国际顶尖数学家唐纳森教授等再揭田刚学术剽窃
作者：东闲
近日伦敦皇家学院首席教授唐纳森，美国纽约石溪大学教授陈秀雄等学者联
名公开发文，揭露田刚的又一起剽窃丑闻。唐纳森是国际顶尖数学家，曾获得菲
尔兹奖、克劳福特奖、邵逸夫数学奖等众多国际数学最高奖。陈秀雄是国际著名
几何学家，曾在国际数学家大会上做过邀请报告。
文章以十页的篇幅逐条列举了田刚在长达1年多时间里多次抄袭、公然抢夺
唐纳森教授等学术成果的来龙去脉。事实清楚，证据确凿。唐纳森教授作为国际
顶尖学者，发长文公开指责田刚抄袭，说明事态已经到了非常严重的程度。
这已经不是田刚第一次被揭发学术不端了。国际顶尖数学家丘成桐，萧荫堂
等都曾多次指出田刚自从读博士起就存在剽窃、夸大等学术不端行为。
唐纳森教授等文章链接
Xiuxiong Chen, Simon Donaldson, Song Sun
September 19, 2013
http://www2.imperial.ac.uk/~skdona/KEDEVELOPMENTS-9-19-2013.PDF部分原文摘录（附中文翻译供参考）
Gang Tian has made claims to credit for these results. The purpose of
this document is to rebut these claims on the grounds of originality,
priority and correctness of the mathematical arguments. We acknowledge
Tian's many contributions to this field in the past and, partly for
this reason, we have avoided raising our objections publicly over the
last 15 months, but it seems now that this is the course we have to
take in order to document the facts. In addition, this seems to us the
responsible action to take and one we owe to our colleagues,
especially those affected by these developments.
田刚声称他也得到了这些结果。本文的目的在于通过对原创性，优先权和论证正
确性的分析驳斥田的声明。我们认可田过去在这个领域的诸多贡献，也正是由于
这个原因，在过去15个月中，我们努力避免公开提出我们的反对意见。但是事态
的发展迫使我们认识到，这是还原事件真相的必由之举。我们觉得这也是我们对
学术界必须承担的责任，特别是对受到这些事件发展影响的同行。
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In sum, our fundamental objections to Tian’s claim over the partial
C^0 estimate are:
- It seems to us highly improbable that Tian independently came on the
proof, involving exactly the same ideas, in the short time interval
(roughly April-June 2012) in question. Here we have in mind that, as
noted above, the techniques which underpin the proof have been
available for ten years or more.
- Even given that it is not impossible that such a coincidence occurred,
we have clear priority in the presentation of both outline and
detailed proofs.
- Even after 15 months from the appearance of Donaldson and Sun's
paper [2] to the date of this writing, Tian has not produced a
convincing complete proof of this result.
总而言之，我们对于田刚声称得到偏C^0估计的反对意见如下：
- 我们认为田独立得到这个证明几乎不可能，他用到和我们同样的思想，而且是
在很短的时间内（大约在2013年4月至6月期间）。要知道，如上所述，我们所用
到的证明技巧已经存在了10年以上。
- 即使这种巧合并非完全不可能，无论在证明的概述和还是细节的公开我们都明
显占先。
- 即使在唐纳森和孙的文章[2]公开15个月以后，田都没有对这一结果给出一个
完整的证明。
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Our fundamental objections to Tian's claims with respect to Yau's
conjecture are:
- that we feel that there is no evidence that Tian was in possession
of anything approaching a complete proof at the time of his
announcement [6] in Stony Brook;
- that both arXiv versions [11], [12] of his paper have serious gaps
and mistakes;
- that, insofar as these gaps and mistakes have been partially filled
and corrected (in comparing [11], [12], [13]), many of the changes and
additions made reproduce ideas and techniques that we had previously
introduced in our publicly available work [7], [8], [9], 10], without
any kind of acknowledgement. We will not attempt to take up every
single gap and mistake that we see in Tian's proposed proofs
(including the necessity of checking carefully the relevant results of
Jeffres, Mazzeo and Rubinstein, noted above), but concentrate on three
points in the subsections 3.1,3.2,3.3 below.
我们对于田所声称的关于丘猜想的证明的反驳如下：
- 我们认为没有任何证据表明，田在石溪报告[6]公开声明时知晓任何可以给出
完全证明的途径。
- 他的arXiv文章[11], [12]存在严重的漏洞和错误
- 目前这些错漏部分的得到了修补（比较田的文章[11], [12], [13]），许多这
些修改和增补仿造了我们之前公开的文章[7], [8], [9]中的想法和技巧，
并无任何的出处说明。我们不试图指出田声称的证明中的每一个漏洞和错误（包
括仔细验证Jeffres, Mazzeo and Rubinstein等人相关结果的必要性）， 我们
将3.1, 3.2, 3,3小节中专注讨论三个要点。
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These assertions are blatant copying without attribution. This is
almost half a year since the appearance of our third paper [10], in
which the detailed proof of the reductivity is provided, based on the
uniqueness theorems proved by Berndtsson and
Berman-Boucksom-Essydieux-Guedj-Zeriahi, and the technical difficulty
in extending the usual proof of the Matsushima theorem is pointed out.
（田的文章中的）这些结论是明显的直接拷贝，而没有任何的指明出处。这已经
是我们第三篇文章[10]公开半年以后，其中给出了可约性的详细证明，基于
Berndtsson 和 Berman-Boucksom-Essydieux-Guedj-Zeriahi等人的唯一性定理。
并且指出了推广Matsushima 定理通常证明的技术上的困难。
