h*h
发帖数: 27852 | 1 【 以下文字转载自 Military 讨论区 】
发信人: hsh (nidaye), 信区: Military
标 题: 莫宗坚谈张益唐：张没有找莫要推荐信
发信站: BBS 未名空间站 (Thu Jun 2 15:59:38 2016, 美东)
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 | y****e
发帖数: 27 | 2 自己的工作成果就是最好的推荐信。张没出成果时，需要莫推荐的日子，他在哪里啊？ | m***o
发帖数: 1367 | 3 这个人的英文写得相当的差，难道他的paper也写得这么前言不搭后语？ | B****n
发帖数: 11290 | 4 有些人平時寫的英文普通 可是寫論文還是寫得不錯的
這是因為論文寫法用語都很制式 而且通常會打磨很多次 不斷的精煉
【在 m***o 的大作中提到】
: 这个人的英文写得相当的差，难道他的paper也写得这么前言不搭后语？
|
|
