陶哲轩评张益唐的论文：正确性还待证实

“手稿的基本正确性尚未得到证实。论文中存在许多印刷错误和技术问题（主要围绕第11节和第12节），这些问题阻碍了验证过程，我已将这些问题转发给益唐。”

张益唐的关于朗道-希格尔的论文出来后，吸引了大众的关注。数学家们自然也关注。

公众更关注张益唐的数学家同行如何看待。

其中，陶哲轩如何评价张益唐先生的论文更是令人期待。想当年，张益唐先生关于孪生素数的猜想出来后，主要是陶哲轩等人在积极改进素数间距。

11月14日，陶哲轩给出了他对张益唐新论文的评论：

Terence Tao on 14 November, 2022 at 8:27 am

At this point the essential correctness of the manuscript is unconfirmed. There are a number of misprints and technical issues in the paper (mostly centering around Sections 11 and 12) that are hindering the verification process and which I have forwarded to Yitang in order to request clarification. For instance, there are references to non-existent equations (8.25) and (8.26) on pages 64, 65, 67, (10.) on page 67, (15.) on pages 98, 99, “(4) and (4)” on pages 67 and 69, “(5) and (5)” on page 63, and (A) and (14) on page 109; there also appears to be a reference missing completely just before Lemma 12.3 on page 70 (as well as the aforementioned reference to (A) on page 109), and the function that appears from page 96 onwards is never defined in the paper. As a consequence, several steps in the manuscript currently have no valid justification provided. It is possible that these (as well as some more serious issues) can be corrected, but it will likely take some time before the process resolves (in particular, I would not want to pressure Yitang to upload a hastily edited revision of the manuscript instead of a carefully proofread one), and so patience is advised.

陶哲轩的观点主要是，张益唐原文有些打印错误和技术问题。（机器）翻译如下：

此时，手稿的基本正确性尚未得到证实。论文中存在许多印刷错误和技术问题（主要围绕第11节和第12节），这些问题阻碍了验证过程，我已将这些问题转发给益唐，以请求澄清。例如，第64页、第65页、第67页（10.）、第98页、第99页（15.）、第67和69页“（4）和（4）”、第63页“（5）和（5）”以及第109页（A）和（14）中提到了不存在的方程式（8.25）和8.26）；在第70页的引理12.3之前，似乎还完全缺失了一个参考（以及前面提到的第109页（a）），从第96页开始出现的函数 从未在论文中定义。因此，手稿中的几个步骤目前没有提供有效的理由。这些问题（以及一些更严重的问题）有可能得到纠正，但这一过程很可能需要一段时间才能解决（特别是，我不想向益唐施压，要求其上传一份仓促编辑的修订稿，而不是一份仔细校对的修订稿），因此建议耐心等待.

另有匿名读者评论陶哲轩的观点：评得好！

Anonymous on 15 November, 2022 at 5:46 am

❝

“in particular, I would not want to pressure Yitang to upload a hastily edited revision of the manuscript instead of a carefully proofread one.” Very well said. Which math publication might seek for his carefully ‘proofread’ one? Is there ANY ? Or is it too early to tell still?

❞

实际上，张益唐在约10天前北大的演讲上，已经提到还需要补充很多细节。容易理解，张益唐先生以一人之力搏击大问题，需要特别多的精力。

怀尔斯证明费马大定理的论文刚出来不久也有数学家发现较大的问题。但怀尔斯最终与其学生泰勒一起弥补了漏洞。

让我们期待完美的结果。

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