加载中…
正文 字体大小:

宇宙几何学家望月新一与ABC猜想 (故事续集)

(2013-02-05 20:59:35)
标签:

abc猜想

望月新一

证明

数学

宇宙几何学

分类: 数学物理

    前文(http://blog.sina.com.cn/s/blog_4f2d32c40102el19.html)已经报道了在数学界引起轰动的日本数学家望月新一宣布证明了ABC猜想的重大消息。本文现在把后续故事进行深度报道。

   望月在2012年8月宣布证明ABC猜想,并公布了长达500多页四篇系列论文后,立即引起数学同行的关注。但是,由于望月的理论非常创新和艰深,即使是小同行专家也都表示目前很难评价这个长篇证明的对与错。

   例如,与望月研究方向非常接近的牛津大学韩国裔数学家金明宇就表示 "There is no one but the author who is familiar with all these things," he writes. "I can't even give an expert summary of the proof because I don't understand it!",意思是世界上除了望月外没有人能熟知望月的所有工作,自己甚至都不能给出一个望月证明的专家级的概要,因为自己不能完全理解望月的证明。

    当然,也有人给出四篇文章中出现的各类问题,其中有代表性的有2012年10月 Vesselin Dimitrov and Akshay Venkatesh曾经指出望月文章中的一个错误,并被其他人认为可能会影响到望月的整个工作,其中后者是美国斯坦福大学数学教授,是很有声望的数学家。但是,望月很快就表示,前两人所提错误的确存在,但不影响证明的正确性,并承诺很快给出修改。

    果然,2012年12月,望月在自己主页贴出了自己对所有四篇文章的修改稿。主要包含27条重要的修改,其中主要是针对第四篇论文的(这非常重要,因为ABC猜想是在第四篇文章中被证明的)

    接着,2012年12月-2013年2月,望月又屡次对文章进行了修订,新修正了18处错误,其中多为打字错误。

    可以说2012年12月的那次修改是非常实质性的,但是从文字表述看,也是非常微小的调整(见后附逐条修改),比如修改了第四篇中Vesselin Dimitrov and Akshay Venkatesh曾经指出的错误,还有一些表述的小错误等。因此,认为望月自己能发现的错误基本上不存在了,剩下就要看数学界的同行们的审查了。   

    因此,本人乐观地认为望月新一的证明很可能是正确的,所缺乏的是数学界的审查认可和正式发表了。

 

附: 望月新一2012年12月对四篇宇宙几何学文章的修改

 

-------------------------------------

Inter-universal Teichmuller Theory I
------------------------------------
Slightly modified the definition of "initial \Theta-data" [i.e.,
by adding "V_{mod}^{bad}"] --- cf. Definition 3.1, (b), (c); made
corresponding adjustments throughout the paper [cf., especially,
the Introduction; Remark 4.2.1; Fig. 4.1; Definition 6.1, (v); Remark
6.12.6, (iv)]

Updated the bibliography

----------------------------------------
Inter-universal Teichmuller Theory II
-------------------------------------
Made adjustments throughout the paper to take into account the
slight modifications in [IUTchI], Definition 3.1

 

Updated the bibliography

-------------------------------------------
Inter-universal Teichmuller Theory III
--------------------------------------
Added Remark 3.9.5 concerning the "holomorphic hull".

 

Slightly modified the statement of Corollary 3.12, Theorem B, as well
as the discussion of log-volumes of the \Theta-pilot object in the
Introduction [cf. the insertion of the phrase "holomorphic hull"].

 

Slightly modified the Step (xi) of the proof of Corollary 3.12 [cf.
the discussion of "holomorphic hulls"].

 

Made adjustments throughout the paper to take into account the
slight modifications in [IUTchI], Definition 3.1

-------------------------------------------
Inter-universal Teichmuller Theory IV
-------------------------------------
Made adjustments throughout the paper to take into account the
slight modifications in [IUTchI], Definition 3.1 [cf., especially,
Remark 1.10.2]

 

Modified the Acknowledgements

 

Modified the paragraph preceding Proposition 1.1

 

Modified the statement and proof of Proposition 1.2, (i), (ii)

 

Made a slight modification to the final portion of the proof of
Proposition 1.2, (iii), (iv)

 

Made a slight modification to the statement of Proposition 1.4,
(i)

 

Modified the statement and proof of Proposition 1.4, (iii)

 

Modified the statement of Proposition 1.6

 

Corrected misprints in the proofs of Proposition 1.8, (i) (i.e.,
"17.5, (i)", "17.5, (ii)" should read "17.5, (a)", "17.5, (b)"),
(iv) (i.e., "trivial" should read "injective")

 

Modified the statement and proof of Theorem 1.10

 

Added Remarks 1.10.5, 1.10.6

 

Modified the statement and proof of Proposition 2.1

 

Corrected a misprint in the discussion immediately preceding
Corollary 2.2 (i.e., "1.4, (iii)];" should read "1.4, (iii)].")

 

Modified the statement and proof of Corollary 2.2

 

Made a slight modification to the final portion of the proof of
Corollary 2.3

 

Added Remark 2.3.1, (v)

 

Modified Remark 2.3.2

 

Modified the two paragraphs preceding Definition 3.1

 

Made slight modifications to the discussion of foundational issues
in the Abstract, the Introduction, and the first paragraph of \S 3

 

Modified the discussion of Remark 3.1.2, (ii)
---------------------------------------------------------------------------

 

0

阅读 评论 收藏 转载 喜欢 打印举报
  • 评论加载中,请稍候...
发评论

    发评论

    以上网友发言只代表其个人观点,不代表新浪网的观点或立场。

      

    新浪BLOG意见反馈留言板 电话:4006900000 提示音后按1键(按当地市话标准计费) 欢迎批评指正

    新浪简介 | About Sina | 广告服务 | 联系我们 | 招聘信息 | 网站律师 | SINA English | 会员注册 | 产品答疑

    新浪公司 版权所有