The activity room in library. 图书馆的活动室。 Faced writes half of blank slate, Lu Zhou took back the symbol pen in hand, withdrew two steps to look at the blank slate to say. 面对着写了一半的白板,陆舟收回了手中的记号笔,退后两步看着白板说道。 „...... To solve the algebra and Geometry unified issue, must ‚’ ‚and shape’ strips from the general indication form number, seeks for them in the abstract concept the general character.” “……想要解决代数和几何的统一性问题,就必须将‘数’和‘形’从一般的表述形式中剥离出来,在抽象的概念中寻找它们之间的共性。” Stands in Lu Zhou side, Chen Yang pondered over a moment later, opened the mouth to ask suddenly. 站在陆舟的旁边,陈阳思忖了片刻之后,忽然开口问道。 „Langlands program?” “朗兰兹纲领？” „Not only the Langlands program,” Lu Zhou said earnestly, „also has the motive theory, wants to solve this problem, we must clarify the different cohomology theory relation.” “不只是朗兰兹纲领,”陆舟认真说道,“还有motive理论,想要解决这个问题,我们必须弄清楚不同上同调理论彼此之间的联系。” In fact, this issue is a very big category. 事实上,这个问题是一个很大的范畴。 „Different cohomology theory relation” this issue will subdivide unceasingly, even can split several tens of thousands and even several million unresolved suspicions, or mathematical proposition. 将“不同上同调理论彼此之间的联系”这一问题不断细分下去,甚至能够分裂成数万乃至数百万个悬而未决的猜想,或者说数学命题。 The algebra Geometry study domain unresolved difficult problem Hodge conjecture, is one of them , is most famous one. 代数几何学领域悬而未决的难题霍奇猜想,便是其中之一,也是最出名的一个。 However interestingly, although has such many extremely difficult suspicions to prevent in front, but proves the motive theory actually not to need these to suspect that solves completely. 然而有意思的是,虽然存在如此之多极其困难的猜想阻挡在前面,但论证motive理论却并不需要将这些猜想全部解决。 Relations of both sides seem the Riemann hypothesis in Dirichlet function the same as be neither friendly nor aloof with the promotion of Riemann hypothesis. 双方的关系就好像黎曼猜想和黎曼猜想在狄利克雷函数上的推广一样若即若离。 „Superficially what...... we study is a complex analysis issue, but in fact it is also the issue of the partial differential equation, algebra Geometry and analysis situs.” “……表面上看我们研究的是一个复分析问题,但事实上它同时也是偏微分方程、代数几何、拓扑学的问题。” Looks at front blank slate, Lu Zhou continues saying that „stands in the strategic altitude, we need in the number and shape abstract formally found one type to be connected both's factor. In the tactic, we from the kunh formula and poinare the general character that can match the wait a series of cohomology theories start, as well as I previously to the l application method of manifold that you demonstrated in complex planes.” 看着面前的白板,陆舟继续说道,“站在战略的高度,我们需要在数和形的抽象形式上找到一种可以关联两者的因子。在战术上,我们可以从kunh公式、poinare对偶等等一系列上同调理论的共性入手,以及我先前向你展示的l流形在复平面上的应用方法。” Saying, Lu Zhou is looking at stood in his nearby Chen Yang. 说着,陆舟将视线投向了站在他旁边的陈阳。 „I need a theory, it can carry forward the classical theory of one-dimensional cohomology is also the jaobi variety theory and abel of variety theory curve the success, to be advantageous all dimensions cohomology.” “我需要一个理论,它能够发扬一维上同调的经典理论也就是曲线的jaobi簇理论和abel簇理论的成功之处,以便于所有维数的上同调。” „Based on this theory, we can study the decomposition into direct sum in motive theory, making h ( v ) be connected with not improper motive.” “基于这个理论,我们可以研究motive理论中的直和分解,使h(v)与不可约motive相关联。” „This I am planned oneself do, but is worth me completing with the important part. I plan to handle the GUT within this year, this gave you.” “原本这一块我是打算自己去做的,但还有跟重要的部分值得我去完成。我打算在今年之内搞定大统一理论,这一块就交给你了。” Facing asking of Lu Zhou, Chen Yang pondered a while, says. 面对陆舟的拜托,陈阳沉思了一会儿,开口说道。 „Sounds Interesting......, if my feeling right, if can find this theory, should become clue that solves the Hodge conjecture.” “听起来有点意思……如果我的感觉没错的话,如果能找到这个理论的话,应该会成为解决霍奇猜想的线索吧。” Lu Zhou selected, said. 陆舟点了下头,说道。 „Can solve the Hodge conjecture I unclear, but as the issue of same class, its solution possibly can inspire the research to the Hodge conjecture.” “能不能解决霍奇猜想我不清楚,不过作为同一类的问题,它的解决可能能够启发对霍奇猜想的研究。” „I knew,” Chen Yang nods, „I go back under the careful research......, but I have no way to guarantee that can solve this problem in a short time.” “我知道了,”陈阳点了点头,“我回去会仔细研究下……但我没法保证能在短时间内解决这个问题。” „Doesn't matter, this is not the duty that the short time can complete, let alone I am not special worry,” Lu Zhou smiles to continue saying that „, but, my suggestion is, best in two months to me an answer. If you have not grasped, best tell me ahead of time one, I make this also yes.” “没关系,这本来就不是短时间能够完成的任务,何况我也不是特别的着急,”陆舟笑了笑继续说道,“不过,我的建议是,最好还是在两个月之内给我一个答复。如果你没有把握的话,也最好提前告诉我一声,我自己来做这一块也是可以的。” Chen Yang shakes the head. 陈阳摇了摇头。 „Two months are insufficient, for half a month...... should enough.” “两个月不至于,半个月……应该就够了。” It is not the self-confident speech, but is an affirmation of almost indicative mood. With tool ready-made, even solves the problem continually the possible mentality, Lu Zhou has given. 并非是出于自信的发言,而是一种几近陈述语气的肯定。采用的工具是现成的,甚至于连解决问题的可能的思路,陆舟都已经给出了。 This type does not need the work of subversive thought as well as creativity, so long as is willing to work hard to solve. 这种并非需要颠覆性的思维以及创造力的工作,只要肯下功夫就能解决。 But he most does not lack, is will of a muscle resentment on road. 而他最不缺的,便是一根筋怼在一条路上的毅力。 Looks at unemotional Chen Yang, Lu Zhou nods, puts out a hand to pat under his arm. 看着面无表情的陈阳,陆舟点了点头,伸手拍了下他的胳膊。 „Un, this gave you!” “嗯,这一块就交给你了！” ...... …… After Chen Yang walks, Lu Zhou returned to the library, arrived at the previous position to sit down, opens the literature that on the table that pack had not read, continued the previous research, while is calculating on the scratch paper with. 陈阳走后,陆舟回到了图书馆,走到了自己先前的位置坐下,翻开了桌上那叠尚未看完的文献,一边继续先前的研究,一边用笔在草稿纸上计算着。 Macroeconomically, algebra Geometry can sum up in the development of modern times is two big directions, one is the Langlands program, another is the motive theory. 从宏观的角度来看,代数几何在近代的发展可以归结为两个大的方向,一个是朗兰兹纲领,另一个就是motive理论。 And Longlands theory, its spiritual kernel then seems like the unrelated content to establish the relation of essence some surfaces in math, because many people have heard, then no longer gave unnecessary detail. 其中朗兰兹理论,其精神内核便是将数学上的一些表面看起来不相干的内容建立起本质的联系,由于很多人都听说过,便不再赘述。 As for the motive theory, the relative Langlands program, without was so famous. 至于motive理论,相对朗兰兹纲领而言,则没那么出名了。 The paper that at this moment, he is reading, is then written by renowned algebra Geometry scientist Professor voevodsky. 此时此刻,他正在研读的这篇论文,便是由著名的代数几何学家voevodsky教授撰写的。 In the paper, this Russian professor from Institute for Advanced Study, proposed a very interesting motive category. 在论文中,这位来自普林斯顿高等研究院的俄罗斯籍教授,提出了一个非常有趣的motive范畴。 But this, is Lu Zhou needs exactly. 而这,恰好是陆舟所需要的。 „...... So-called motive, is the roots of all numbers.” “……所谓motive,便是一切数的根源。” With the sound that only then can hear is pronouncing unstressed low voice, Lu Zhou is comparing a all various professions mathematical formula on literature, while writes with vigor on the scratch paper is calculating. 用只有自己才能听见的声音小声轻念着,陆舟一边对照着文献上的一行行算式,一边在草稿纸上奋笔疾书地演算着。 Cites a popular example, if counts us to call it n, n under the decimal base can be expressed as 100, then in fact it can be 1100100, can be 144. 举个通俗的例子,如果一个数我们称之为n,在十进制下n可以表示为100,那么实际上它既可以是1100100,也可以是144。 The way of indication is different, merely what the difference lies in we chooses is the binary system or the octonary number system counts it. In fact 1100100 are 144, they correspond is n this number, but is the n different elaboration form. 表述的方式不同,区别仅仅在于我们选择的是二进制还是八进制来统计它。事实上无论是1100100还是144,它们对应的都是n这个数字,只不过是n的不同阐述形式而已。 Here, n was given a special significance. 在这里,n被赋予了一种特殊的意义。 It is not only an abstract number, is the essence of digit. 它既是一种抽象的数字,也是数字的本质。 the motive fundamental research, is the named capital letter n set of innumerable n comprised. motive理论研究的,便是由无数个n组成的名为大写n的集合。 As all mathematical indication form roots, n can map in the random sector set, 【0,1】 【0,9】, But all mathematics methods about motive theory, same is suitable on it. 作为一切数学表述形式的根源,n可以映射到任意区间的集合内,无论是【0,1】还是【0,9】,而关于motive理论的一切数学方法,在它身上都同等适用。 In fact, this has involved the algebra Geometry core issue, is the abstract form of number. 事实上,这已经涉及到了代数几何的核心问题,也就是数的抽象形式。 Different with all human through differently to enter system notation „translation” the later language, this abstract indication method, is the universe in the true sense language. 有别于一切人类通过不同进制计数法“翻译”之后的语言,这种抽象的表述方法,才是真正意义上的宇宙的语言。 If we use the mathematical for the daily life the words, may not realize this point for a lifetime, gives the digital special significance the religion and culture, in fact has not understood „language of God” truly 而如果我们只是为了日常生活而使用数学的话,可能一辈子也不会意识到这一点,许多赋予数字特殊意义的宗教和文化,事实上也并没有真正地听懂“上帝的语言” Some people may ask that this besides making the computation more troublesome beside can also be useful, however in fact actually just right opposite, strips with its indication form the digit, instead helps people study its behind abstract significance. 有人可能会问这除了让计算变得更加麻烦之外还能有什么用,然而事实上却正好相反,将数字本身与其表述形式剥离开来,反而更有助于人们研究其背后的抽象意义。 Grothendieck besides laying the rationale of modern algebra Geometry study, another great work then lies in this. 格罗滕迪克除了奠定了现代代数几何学的理论基础之外,另一个伟大的工作便在于此。 He created a sole theory, built a bridge between algebra Geometry and all kinds of cohomology theories. 他创造了一个单一的理论,在代数几何与各种各样的上同调理论之间架起了一座桥梁。 It seems like a theme of symphony to be the same, each special cohomology theory can extract its subject material, according to own main key and major, or the folk song even is the bat of original creation conducts the performance. 它就好像是一场交响乐的主旋律一样,每一个特殊的上同调理论都可以从中抽出它自己的主题素材,按照自己的基调、大调、或者小调甚至是独创的拍子进行演奏。 „...... All cohomology theories composed a Geometry object together, but this Geometry object, can be admitted under the frame that he opens to study.” “……所有上同调理论共同组成了一个几何对象,而这个几何对象,可以被放进他所开辟的框架下研究。” „...... So that's how it is.” “……原来如此。” In the pupil caught an exciting appearance gradually, the pen tip in Lu Zhou hand stopped. 瞳孔中渐渐染上了一丝兴奋的神采,陆舟手中的笔尖停了下来。 During one type is dark the premonition, making him feel that oneself has been close from the goal line very much. 一种冥冥之中的预感,让他感觉自己距离终点线已经很接近了。 This excitement from innermost soul, simply compared with the feeling of his first witness virtual reality world, but must command joyful...... 这种来自灵魂深处的兴奋,简直比他第一次目睹虚拟现实世界的感受,还要更加的令人愉悦…… ...... …… ( Part about motive theory, what reference is barry mazur that famous «whatisamotive», is a paper of popular science nature, looked, truly made one broaden the outlook.) (关于motive理论的部分,参考的是barry・mazur那篇著名的《whatisamotive》,算是一篇科普性质的论文,看完之后确实令人大开眼界。)