As revolves the argument of would-be Riemann hypothesis to settle down finally, «Math Yearly journal» editorial department in receiving Lu Zhou after „ultra elliptic curve analytic method” the contribution of paper, to the Lu Zhou mailbox sent in the mail in the shortest time. 随着围绕准黎曼猜想的争论终于尘埃落定,《数学年刊》编辑部在收到了陆舟的关于“超椭圆曲线分析法”论文的投稿之后,在最短时间内向陆舟的邮箱发来了邮件。 In the mail, " Math Yearly journal » editorial department first expressed to him that paper that previously he submitted a piece of writing had adopted „peer review” successfully the link, at the same time «Math Yearly journal» before this month ended, is „the would-be Riemann hypothesis” the proof publishes an issue of special issue alone, for publishing the paper of his more than 30 pages of papers, as well as uses „ultra oval analytic method” this unique mathematical instrument. 在邮件中,《数学年刊》编辑部首先向他表示了先前他投稿的那篇论文已经成功通过了“同行评审”的环节,与此同时《数学年刊》将在本月结束之前,为“准黎曼猜想”的证明单独刊发一期特刊,用于刊登他那篇长达三十多页纸的论文,以及其中所用到的“超椭圆分析法”这件独特的数学工具。 Generally speaking, when the significant mathematical proposition yields the unprecedented achievement, may make as four big go against of «Math Yearly journal» publications, publishes an issue of special issue to publish this paper for it specially. 一般而言,只有重大的数学命题获得突破性的成果时,才有可能令作为四大顶刊之一的《数学年刊》,为其专门出一期特刊来刊登这篇论文。 But by accurate Riemann hypothesis this proposition in the weight/quantity of analytic theory of numbers educational world, matches on this great honor without doubt. 而以准黎曼猜想这一命题在解析数论学界的分量,无疑是配的上这份殊荣的。 And at the same time, considering that the research of ultra elliptic curve analytic method to the Riemann hypothesis may play the inspirational role , if not grasp this mathematical instrument probably cannot to understand some processes in paper, therefore " Math Yearly journal » editorial department then made placed the decision that in the same this special issue emitted together two papers. 并且与此同时,考虑到超椭圆曲线分析法对黎曼猜想的研究可能将起到启发性的作用,以及如果不掌握这门数学工具可能无法理解论文中的部分过程,于是《数学年刊》编辑部便做出了将两篇论文放在同一本特刊里一起放出的决定。 Regarding the arrangement of «Math Yearly journal» editorial department, Lu Zhou does not care specially, regardless of they are the plan disassemble to publish, merges is publishing an issue of special issue together, to him has no influence. 对于《数学年刊》编辑部的安排,陆舟并不是特别在意,无论他们是打算拆开刊发,还是合并在一起出一期特刊,对于他来说都没有什么影响。 Perhaps regarding the topic of would-be Riemann hypothesis, has possibly brushed the screen to stop by the beginning of next year gradually, can perhaps popularize him to be at the certificate would-be Riemann hypothesis when until the end of next year mathematics circles slowly the mathematical thought of utilization. 也许围绕着准黎曼猜想的话题,可能会一直刷屏到明年年初才会渐渐消停,也许直到明年年底数学界才能慢慢普及他在证明准黎曼猜想时运用的数学思想。 However regarding Lu Zhou, this proposition, since was proven after by him, is past tense. 不过对于陆舟自己来说,这个命题自从被他证明之后,便已经是过去式了。 Let alone, he had hung on the pre- printed book Arxiv again before, now the scholar at least half mathematics circles has visited him to hang that pre- printed book on Arxiv, the matter that he expects has completed. 更何况,再次之前他已经将预印本挂到了Arxiv上,现在至少半个数学界的学者都已经看过了他挂在Arxiv上的那篇预印本,他所期望的事情已经完成了。 The remaining needs he does, then the achievement of would-be Riemann hypothesis, further promotes to „really Riemann hypothesis”...... 剩下需要他做的,便是将准黎曼猜想的成果,进一步推广到“真・黎曼猜想”身上…… What is worth mentioning is, in the pre- printed book emits these in three days, as if unceasingly some people in Epsilon in the value made the unprecedented progress. 值得一提的是,就在预印本放出的这三天里,似乎不断地有人在ε的取值上取得了突破性的进展。 But this digit also from initial infinitely great, turned had the poor value. 而这个数字也从最初的无穷小,变成了有穷的数值。 Forum according to Arxiv the data and statistics of Mathoverflow this mathematics circles Eight Trigrams (gossip) on, Epsilon the value is renovated each hour every day and even, toward 1 / 2 direction great leap. 根据Arxiv上的数据以及Mathoverflow这种数学界八卦论坛的统计,ε的数值每天、甚至是每小时都在被刷新,向着1/2的方向大步前进。 But so far, this number had been renovated 1/60000000. 而截止到目前为止,这个数字已经被刷新到了六千万分之一。 In almost half mathematics circles, when participates crazily this seeks in a big way Epsilon „math competition”, had not a very awkward matter. 就在几乎半个数学界,都在疯狂地参与到这场寻找更大的ε的“数学竞赛”中的时候,同时也发生了一件令人啼笑皆非的事情。 It is well known, the paper is tasteful time-limited. 众所周知,论文是讲究时效性的。 Who studies to be successful to take the lead to be completed, that research results then belong to anyone, because Journal academic rigorous will cause the verification cycle is very usually long, therefore many people will choose the way of hanging the pre- printed book to occupy the pit. 一个研究成功谁率先完成,那研究成果便归属于谁,然而由于期刊的学术严谨性导致审核周期通常会很长,因此很多人会选择挂预印本的方式占坑。 However hangs the pre- printed book unable to solve all problems once and for all, for example your front leg just made the research success of ε = 0.01, others have achieved ε = 0.1, that after his research results issue, your research then lost the value of publishing the publication. 然而挂预印本并不能一劳永逸的解决所有问题,比如你前脚刚做出来了ε=0.01的研究成功,别人已经做到了ε=0.1,那么在他的研究成果发布之后,你的研究便失去了登刊的价值。 This regarding the mathematics circles is a good matter, but regarding a doctor who needs the paper to graduate, without doubt is a disaster. 这对于数学界来说是一件好事儿,但对于一名需要论文去毕业的博士来说,无疑是一场灾难。 Therefore, will hang in the research results after Arxvi, almost all people expected that first publishes own result, even does not hesitate to choose some fame is not big, edit cycle slightly short Journal. 因此,在将研究成果挂在Arxvi上之后,几乎所有人都期望第一时间发表自己的结果,甚至是不惜选择一些名气没那么大、审稿周期稍短的期刊。 However what unfortunately is, because these papers quote the partial content that in ultra oval Geometry analytic method Lu Zhou proposed, however Lu Zhou own paper actually still in the edit stage, has no way to label the quotation. 然而不巧的是,由于这些论文引用了陆舟提出的超椭圆几何分析法中的部分内容,然而陆舟自己的论文却还在审稿阶段,根本没法标注引用。 What? 什么？ You said that Lu Zhou does hang the pre- printed book on Arxiv? 你说陆舟挂在Arxiv上的预印本？ Wants not to need to think, most regular Journal and reviewers are very stubborn, rejects the contributor in the paper quotes „has not undergone peer review” the pre- printed book. If not quote to label, directly uses the achievement on Arxiv, actually exists is regarded as the suspicion of plagiarism. 想都不用想,大多数正规期刊和审稿人都是很倔强的,是拒绝投稿人在论文中引用“未经过同行评审”的预印本的。然而若是不加引用标注,直接使用Arxiv上的成果,却又存在被视作抄袭的嫌疑。 Therefore, then happened made one that one did not know whether to laugh or cry. 因此,便发生了如此令人哭笑不得的一幕。 Knows obviously this conclusion is right, but everyone has no way to use. 明明都知道这结论是对的,但大家都没法用。 Many people after completing paper, wants to submit a piece of writing not to have the means to throw, must also hang the pre- printed book the form to emit own paper, simultaneously closely pays attention to " Math Yearly journal » trend at the same time, strives to submit a piece of writing own paper in Lu Zhou the earliest possible time of theory Wendeng publication. 不少人在完成了论文之后,想投稿都没办法投,只得把自己的论文也挂成预印本的形式放出,同时一边紧紧关注《数学年刊》的动向,争取在陆舟的论文登刊的第一时间投稿自己的论文。 This was the first time, the Journal publication manuscript speed is flung by the scientific research speed probably after behind...... 这大概还是第一次,期刊的刊稿速度被科研速度甩在了身后…… ...... …… Another side, sent off Lu Zhou of old friends, sat SUV that stopped in the airport entrance, returned to the Zhongshan international villa. 另一边,送走了老朋友们的陆舟,坐上了停在机场门口的SUV,返回了钟山国际的别墅。 Although the entire mathematics circles looked like raises the gold rush to be the same now, the scholars of almost all relevant areas invested in the exploration to Epsilon value, but regarding Epsilon the value studied, Lu Zhou was actually not interested specially. 虽然现在整个数学界就像是掀起了淘金热一样,几乎所有相关领域的学者都投入到了对ε取值的探索中,但对于ε的取值研究,陆舟却并不是特别感兴趣。 If unable Epsilon to advance to 1 / 2 directly, the big probability final result will be the same with the research of Twin Prime Conjecture initially, in any event ingenious selects that ultra elliptic curve in the complex planes, finally can only be close to 1 / 2 infinitely, but is unable to span the last step. 如果无法直接将ε推进到1/2的话,大概率最后的结果会和当初孪生素数猜想的研究一样,无论如何巧妙的在复平面上选取那条超椭圆曲线,最终都只能无限接近1/2,而无法跨越最后一步。 These days, did he under on Arxiv besides the attention have the person to make the groundbreaking achievement with his ultra elliptic curve analytic method occasionally, or developed what beyond the new method, then draws support from the resources of Jinling University, the important document of the world collection about Riemann hypothesis. 这段时间里,他除了偶尔关注下Arxiv上有没有人用他的超椭圆曲线分析法做出了开创性的成果之外,或者开发出什么新玩法之外,便是借助金陵大学的资源,满世界搜集关于黎曼猜想的重要文献。 When the research falls into the bottleneck divorces oneself from reality is the taboo, contacts some novel ideas to be many, or with being engaged in the scholar exchange of same domain, may scratch the thought the spark. 在研究陷入瓶颈的时候闭门造车是大忌,多接触一些新奇的想法多,或者与从事同一领域的学者交流,才有可能擦出思想的火花。 Also therefore, Professor Faltings is giving his big present just before leaving, appeared precious...... 也正是因此,法尔廷斯教授在临走送他的那份大礼,就显得弥足珍贵了…… Goes home, arrives at the study room to sit down directly, Lu Zhou put out that note impatiently, spread out it on the table. 回到家中,径直来到书房坐下,陆舟迫不及待地拿出了那本笔记,将它摊开在了桌上。 Just as Terence Tao said that this wrote down to record many interesting idea. 正如陶哲轩所说的,这本笔记上记录了许多很有意思的想法。 Part is examined by Professor Faltings, and certificate is invalid , some simply are the pure brain holes, or he feels a little hopes, but also attempts without enough time. 其中一部分是已经被法尔廷斯教授本人检验过,并证明行不通的,也有一些干脆就是纯粹的脑洞,或者说他觉得有点希望,但还来不及去尝试的。 This writes down, if to others' hand, perhaps understands is not quite easy. 这本笔记若是到了别人的手上,恐怕看懂都不太容易。 But regarding Lu Zhou, the thing that actually he most needs! 但对于陆舟来说,却正是他最需要的东西！ All various professions glanced through the note, the Lu Zhou look were catching several exciting expressions gradually, but when he turned one page of folding the corners positions, actually gawked suddenly slightly. 一行行翻阅着笔记,陆舟的眼神渐渐染上了几丝兴奋的表情,不过就在他翻到了一页折角的位置的时候,却是忽然微微愣了一下。 Different with the records of front these fragmentations, in one page that this folds the corners, is printing an all various professions neat handwriting. But is different from the first half content, part of contents write in German. 有别于前面那些碎片化的记载,在这折角的一页上,印着一行行工整的字迹。而有别于前半部分的内容,这一部分的内容是用德语书写的。 Lu Zhou not German, but has Xiao Ai fortunately here. 陆舟并不会德语,但所幸有小艾在这里。 With the help of Xiao Ai, he then completed very much with ease to the translation of this page of contents. 在小艾的帮助下,他很轻松地便完成了对这一页内容的翻译。 What is accidental/surprised, this page of contents do not write about any research result, seems like one...... 令人意外的是,这一页的内容并非是记叙什么学术成果,反倒像是一篇…… Diary? 日记？ 【When studying the paper of Professor Hilbert, I discovered a very interesting guess in his work. If wrote the ρ = 1 / 2 + it form the non- ordinary zero point of Riemann Zeta function, then the eigenvalue one-to-one correspondences of these t and some Hermitian operator. If this guess establishes, then Riemann operator should be a special random Hermitian matrix.】 【在研究希尔伯特教授的论文时,我在他著作中发现了一个很有意思的猜测。如果将黎曼ζ函数的非平凡零点写成ρ=1/2+it的形式,则那些t与某个厄密算符的本征值一一对应。如过这一猜测成立的话,那么黎曼算符应该是一个特殊的随机厄密矩阵。】 【In the afternoon tea time of MPI learned, I have earnestly discussed this issue with Professor Klitzing of institute of physics, we by own discovery having a scare.】 【在马普学会的下午茶时间,我与物理研究所的克利青教授认真讨论过这个问题,我们都被自己的发现给吓了一跳。】 【Accidental/Surprised, probably Riemann Zeta function such pure mathematical problem, can have the relation with the quantum mechanics unexpectedly! Afterward, I and Edward Weiteng has exchanged this issue in the mail, but it is a pity that has not discussed any useful thing.】 【令人意外,像是黎曼ζ函数这样纯粹的数学问题,居然会与量子力学产生联系！事后,我与爱德华・威腾在邮件中交流过这个问题,但很遗憾的是并没有讨论出什么有用的东西。】 【If before , I took as an elective quantum mechanics to be good, making present me study physics again, perhaps already without enough time......】 【如果以前我有选修过量子力学就好了,让现在的我再去研究物理,恐怕已经来不及了……】 Index finger from folding the corners on the trace has slid gently, Lu Zhou that the note put down, on the face starts to reappear to shock gently gradually. 食指从折角的痕迹上轻轻滑过,轻轻将笔记放下的陆舟,脸上渐渐开始浮现了一丝震撼。 Not only Montgomery and Professor Dyson...... 不只是蒙哥马利和戴森教授…… Professor Faltings in Germany, noticed projection of Riemann Zeta function similarly in quantum physics, even also with his another old friend Professor Klitzing, as well as theory Physics big cow Edward Weiteng has exchanged this issue. 远在德国的法尔廷斯教授,同样注意到了黎曼ζ函数在量子物理中的投射,甚至还与他的另一位老朋友克利青教授、以及理论物理学界的大牛爱德华・威腾交流过这个问题。 However it is a pity that they, although realized complicated relation as if by prior agreement, but cannot successfully unearth this back secret. 然而遗憾的是,他们虽然不约而同地意识到了这其中千丝万缕的联系,但并没能成功地挖掘出这背后的秘密。 Actually does this mean what? 这究竟意味着什么？ If Zeta function the energy level of some non- ordinary zero point correspondence in quantum mechanics system, non- ordinary zero point all , then corresponds to the power spectrum of this/should quantum mechanics system, is called Riemann operator the Hamiltoian of this system, if the Riemann hypothesis will be tenable...... will correspond mysterious quantum mechanics system? 如果将ζ函数的非平凡零点对应于某个量子力学体系的能级,非平凡零点的全体则对应于该量子力学体系的能谱,把这一体系的哈密顿量称为黎曼算符,如果黎曼猜想成立的话……将对应怎样神秘的量子力学体系？ The Hermitian operator that in turn, if can seek for all and Riemannζ that function non- ordinary zero point an eigenvalue corresponds, found popularly such „Riemann system”, whether also means can prove the Riemann hypothesis from the Physics angle? 反过来,如果能够寻找到一个本征值的全体与Riemannζ函数非平凡零点相对应的厄密算符,或者说的更通俗点,找到这样的“黎曼体系”,是否也意味着能够从物理学的角度证明黎曼猜想？ Expression that on the Lu Zhou face that is interested, was getting more and more intense. 陆舟脸上那感兴趣的表情,越来越强烈了。 Although he favors in the research through pure mathematics reveals the Riemann hypothesis back physics significance, but this does not hinder him, and tip of the iceberg that exposes from that unknown mysticalness feels to shock to the present all. 虽然他更倾向于通过纯粹数学上的研究去揭示黎曼猜想背后的物理意义,但这并不妨碍他对眼前的一切、以及从那未知的神秘中所揭露出的冰山一角而感到震撼。 Two do not have the connection parallel line, after spanning time of-and-a-half centuries, unexpectedly connected in one. 两条毫无关联平行线,在跨越了一个半世纪的时间之后,居然交汇在了一起。 Remote the 19 th century, did not have what quantum mechanics, however had such a function, can coordinate with each other across a great distance in it...... 遥远的十九世纪,可不存在什么量子力学,然而却有那么一个函数,能够于之遥相呼应…… At this time, placed the table corner cell phone to resound the ting suddenly, interrupted the Lu Zhou train of thought. 就在这时候,放在桌角的手机忽然响起铃声,打断了陆舟的思绪。 Puts out a hand to take up cell phone, Lu Zhou pressed down the button of connection, gathered near the ear it. 伸手将手机拿起,陆舟按下了接通的按钮,将它凑到了耳边。 When he just prepared not to say one patiently „feeding”, of telephone that head actually first opens the mouth. 就在他刚准备不耐烦地说一句“喂”的时候,电话那头的那位却是先开口了。 Brought several points of intent taste, that person of telephone that head to cough awkwardly lightly the sound. 带着几分尴尬地意味儿,电话那头的那人轻咳了声。 „...... That, Academician Lu, do you still remember me?” “……那个,陆院士,您还记得我吗？”