚的话，老张和我一样没有找老板要推荐信。为什么？尼玛知道要不到或者评
价不好 lol
every
【在 h*h 的大作中提到】
: Zhang, Yitang’s life at Purdue
: (Jan. 1985-Dec, 1991)
: T.T.Moh1
: Dr. Zhang Yitang made a major advancement to the twin prime conjecture
: as verified by Prof. H. Iwaniec, a famous number theorist. This is a
: historic result. I congratulate Dr. Zhang, Yitang.
: The concept of prime nummbers started with Greek mathematics. Euclid
: shown that there were infinitly many primes. We may view the integers as
: houses built on the integer spots on the real line, and put a light in every
: prime number houses. Then infinitely many houses are lighted (Euclidean
| h*h
发帖数: 27852 | 5 我到觉得莫会给个好推荐
张显然是个极其有性格的人
不过莫应该主动说，如果需要，我会给很好的推荐信
张博士阶段的研究，虽然结果悲剧，但是水平还是展示了
thunders
【在 d******r 的大作中提到】
: It was the “tenure track” and that the students should look for jobs on
: their own. So after Yitang graduated, I told him the normal way of
: seekingjobs. When I looked into his eyes, I found a disturbing soul, a
: burningbush, an explorer who wanted to reach the north pole, a mountaineer
: who determined to scale Mt. Everest, and a traveler who would brave thunders
: and lightnings to reach his destination. Yitang never came back to me
: requesting recommendation letters. Apparently, he did not seek a job.
: 根据莫宗坚的话，老张和我一样没有找老板要推荐信。为什么？尼玛知道要不到或者评
: 价不好 lol
:
| d******r
发帖数: 16947 | 6 看来你对老张的事迹了解很少啊。
老张的博士论文亚克比猜想用到了老莫的
一个定理，这个定理是老莫的终身成就。
很可惜，这个定理的证明是有问题的，所以老张的亚克比猜想证明就被期刊退稿了。
他博士这些年白浪费了，而老莫却不认为是自己的错。两个人肯定有争论。。。
：我到觉得莫会给个好推荐
：张显然是个极其有性格的人 | h*h
发帖数: 27852 | 7 这个我早就知道
这真不能怪老莫，他又不知道他的证明有问题，揭出来他一辈子最主要的成果有问题，
他不要太郁闷
张郁闷可以理解，但是真不应该怪导师
【在 d******r 的大作中提到】
: 看来你对老张的事迹了解很少啊。
: 老张的博士论文亚克比猜想用到了老莫的
: 一个定理，这个定理是老莫的终身成就。
: 很可惜，这个定理的证明是有问题的，所以老张的亚克比猜想证明就被期刊退稿了。
: 他博士这些年白浪费了，而老莫却不认为是自己的错。两个人肯定有争论。。。
:
: ：我到觉得莫会给个好推荐
: ：张显然是个极其有性格的人
| d******r
发帖数: 16947 | 8 你读过博没有，老中导师口碑很差的 LOL
我完全能猜到发生过什么，因为我自己毕业后再也没有和前老板联系过
：这个我早就知道
：这真不能怪老莫，他又不知道他的证明有问题，揭出来他一辈子最主要的成果有问题
，他不要太郁闷 | h*h
发帖数: 27852 | 9 莫是湾湾。我对湾湾印象还可以
【在 d******r 的大作中提到】
: 你读过博没有，老中导师口碑很差的 LOL
: 我完全能猜到发生过什么，因为我自己毕业后再也没有和前老板联系过
:
: ：这个我早就知道
: ：这真不能怪老莫，他又不知道他的证明有问题，揭出来他一辈子最主要的成果有问题
: ，他不要太郁闷
| d******r
发帖数: 16947 | 10 大陆弯弯这个方面基本没有区别 LOL
：莫是湾湾。我对湾湾印象还可以
：【 在 dinassor (牛磨王) 的大作中提到: 】 | | | l**d
发帖数: 189 | 11 扯啊。博士生跟导师的关系不是一般的师生关系。毕业找工作这么大的事，学生都不跟
导师要推荐信，就已经很说明问题，说明俩人关系很僵，几个月都不一定见一次面那种
，所以张干脆不去找他要，因为很清楚会碰壁。
【在 h*h 的大作中提到】
: 我到觉得莫会给个好推荐
: 张显然是个极其有性格的人
: 不过莫应该主动说，如果需要，我会给很好的推荐信
: 张博士阶段的研究，虽然结果悲剧，但是水平还是展示了
:
: thunders
| h*h
发帖数: 27852 | 12 我觉得是，张很恼怒，老子不要你的狗屁推荐信
张很有性格，绝对不要以我等萎缩男心态去揣测他
【在 l**d 的大作中提到】
: 扯啊。博士生跟导师的关系不是一般的师生关系。毕业找工作这么大的事，学生都不跟
: 导师要推荐信，就已经很说明问题，说明俩人关系很僵，几个月都不一定见一次面那种
: ，所以张干脆不去找他要，因为很清楚会碰壁。
| n*l
发帖数: 1126 | 13 笑疯了，莫的洗地文还有人跪舔的
首先张对莫从来一字不提，即使被问到有关导师的时候都回避，只说两人没有联系，这
叫君子绝交，不出恶声
莫则是得知张出名之后，即使没人搭理也要忙不迭的搞出这么个洗地文挂在自己网站上
，显然是心虚，欲盖弥彰
那句不屈的灵魂我看到都要吐了，神马玩意
张毕业后自己去联系过博后的，而且搞数学的导师帮忙联系个博后很常见，张连博后都
没搞上说明导师是在赶尽杀绝
【在 h*h 的大作中提到】
: 我到觉得莫会给个好推荐
: 张显然是个极其有性格的人
: 不过莫应该主动说，如果需要，我会给很好的推荐信
: 张博士阶段的研究，虽然结果悲剧，但是水平还是展示了
:
: thunders
| s*****r
发帖数: 11545 | 14 劳模在这声明里也坚称自己的证明没错，
老张在访谈时候提过这事，说有人认为他是错的，
没人证明他是对的，劳模认为自己对的，可是没
法服人.估计这不会是他们翻脸的缘故吧? 除非
劳模坚持老张用劳模他自己的定理去干一件老张
不想干的事. | h*h
发帖数: 27852 | 15 难道老莫不是委婉的承认他的证明有问题了吗？不然提爱因斯坦的逻辑何在？
【在 s*****r 的大作中提到】
: 劳模在这声明里也坚称自己的证明没错，
: 老张在访谈时候提过这事，说有人认为他是错的，
: 没人证明他是对的，劳模认为自己对的，可是没
: 法服人.估计这不会是他们翻脸的缘故吧? 除非
: 劳模坚持老张用劳模他自己的定理去干一件老张
: 不想干的事.
| h*h
发帖数: 27852 | 16 张联系博后的事儿，你掰开讲讲。我何必跪舔湾湾呢
【在 n*l 的大作中提到】
: 笑疯了，莫的洗地文还有人跪舔的
: 首先张对莫从来一字不提，即使被问到有关导师的时候都回避，只说两人没有联系，这
: 叫君子绝交，不出恶声
: 莫则是得知张出名之后，即使没人搭理也要忙不迭的搞出这么个洗地文挂在自己网站上
: ，显然是心虚，欲盖弥彰
: 那句不屈的灵魂我看到都要吐了，神马玩意
: 张毕业后自己去联系过博后的，而且搞数学的导师帮忙联系个博后很常见，张连博后都
: 没搞上说明导师是在赶尽杀绝
| s*****r
发帖数: 11545 | 17 俺有短暂失忆的毛病，还真是.
【在 h*h 的大作中提到】
: 难道老莫不是委婉的承认他的证明有问题了吗？不然提爱因斯坦的逻辑何在？
| C*****l
发帖数: 3211 | 18 楼主图样
莫自己写的你还能信？
张汤姆要是找了，莫在推荐信里写他非常烂，他能找到啥工作？
【在 n*l 的大作中提到】
: 笑疯了，莫的洗地文还有人跪舔的
: 首先张对莫从来一字不提，即使被问到有关导师的时候都回避，只说两人没有联系，这
: 叫君子绝交，不出恶声
: 莫则是得知张出名之后，即使没人搭理也要忙不迭的搞出这么个洗地文挂在自己网站上
: ，显然是心虚，欲盖弥彰
: 那句不屈的灵魂我看到都要吐了，神马玩意
: 张毕业后自己去联系过博后的，而且搞数学的导师帮忙联系个博后很常见，张连博后都
: 没搞上说明导师是在赶尽杀绝
| y*****s
发帖数: 2028 | | h*h
发帖数: 27852 | 20 我从来没有见到可靠的消息说莫对张很坏
问题是张没有找莫写推荐信
【在 C*****l 的大作中提到】
: 楼主图样
: 莫自己写的你还能信？
: 张汤姆要是找了，莫在推荐信里写他非常烂，他能找到啥工作？
| | | h*h
发帖数: 27852 | | C*****l
发帖数: 3211 | 22 张汤姆是君子，这种师生之间的事情，除了当事人还会有谁知道？
张汤姆是君子，自然不会对外人说道，就算有知情人，他也不会说的。
【在 h*h 的大作中提到】
: 我从来没有见到可靠的消息说莫对张很坏
: 问题是张没有找莫写推荐信
| C*****l
发帖数: 3211 | 23 教学和研究是百分之百联系在一起的。
真正研究做得好的人，极少是教学不好的。
而且你去看看评论，很多是态度方面的问题。
【在 h*h 的大作中提到】
: 说明他教学不好而已
| h*h
发帖数: 27852 | 24 学生对老师的评分，我历来不觉得客观
莫学术也许不行，但是不证明他对张苛刻
【在 C*****l 的大作中提到】
: 教学和研究是百分之百联系在一起的。
: 真正研究做得好的人，极少是教学不好的。
: 而且你去看看评论，很多是态度方面的问题。
| f**********d
发帖数: 4960 | 25 这是一篇自我辩护。
Moh是指导不了张益唐的。
every
【在 h*h 的大作中提到】
: Zhang, Yitang’s life at Purdue
: (Jan. 1985-Dec, 1991)
: T.T.Moh1
: Dr. Zhang Yitang made a major advancement to the twin prime conjecture
: as verified by Prof. H. Iwaniec, a famous number theorist. This is a
: historic result. I congratulate Dr. Zhang, Yitang.
: The concept of prime nummbers started with Greek mathematics. Euclid
: shown that there were infinitly many primes. We may view the integers as
: houses built on the integer spots on the real line, and put a light in every
: prime number houses. Then infinitely many houses are lighted (Euclidean
| f**********d
发帖数: 4960 | 26 你是不是念书念啥了，
这还不够可靠么。
【在 h*h 的大作中提到】
: 我从来没有见到可靠的消息说莫对张很坏
: 问题是张没有找莫写推荐信
| h*h
发帖数: 27852 | 27 莫学术水平不行，但是莫对张苛刻吗？
【在 f**********d 的大作中提到】
: 这是一篇自我辩护。
: Moh是指导不了张益唐的。
:
: every
| s*****r
发帖数: 11545 | 28 问个题外的事，就老张目前的成就比起劳模的如何？高出多少？ | h*h
发帖数: 27852 | 29 肯定高于老莫，高多少我无从判断
【在 s*****r 的大作中提到】
: 问个题外的事，就老张目前的成就比起劳模的如何？高出多少？
| s*****r
发帖数: 11545 | 30 老张对中国古典文学还真挺有研究的，起码乐毅报燕王书就肯定钻研过。 | | | k*******r
发帖数: 16963 | 31 陈景润不服气
【在 C*****l 的大作中提到】
: 教学和研究是百分之百联系在一起的。
: 真正研究做得好的人，极少是教学不好的。
: 而且你去看看评论，很多是态度方面的问题。
| y*z
发帖数: 3244 | 32 莫虽然是湾湾，但是却是红卫兵。
张一堂虽然是陆陆，但是却是民运。
【在 h*h 的大作中提到】
: 莫是湾湾。我对湾湾印象还可以
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