今天我用我喜欢的语速读着我喜欢读的句子。
法国高等科学研究所 French institute of advanced science 菲尔兹奖获得者 Fields award winner 胡德奖获得者，国家科学研究院金质奖章获得者 Winner of the hood award and the national academy of sciences gold medal 在此树是数学界的最高奖项， The tree is the highest prize in mathematics, 下面我们来听他的这片严酷的现实， Let's listen to his harsh reality. 严 yan 本文描述的一种与数学之间的非常个人化的关系， A very personal relationship with mathematics described in this paper, 我们不要忘记每一位数学家都是一个特例， Let's not forget that every mathematician is a special case, 以下所述内容都只涉及他的作者，在任何情况下都不应被认为是一般的 The following is only relevant to his author and should not be considered general under any circumstances 在我看来， In my opinion, 数学首先是最精致的思维工具，是概念的发生器 First of all, mathematics is the most delicate thinking tool and the generator of concepts 有了数学，我们可以理解各种食物，尤其是理解我们身处其中的这个世界。 With mathematics, we can understand all kinds of food, especially the world in which we live. 新的概念就是通过在思想的熔炉中长期经典才产生出来的 New concepts emerge from the classics in the melting pot of ideas 我将数学划分为一些独立领域的想法，最初是吸引人的 My idea of dividing mathematics into separate fields was initially appealing 例如几何是研究空间的科学 Geometry, for example, is the science of space 代数式符号，运算的艺术，数学分析则是我们理解无限可连续的概念，还有数论等等 Algebraic notation, the art of operation, mathematical analysis is our understanding of the concept of infinite continuity, number theory and so on 但是这并没有考虑到数学世界的一个本质特征，也就是说不可能将他的某一部分不伤筋动骨的隔离出来。 But this does not take into account an essential feature of the mathematical world, that is, it is impossible to isolate parts of it without breaking them. 在我看来，关于数学首先要知道我们无法通过学习成为数学家，而是通过做数学才能成为数学家 In my opinion, the first thing to know about mathematics is that we can't become mathematicians by learning it, but by doing it 因此重要的并不是学问，而是本领 So the important thing is not knowledge, but ability 当然支持是绝对必要的，完全没有必要抛弃前人所获得的成就。 Of course, support is absolutely necessary. There is no need to abandon the achievements of our predecessors. 但是我始终认为努力的思考一个几何问题，比起半生不熟的积累，所谓知识来可以让人有更大的进步。 But I always think that hard thinking about a geometric problem, compared with the half-cooked accumulation, the so-called knowledge can make people have greater progress. 这样在我看来， So in my opinion, 我们或多或少是通过某个反叛行为才开始成为数学家的 We more or less became mathematicians by some act of rebellion 这话怎么讲呢？ How do you say that? 我他的意思就是未来的数学家将开始对某个问题进行思考， What I mean by that is that future mathematicians are going to start thinking about a problem, 然后他会明白，实际上他在文献资料和书籍当中所读到的并不符合。当他面临问题时的个人看法， Then he will understand that what he has actually read in the literature and in the books does not correspond. His personal view when faced with a problem, 当然， Of course, 很多时候这是因为没有学到家 A lot of times it's because you haven't learned enough 此时他讲明白，在数学里面没有权威 Now he makes it clear that there is no authority in mathematics 如果一个12岁的学生能够证明自己的论断， If a 12-year-old student can prove his claim, 就完全可以在他的教师面前坚持己见， He could stand up to his teacher, 并且因为如此，才能够让数学与其他学科相比显示出它的独特之处。 And because of this, mathematics can be compared with other disciplines to show its unique. 在那些学科里， In those disciplines, 教师很容易以学生所不具有的知识作为挡箭牌， It is easy for teachers to use the knowledge that students do not have as a shield. 一个五岁的孩子可以对他父亲说，爸爸没有最大的数，并且对此十分肯定。 A five-year-old can tell his father that he doesn't have the biggest number, and he's pretty sure of it. 这并不是因为他在书中看到过，而是因为他的头脑当中已经论证过了 This was not because he had seen it in books, but because it had been argued in his head 对于善于按照规则进行探索的人来说，这里有着广阔的自由空间。 There is plenty of freedom for those who are adept at following the rules of discovery. 最为重要的事情就是成为自己的权威 The most important thing is to be your own authority 也就是说，为了理解某些事情，不要立刻去尝试确认是否写在某本书里，不要 That is, in order to understand something, don't immediately try to confirm whether it's in a book, don't 这样做，只会延迟独立性的觉醒 Doing so will only delay the awakening of independence 需要做的事情是在他的头脑当中验证，这是否是真的 What needs to be done is to test in his mind whether this is true 从我们明白这一点的时刻开始，我们就可以逐渐的去了解熟悉数学王国的某个很小的部分，并且从此开始在这个王国的神奇里地上以自己的方式进行一次 From the moment we know this, we can gradually get to know a small part of the mathematical kingdom, and from then on begin to play it out in our own way in the magic of the kingdom 长途的寻宝之旅。 A long treasure hunt. 我们可以说数学家的工作当中有两个方面 We can say that there are two aspects to the work of a mathematician 一方面在于证明验证等等。他要求全身贯注要求高度的理性主义 One is proof, validation and so on. He calls for total absorption and a high degree of rationalism 然而幸运的是，还有另一个方面眼光 Fortunately, however, there is another perspective 眼光，这个东西有点像是受到直感的驱使而得到的 Vision, this thing is sort of driven by a sense of intuition 他并不服从某些确定性 He is not subject to certain certainties 简而言之，在数学发现当中，有着两个时间阶段 In short, there are two time periods in mathematical discovery 在第一个阶段里还无法以推理的方式有公式化语言来明确表达出直觉。 In the first stage there is no formulaic language to express intuition in an inferential way. 在这个阶段里，重要的是眼光 At this stage, it is the vision that matters 这并不是静态的那一方面，而是一种诗情荡漾的境界。 This is not a static aspect, but a poetic state. 这种事情当阳几乎无法用话语来传达 This kind of thing can hardly be conveyed by words 可以毫不夸张的说，一旦当我们尝试将他说出来的时候， It is no exaggeration to say that once we have tried to speak him out, 我们就会使他变成石头 We'll turn him to stone 而且我们会丧失这种动感 And we lose that dynamic 而他在数学发现当中是至关重要的。 And his mathematical discoveries were crucial. 然后，当我们理清了问题的足够多的方面时， Then, when we have sorted out enough aspects of the problem, 事情就会发生变化， Things will change, 并且，当我们认识到这种眼光最终帮助我们解决问题时， And when we realize that this vision ultimately helps us solve problems, 例如，当我开始成为数学家，是在我所有的发现当中，最让我感到震动的一件事就是 For example, when I started as a mathematician, one of the things that struck me the most about all of my discoveries was that 一个非交换代数。随着时间在发生变化， A noncommutative algebra. It's changing over time, 那是我在雅克比斯米埃的指导下，准备博士论文时期 That was when I was preparing my doctoral thesis under the guidance of Jacques besmier 我所证明的事实际上一个非交换代数都有一个随时间的演化 What I'm proving is that every non-commutative algebra actually has an evolution over time 这个眼花是完全点则的，更加准确的说 This vertigo point is completely accurate, to say the least 泡面，他理论所定义的演化，信赖于某种体态 Instant noodles, as his theory defines evolution, rely on a certain posture 实际上这种演化只是在磨掉那一次同构的意义上，才依赖于这个台 In fact, this evolution is only dependent on the platform in the sense of grinding away that isomorphism 这些内自同构是频繁的，不存在的 These inner automorphisms are frequent and nonexistent 因此这里所展示的就是这种非交换性生成的时间 So what's shown here is the time of this noncommutative generation 而且是从虚无当中生成的 And from nothing 如此简单就是这样当然立刻由此得出的结果就是一个代数会包含大量的不变量，例如它的周期，也就是说，史演化成为频繁所需的时间。T It's that simple and of course the immediate consequence of this is that an algebra has a lot of invariants, such as its period, which is to say, the time it takes for history to become frequent. T 办事 Handle affairs 尽管这些结果完全是可以公式化表达的和可以传达的，却并不会耗尽他们诗歌版的内容。 Although these results are completely formulaic and deliverable, they do not exhaust their poetic editions. 也不会耗尽将最初的心发现付诸行动时的精彩之处。 Nor does it exhaust the beauty of putting your initial discovery into action. 我的有些湿润，非常欣赏 My eyes were moist and I enjoyed it 他是法国诗人和散文家 He is a French poet and essayist 这是由于它在方法论层面上与数学相近， This is because it is close to mathematics in methodology, 在我看来，数学家和诗人的不同之处在于诗人所使用的原材料使用 To me, the difference between a mathematician and a poet is the raw materials that the poet USES 人类经验中的物质现实 The physical reality of human experience 诗词的主主要成分是一个人的内心世界和外部现实之间的冲突。 The main component of poetry is the conflict between one's inner world and external reality. 这种冲突之激烈总是使得我们震惊 We are always shocked by the intensity of the conflict
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