f******h
发帖数: 104 | 1 这真的假的？哪个大牛给鉴定一下?
First letter:
-------------------------
成桐兄：
钟家庆自Austin回Harvard后与我谈及他Austin一行见闻。其中一事使我甚为困
扰。此事乃关乎你学生田刚在Kahler-Einstein Metric 问题上之结果。钟家庆对此
问题甚感兴趣。他来Harvard后曾阅读我在Columbia所讲之文章，即我托他带给你的
那篇。他在Austin时向田刚及曹怀东问及田刚Kahler-Einstein Metric的结果。他
主要是从曹怀东处大约获知田刚所寄Kahler-Einstein Metric文章之方法及结果。
他回来后将所知一一转告我。因他Austin之行短暂，所知自多有未尽之处。单从据
他所拿到的部分看，除田刚自信应该有办法将来可做出之结果不算外，田刚确实做
到的部分中他所用方法与我在Columbia讲的基本上一样，结果也未出我所能做出的
范围。该方法我四月在Columbia及Maryland并六月在巴黎都曾在演讲中讲述。我四
月在Columbia讲时你和田刚及其他数位你的学生均在座。若田刚有新方法，当然极
好。但若只将在Columbia拿到我讲的方法改头换面据为己有，则事关业务道德，我
认为事态严重，不容坐视。你在Harvard与我说及田刚结果时，说及田刚所做已将问
题的二维情形全解决，在高维也大有突破，远远超出我所做的。我从钟家庆处拿到
田刚之方法与结果，乃间接辗转相闻，事易失其实。希望田刚只将我的方法改头换
面据为己有之事并非属实。我寄这信谨防万一，禁于未然之前。此事尚希垂注。
荫堂
一九八六年十月二十五日
-------------------
Second letter
---------------------
成桐兄：
前几天英语回信念卒守就，怀有未尽，在此复略言一二。闻说你学生之文章早已寄
出发表，若属实，则做法极不寻常。相信文章中提及我方法，仅言"萧亦有一方法，
但不能用于任何例上"之类的话，若是如此，则作法更不寻常。就是素不相识的数学
家，在columbia听我讲方法之后有些新想法，就是不想将新想法告诉我或根本不想
我知他有新想法，也会问我文章寄出没有，有没有例子已验算出。相信不会马上写
好一篇相若方法的文章背着赶快发表，寄出发表后也不通知或寄下一份。
其实，我在本年初做Kahler-Einstein metric 的主要原因是要在Mok的会议讲一些
东西，所以选些东西来做。且王必敏及Kalka在Harvard，我做问题时一边做一边在
每周的seminar讲，制造些多复变的活动。做到五月后Kalka及王必敏都离开，我就
没有再做。
我的方法有两部分。第一部分$sup\phi$, $-inf\phi$, $log\int e^{\alpha\phi}
$, $log\int e^{-\alpha\phi-t\phi+F}$, $\int\phi$, $-\int\phi e^{-t\phi+F
}$等价的结果是约九年前做的。这些结果当时已写在我手写的笔记中，我称之为"r
eflection method。"约九年前我已将笔记一份寄给你，我文章中第一部分只是从该
笔记中抄出来而已。
第二部分用到几个成份：$\phi$差不多plurisubharmonic, restriction to a com
plex curve, log singularity of Green's function of curve, finite symmetr
y, 并关于arithmetic mean, geometric mean一类不等式（我用$xy\leq xlogx+e^
{y-1}$乃该类不等式其中之一）。用这几成份有很多不同方法，表面看来不一样，
其实本质相同，能用到的例也一样。例如可用Moser本来方式写出。我选择我用的写
法是觉得讲解时明显些而已。你说你学生的方法不同，我相信只是用同样成份而写
起来不同而已。
我未去columbia前已在验算一些例。验算只是数一些整数及比较一些整数而已。数
数目及数cases很容易有错失。因为时间关系，我怕我有数错的地方，所以在colum
bia讲时只说正在验算例子。我知道我的方法可用的例子极有限，我不想讲了之后，
后来发觉自己数错了数目或数漏了一些cases。有些人是光讲了然后以后设法补上，
后来补不上就算了。因原则关系我不这样做。
回Harvard后我在每周的Seminar上当众数了一下Fermat cubic，大家觉得可以，我
才放心没有验算错。回Harvard后两星期内，有Fermat surface例的文章已全打好，
发给来Seminar的人。我在六月初要去欧洲，为了欧洲的Lecture我将打好的文章重
看加上$\cal{P}_2$上blow up 3点的例。五月后文章就一直搁置，没有再做。验算
例子只是一个简单过程，极之routine，主要的是方法及技巧。那时我叫学生们看看
有没有其他的例，学生们也不屑花时间去验算，认为太routine没意思。
我初出道时，经历了一相类的事。一次我与几个数学家在私人讨论中说出我解决一
问题的方法及技巧的重点。一个法国数学家马上用Bourbaki形式写出我的方法，交
由他一个编辑朋友在一份很快可以印出的杂志发表了。后来我写好我的方法发表时
，他的一朋友翻阅（可能全不知情），说问题已有更好方法解决了，将我文章压着
。最后我直接与编辑说明原委，文章才可印出。因为我是在私人讨论中说出我的方
法，很难追究。我的朋友Trautmann当时在场，他觉得很不公平，自己去将那法国数
学家大骂一顿。那法国数学家辩说我方法细节未写出而他的方法与我的并不全一样
。对一个不熟识该问题的人来看，表面上两方法有不同之处，但有识之士一看就知
基本上是同一样东西，只写法有别矣。我与那法国数学家只泛泛之交，因利忘义，
未足为怪，只是我自己经一事长一智，以后见到他小心点就是了。但这种事发生在
好朋友中，则令人心寒。
关于Weil-Petersson metric曲率之文章，其实我看此问题只是为Stoll祝寿会上要
说些东西。我没有办法将问题解决，只是用了附加条件后做到些不大满意的结果。
因为你说你学生已将问题全解决，我才好奇问你要一份看看怎样做，并不是要争谁
先做出结果。Royden告诉我他懂得如何做，就是我不大明白，也在文章的引言上写
Royden说已做出结果，述出Royden说他用的方法，在文章之后的文献上写Royden,
oral communication,detailed paper in preparation。你学生的文章困难是概念
上基本的错误，我仔细看他的文章，设法帮他补救，也无能为力。说成"略有小错，
则不敢发表"似甚不贴切。你学生有方法可解决Weil-Petersson metric曲率的问题
，应鼓励他马上发表。
我的Kahler-Eingtein metric及finite symmetry的结果并非什么了不起的结果。此
结果，就是不算我在Boston区Seminar的演讲,我也曾在几处公开讲出。要在听过我
方法后背着赶紧马上发表相若方法的文章，不见得能讨到什么便宜。就是能讨到便
宜，也不见得值得上所付的代价。所利不能乐其所伤，所获不能补其所亡。缔交十
余载，数度携手，尚且如是，不胜伤痛失望，感叹不已。
荫堂
一九八六年十一月十五日
-----------------------
Third letter
--------------------
Dear Shing-Tung:
Thank you for your letter of November 6, 1986. In response to your lette
r I would like to bring up a few points.
1. In my talk in Columbia I presented my method of proving the existence
of Kahler-Einstein metrics on compact Kahler manifolds with positive an
ticanonical line bundle and a suitable finite group of symmetry. I menti
oned at the end that I was still checking some concrete examples. Right
after my return to Harvard I verified the case of the Fermat cubic surfa
ce. Within two weeks after the Columbia Conference a typed manuxxxx wa
s available. Morris Kalka and Pit-Mann Wong had copies at that time. Whe
n I looked over my manuxxxx to prepare my talk in Paris in June I adde
d the examples of blowing up three point in $\cal{P}_2$ and higher-dimen
sional Fermat hypersurfaces. All those examples were verified before las
t summer. In any case what is important is the method. Checking concrete
examples is only the simple task of counting the degrees of certain cur
ves and the number of points of the curves belonging to the same orbit.
2. Concerning your student's independent derivation of the equivalence o
f $sup\phi$ and $-inf\phi$, I would like to point out that the equivalen
ce of bounds for $sup_M\phi$, $-inf_M\phi$, $\int\phi$, $-\int\phi e^{-t
\phi+F}$, $log\int e^{-\alpha\phi-t\phi+F}$, and $log\int c^{\alpha\phi}
$ was already in the handwritten notes entitled "Reflection Methods" whi
ch I sent you about nine years ago. That was way before your student cam
e to the Unites States. Even a few year later you mentioned to me that y
ou were still keeping those notes. Unless in your discussions with your
students you were deliberately keeping back from them what you already k
new, I do not see how independent your student's derivation can be.
3. Since I have not seen your student's manuxxxx, it is impossible for
me to determine exactly how much your student's method is similar to or
different from the one I presented at the Columbia Conference. However,
from the inxxxxation that I have, it seems to me that his method is ess
entially a rexxxxulation using the equivalent bound of $\int e^{-\alpha\
phi}$.
It is against my nature to argue over priorities (and as a matter of fact to
argue over anything). I always pride myself on being fair and careful in
such matters. In this case I was rather upset to learn what seems to be
somebody claiming as his own a rexxxxulation of a method of mine already
presented in public lectures. Since according to a number of people your
student’s manuxxxx is available, it seems that the easiest way to clarify
this is for me to have a look at a copy of this manuxxxx.
Best regard,
Yum-Tong Siu | B****n
发帖数: 11290 | 2 無能力分辨真假 只能說如果是假的 那作者也是牛人阿
【在 f******h 的大作中提到】
: 这真的假的？哪个大牛给鉴定一下?
: First letter:
: -------------------------
: 成桐兄：
: 钟家庆自Austin回Harvard后与我谈及他Austin一行见闻。其中一事使我甚为困
: 扰。此事乃关乎你学生田刚在Kahler-Einstein Metric 问题上之结果。钟家庆对此
: 问题甚感兴趣。他来Harvard后曾阅读我在Columbia所讲之文章，即我托他带给你的
: 那篇。他在Austin时向田刚及曹怀东问及田刚Kahler-Einstein Metric的结果。他
: 主要是从曹怀东处大约获知田刚所寄Kahler-Einstein Metric文章之方法及结果。
: 他回来后将所知一一转告我。因他Austin之行短暂，所知自多有未尽之处。单从据
| w******o
发帖数: 726 | 3 做数学做到这份上就别做了，干点挣钱的比争这个有意思多了。 | F*******n
发帖数: 8 | 4 The following is copied from p.622 of Siu's 1988 Annals paper "The Existence
of Kahler-Einstein...". Siu is really angry at Tian's plagiarism.
Added after submission of paper. I presented the results and methods of this
paper in the Geometry and Analysis Conference at Columbia University in
April, 1986. G. Tian in August, 1986 wrote a paper "On Kihler-Einstein
metrics on certain Kihler manifolds with cl(M) > 0" (Invent. Math. 89 (1987)
, 225-246) in which he constructed Kdhler-Einstein metrics for Fermat
hypersurfaces of degree m and m + 1 in Pm+1. His paper used the same idea of
restriction to a complex curve, the logarithmic singularity of the Green's
kernel for a complex curve, and the use of symmetry to reduce the effective
area of the complex curve. He used the integral of the exponential of a
negative multiple of (9 instead of the supremum norm of 'p for the zero-th
order a priori estimate of Ap. Though a priori estimates of the supremum
norm of (9 and the integral of the exponential of a suitable negative
multiple of 'p are equivalent (see Proposition (4.3)), the use of the latter
has the advantage of avoiding the use of the lower bound of the bisectional
curvature and making the verification of the symmetry condition easier. He
also used L2 estimates of d in his paper. Actually the use of the L2
estimates of d is unnecessary. We give below the formulation of the argument
of this paper using the integral of the exponential of a suitable negative
multiple of 'p instead of the supremum norm of 'p and apply it to the case
of Fermat hypersurfaces of degree m + 1 in Pmi+. (Tian obtained also the
case of degree m from the same inequality concerning the volume of a complex
curve and the number of group elements, because the normalization constant
1/2wT which we derived in (6.1) for the Green's kernel was taken to be 1/4wT
in his computation.) | v*********n
发帖数: 573 | 5 田院士曰：“窃idea不算偷”。
The following is copied from p.622 of Siu's 1988 Annals paper "The Existence
of Kahler-Einstein...". Siu is really angry at Tian's plagiarism.
Added after submission of paper. I presented the results and methods of this
paper in the Geometry and Analysis Conference at Columbia University in
April, 1986. G. Tian in August, 1986 wrote a paper "On Kihler-Einstein
metrics on certain Kihler manifolds with cl(M) > 0" (Invent. Math. 89 (1987)
, 225-246) in which he constructed Kdhler-Einstein metrics for Fermat
hypersurfaces of degree m and m + 1 in Pm+1. His paper used the same idea of
restriction to a complex curve, the logarithmic singularity of the Green's
kernel for a complex curve, and the use of symmetry to reduce the effective
area of the complex curve. He used the integral of the exponential of a
negative multiple of (9 instead of the supremum norm of 'p for the zero-th
order a priori estimate of Ap. Though a priori estimates of the supremum
norm of (9 and the integral of the exponential of a suitable negative
multiple of 'p are equivalent (see Proposition (4.3)), the use of the latter
has the advantage of avoiding the use of the lower bound of the bisectional
curvature and making the verification of the symmetry condition easier. He
also used L2 estimates of d in his paper. Actually the use of the L2
estimates of d is unnecessary. We give below the formulation of the argument
of this paper using the integral of the exponential of a suitable negative
multiple of 'p instead of the supremum norm of 'p and apply it to the case
of Fermat hypersurfaces of degree m + 1 in Pmi+. (Tian obtained also the
case of degree m from the same inequality concerning the volume of a complex
curve and the number of group elements, because the normalization constant
1/2wT which we derived in (6.1) for the Green's kernel was taken to be 1/4wT
in his computation.)
【在 F*******n 的大作中提到】
: The following is copied from p.622 of Siu's 1988 Annals paper "The Existence
: of Kahler-Einstein...". Siu is really angry at Tian's plagiarism.
: Added after submission of paper. I presented the results and methods of this
: paper in the Geometry and Analysis Conference at Columbia University in
: April, 1986. G. Tian in August, 1986 wrote a paper "On Kihler-Einstein
: metrics on certain Kihler manifolds with cl(M) > 0" (Invent. Math. 89 (1987)
: , 225-246) in which he constructed Kdhler-Einstein metrics for Fermat
: hypersurfaces of degree m and m + 1 in Pm+1. His paper used the same idea of
: restriction to a complex curve, the logarithmic singularity of the Green's
: kernel for a complex curve, and the use of symmetry to reduce the effective
| v*********n
发帖数: 573 | 6 http://www1.bbsland.com/education/messages/240997.html
有人分析了田的工作，看来这厮是惯犯:)
yautian's comments on Tian's work are fair, but here are some more
information about these works:
The n=2 case of the KE metric of positive first Chern class was developed
from Tian's thesis by using a trick first found by Siu. Siu gave lectures at
Columbia and other occasions and Tian was in the audience. After that Tian
wrote up a
paper which became part of his thesis. Siu was very angry, and said that
Tian
had moral problem. He wrote two emotional letters to Yau asking for a copy
of
Tian's paper. But Tian did not even show Siu the paper before it was
published in Inventiones which was very unsual. Siu published his paper in
Annals of Math with remarks about the history of the work and the lectures
he
gave on various occasions on which Tian was in audience. Tian got offer from
Princeton when he graduated with Yau's strong recommendation. But he did not
get NSF grant, and after Siu told him the story, J. Kohn of Princeton asked
Tian to withdraw the offer from Princeton because he thought they made a
mistake to offer him. Even now Siu still claims that Tian's work on the n=2
case has serious gap, so incomplete. In fact Nadel gave simple proofs of
most
of the n=2 cases, except when 6 points are blown-up which may have problem.
About his work on Gromov-Witten invariants. As yautian said, Ruan needed
some
analysis to define such invariants on semipositive symplectic manfolds, but
it was known that the analysis is more or less the same as in the gauge
theory case which Taubes had developed. In fact GW theory was an analogue of
Gauge theory in some sense. Tian basically copied Taubes' analysis, but
still
missed some key point: Taubes only needs to consider 1 bubbling which is
enough for gauge theory, but the more bubbling in the Gromov-Witten cases
should be considered to define invariants. This is why Taubes insisted on
that Tian should not be considered for Veblen prize based on his work on
Gromov-Witten which he considered trivial.
Tian's work on calibrated geometry and gauge theory has been well-known for
having serious gap as Yau has beeen criticising him publicly for this.
About Tian's recent work with Qing. Huisken-Yau proved existence and
uniqueness of the foliation which were enough for their applications in
general
relativity. The extension of uniqueness on slightly larger reason was
mentioned in their paper but not important for application. Qing-Tian
extended the region, but in their first version wrote that "the remaining
challenge is the uniqueness, and we prove the uniqueness in this paper". So
they want to eat all credit of uniqueness based on not so interesing
generalization, this is why Yau was so angry. After Yau accused him,
Qing-Tian revised their writing. In fact Tian did similar things before,
just
this time Yau caught him seriously.
When mentioning Fields medal, one member of the Fields selection committee
said that Tian was out in the first round. Note that Manin was the committee
chair. This should have nothing to do with Yau. I guess it was Tian himself
created the rumor that he missed one vote from Kontsevich.
********************************************************************
Some comments on Tian's work by yautian
Tian's most important work is about the Kahler-Eienstein metric on the
compact complex manifold with positive chern class. Basiclly, he followed
Yau's idea. (please don't argue about it, I just tell a truth). Tianadmited
in his published paper that it was Yau introduced him into this field and
shared with him the important idea that the existence of the K-E metric
should relate to some stability in algebraic geometry. After more than 10
years, Tian got some important results, (including the solution for the n=2
case which brought him Waterman prize). But, the most important equivalence
between the existence and stability still COMPLETELY OPEN. Tian's lastest
contribution to this problem was 1996, 9 years have past.
The second important work of Tian Gang is about Gromov-Witten. Basically,
there are two approches to this problem. One is algebraic geometry, started
by Manin-Kontesevic. the other way is differential geometry, started by
Ruan,YongBin. Ruan already realized there was away to define invariant, and
wrote one paper. But Ruan is not good at analysis, he asked Tian for help.
This was the famous Ruan-Tian paper published on 1995 JDG. After that Tian
continued to do important work on Gromov-Witten theory. This time, his
collaborator was Li Jun, who is a famous algebraic geometer. Their theory
was
called "Li-Tian's work. It is not was Tian's single work. Their
collaboration
was 50%-50%, nobody played the dominent role.
After that, Tian never did Grmov-Witten theory again. But Li Jun write 2
very
important long papers, made a fundamental contribution to the algebraic-
geomet
ry understanding of Gromov-Witten theory.
Tian's third important work was his 2000 annals paper--gauge theory and
calibrated geometry. But this worked was inspired by Donaldson-Thomas theory,
and borrowed heavilly analysis technique from Fanghua Lin's 2001 annals
paper
about harmonic map.
"No works initiaed from Tian, no work ended by Tian". It is a correct
comment. | f******h
发帖数: 104 | 7 支持，田刚不去当中国的克格勃真是可惜了。
【在 w******o 的大作中提到】
: 做数学做到这份上就别做了，干点挣钱的比争这个有意思多了。
| w******o
发帖数: 726 | 8 你误解我了，我不是说田刚，是说老萧，唧唧歪歪的，没有意思。丘成统嫉妒自己的学
生，令人不齿。 | f******h
发帖数: 104 | 9 被人剽窃的感觉应该是很不爽的~~。说点别的吧。
今年好像是几何突破年啊，Open了47年的Willmore猜想
和Open了42年的Lawson猜想相继被Neves 和Brendle解决，
这两人看来下届菲尔兹奖必上一人了。
【在 w******o 的大作中提到】
: 你误解我了，我不是说田刚，是说老萧，唧唧歪歪的，没有意思。丘成统嫉妒自己的学
: 生，令人不齿。
| w**********r
发帖数: 128 | 10 I just searched Simon Brendle's homepage, it looks like the proof of the
Lawson conjecture is only 10 pages? Both Neves and Brendle are incredibly
strong. | | | f******h
发帖数: 104 | 11 查了一下Neves75年的，不过解决Willmore猜想的95页长文是与Marques合作的，感觉14
年拿菲尔兹不太可能。有点像10年时候的Hacon。他们的文章似乎把Brendle的Lawson猜
想和球拼挤猜想给比下去了。参考Schoen当年都没有拿到菲尔兹奖，看来Brendle还需
要继续奋斗，拼一下18年的菲尔兹奖。
【在 w**********r 的大作中提到】
: I just searched Simon Brendle's homepage, it looks like the proof of the
: Lawson conjecture is only 10 pages? Both Neves and Brendle are incredibly
: strong.
| l********e
发帖数: 3632 | 12 10页不算太短啦。
当年Perelman证明Soul Conj的文章也只有4页。
有一种厉害的人很多时候就是能看见很多常人看不见的东西，我们看到他们的文章之后
才会觉得，原来证明也不是那么难。
【在 w**********r 的大作中提到】
: I just searched Simon Brendle's homepage, it looks like the proof of the
: Lawson conjecture is only 10 pages? Both Neves and Brendle are incredibly
: strong.
| a****a
发帖数: 5763 | 13 关键是往哪里看？
有些人只看胸，有些人看屁股
比较幼稚的是只看脸的
【在 l********e 的大作中提到】
: 10页不算太短啦。
: 当年Perelman证明Soul Conj的文章也只有4页。
: 有一种厉害的人很多时候就是能看见很多常人看不见的东西，我们看到他们的文章之后
: 才会觉得，原来证明也不是那么难。
| f******h
发帖数: 104 | 14 几篇精短的博士论文
详见
http://mathoverflow.net/questions/54775/what-is-the-shortest-ph
http://meta.mathoverflow.net/discussion/946/shortest-phd-thesis
Burt Totaro
Milnor K-theory is the simplest part of algebraic K-theory, Ph.D. thesis,
University of California, Berkeley, 1989; K-Theory 6 (1992), 177-189.
Martens, Henrik H.
A NEW PROOF OF TORELLI'S THEOREM. Thesis (Ph.D.)–New York University. 1962.
12 pp, ProQuest LLC, Thesis.
A new proof of Torelli's theorem. Ann. of Math. (2) 78 1963 107–111.
David Rector
An Unstable Adams Spectral Sequence, (MIT 1966) is 9 pages, Thesis Math 1966
Ph.D.
http://library.mit.edu/item/000612341
An unstable Adams spectral sequence. Topology 5 1966 343–346.
【在 l********e 的大作中提到】
: 10页不算太短啦。
: 当年Perelman证明Soul Conj的文章也只有4页。
: 有一种厉害的人很多时候就是能看见很多常人看不见的东西，我们看到他们的文章之后
: 才会觉得，原来证明也不是那么难。
| F*******n
发帖数: 8 | 15 ◇◇新语丝(www.xys.org)(xys.dxiong.com)(xys.3322.org)(xys.xlogit.com)◇◇
田刚是一个非常不诚实的人
加州大学Santa Cruz分校数学教授Andrey Todorov信件（译文）
关于卡拉比－丘流形模空间无阻碍性的证明历史，1980年 Bogomolov提出了
证明典则类为零的簇的模空间无阻碍性的方法。他的论证非常漂亮，可是只对超
凯勒情形有效。我从1986年开始研究卡拉比－丘流形模空间无阻碍性的问题。同
年我在MPI公布了预印本。1986年12月，我收到田刚的来信，说他也发现了同样
的公式，就是现在所称的Tian- Todorov公式。
1992年我到普林斯顿访问，遇到Nadal（萧荫堂的一个学生）。我从他那里
得知，田刚是一个非常不诚实的人。他告诉我，田刚在写自己的那篇卡拉比－丘
流形模空间之前，就知道了我所发表的预印本。Nadal告诉我他亲眼看到田刚在
哈佛的时候，研读我的预印本。事实上，我的文章中包含了更多的结果。
Kazdan教授曾问我对于田刚的看法。我告诉他，田刚还算是个有能力的数学
家。可是Kazdan却告诉我，田刚一生中从来没有证明过哪怕是一个未知的或不在
预料之中的定理。
Andrey Todorov
（1）
丘先生，您好！
得知您因为田刚而陷入麻烦之中，令我颇为忧虑。在这件事上，我可说是局
外人，不但因为我在数学上的研究领域有所不同，也因为讨论集中在中国人的圈
子里。
不过，我还是想告诉您，我与田刚的交往经历也是非常的糟糕，这绝不仅仅
是我个人的观点，他在与我合作的过程中非常的不守诚信。
我指的是他与V的关于四维流形上度量模空间的工作。田刚在石溪分校的时
候，我想大约是92-93年，他向我建议合作研究这类问题，因为这类似于与爱因
斯坦度量的模空间，所以我答应下来。在那期间，我们也各自忙其他的研究工作，
大概一年或两年后，我把解决问题的方法向他讲解了一遍。他同意我的想法，于
是我们开始着手写文章。
田刚其实对这个问题一点贡献也没有，而且他也根本不想写这篇文章，而只
是想把他的名字放到最后写成的文章上。我当然拒绝了他的无理要求，直到他答
应写其中的几章。后来让我震惊的是，田刚和V把他们的文章放到了预印本网站
arXiv上。其中几乎所有的想法都是我告诉田刚的，有的只不过稍微做了改动，
而且只字未提是从我这里得到这些想法的。他从来没有告诉过我，他与V正在合
作研究，而是假惺惺的继续我们的合作，剽窃我的思想。
为了维护我个人的权益，我决定找出我积累下来的研究笔记，把研究成果写
成一篇文章，其中的结果比田刚他们的要广泛的多。这篇文章也已经放到预印本
网站了。
（2）
丘先生，您好！
非常感谢您寄给我有关田刚的信件。在这件事上，我毫无保留的支持您。我
在90年代初时，与田刚讨论黎曼几何的问题，我惊讶的发现他对这个领域的了解
极度贫乏。甚至连一些基本的东西他也不懂。在我们的合作中，他只是做了一个
很小的评论（对我的一个想法提出了一点异议）。所以，我总是以为，如果要评
价田刚是一流数学家，那么只能是针对他在其他我不是专家的领域的工作。您在
给Jeff的信中的评价支持了我的观点，田刚决不是一流的数学家。
The history about the proof that the moduli space of CY manifolds is
unobstructed. In 1980 Bogomolov proposed a method how to prove that
the moduli space of varieties with canonical class zero is unobstructed.
His arguments are beautiful and work only for Hyper-Kahler. I started
to work on the problem that the moduli space of CY manifolds is
unobstructed in 1986. The same year I published a preprint in MPI. In
December of 1986 I received a letter from Tian stating that he had
discovered the same formula, which now is called Tian-Todorov Lemma.
In 1992 during my visit to Princeton I met Nadal (a student of
Yum-Tung). He explained me that Tian is very dishonest person. He told
me that Tian knew about my preprint before he wrote the paper about
the moduli of CY. Nadal told me that he saw Tian to study my preprint
in Harvard.
My paper contains more results. Unfortunately Cumrum Vafa and his
authors called Tian gauge one of my observations in the paper. I told
Cumrum about it and he put the reference to my MPI preprint of 1986 in
his paper with Bershadky, Cecotti and Ouguri.
Once Kazhdan asked me what I think about Tian. I told him that I think
that he is a capable mathematician. Then Kazdan told me that Tian
never in his life proved any Theorem that was not known or expected.
I found out that Robert Dijkgraaf refereed to my preprint of 1986 in
his Les Houses lectures on duality.
(XYS20060823)
◇◇新语丝(www.xys.org)(xys.dxiong.com)(xys.3322.org)(xys.xlogit.com)◇◇ | r**q
发帖数: 251 | 16 brendle好像说自己用很多方法尝试过很久才找到合适的途径的, 这短文章估计包含了
这种牛人的很长时间的思考
【在 l********e 的大作中提到】
: 10页不算太短啦。
: 当年Perelman证明Soul Conj的文章也只有4页。
: 有一种厉害的人很多时候就是能看见很多常人看不见的东西，我们看到他们的文章之后
: 才会觉得，原来证明也不是那么难。
| f******h
发帖数: 104 | 17 牛人有很多不同的类型，有的文章很少，比如L. Lafforgue。还有一些文章奇多的数学
家，却不怎么出名的，比如Tata研究所的Indranil Biswas (born 1964)，已经发表的
文章有289篇。还是做纯数的，额的神啊~~
【在 r**q 的大作中提到】
: brendle好像说自己用很多方法尝试过很久才找到合适的途径的, 这短文章估计包含了
: 这种牛人的很长时间的思考
| N***m
发帖数: 4460 | 18 和bbs关税一个道理。
【在 f******h 的大作中提到】
: 牛人有很多不同的类型，有的文章很少，比如L. Lafforgue。还有一些文章奇多的数学
: 家，却不怎么出名的，比如Tata研究所的Indranil Biswas (born 1964)，已经发表的
: 文章有289篇。还是做纯数的，额的神啊~~
| g*****l
发帖数: 424 | 19 Brendle 神人啊，81年的，汗
【在 f******h 的大作中提到】
: 被人剽窃的感觉应该是很不爽的~~。说点别的吧。
: 今年好像是几何突破年啊，Open了47年的Willmore猜想
: 和Open了42年的Lawson猜想相继被Neves 和Brendle解决，
: 这两人看来下届菲尔兹奖必上一人了。
| f******h
发帖数: 104 | 20 Brendle的文章被Acta接受了
【在 r**q 的大作中提到】
: brendle好像说自己用很多方法尝试过很久才找到合适的途径的, 这短文章估计包含了
: 这种牛人的很长时间的思考
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