华裔之光！邓煜斩获2026年菲尔兹奖：新一代数学天才如何改变
字幕摘录
| 时间 | 英文 | 中文 |
|---|---|---|
| 0:28 | As you watch the waves, you realize it has such a simple, formally simple motion, but | 当你看着波浪,你意识到它有这样一个简单, 形式上简单的运动,但是 |
| 0:34 | realize there's something actually very complicated inside. | 其实里面有些事情很复杂 |
| 0:37 | The question is how do these simple motions come from these complicated interactions? | 问题是这些简单的动议是如何从这些复杂的相互作用中产生的? |
| 0:44 | One of the things that we are interested in is to find patterns within randomness. | 我们感兴趣的一件事就是在随机性中找到规律。 |
| 0:52 | I usually like to walk close to water, close to the river, the lake, or the forest areas that | 我通常喜欢走在水边 靠近河边 湖边 或森林地带 |
| 0:59 | is close to nature. | 接近自然界 接近自然界 接近自然界 |
| 1:00 | I tend to be relaxed and that makes the chance higher to have some real good | 我总是放松,这样就更有机会 有一些真正的好 |
| 1:06 | ideas. | 点子。 |
| 1:10 | I had dreams about math. | 我梦到数学 |
| 1:12 | Sometimes I dream about questions that I actually haven't worked on. | 有时候我梦到一些我还没有研究过的问题。 |
展开字幕全文（77 条）
| 序号 | 英文 | 中文 |
|---|---|---|
| 1 | As you watch the waves, you realize it has such a simple, formally simple motion, but | 当你看着波浪,你意识到它有这样一个简单, 形式上简单的运动,但是 |
| 2 | realize there's something actually very complicated inside. | 其实里面有些事情很复杂 |
| 3 | The question is how do these simple motions come from these complicated interactions? | 问题是这些简单的动议是如何从这些复杂的相互作用中产生的? |
| 4 | One of the things that we are interested in is to find patterns within randomness. | 我们感兴趣的一件事就是在随机性中找到规律。 |
| 5 | I usually like to walk close to water, close to the river, the lake, or the forest areas that | 我通常喜欢走在水边 靠近河边 湖边 或森林地带 |
| 6 | is close to nature. | 接近自然界 接近自然界 接近自然界 |
| 7 | I tend to be relaxed and that makes the chance higher to have some real good | 我总是放松,这样就更有机会 有一些真正的好 |
| 8 | ideas. | 点子。 |
| 9 | I had dreams about math. | 我梦到数学 |
| 10 | Sometimes I dream about questions that I actually haven't worked on. | 有时候我梦到一些我还没有研究过的问题。 |
| 11 | I had these dreams while I was writing these papers about legitimate math questions, but | 我写这些关于数学问题的文件时做了这些梦 但是 |
| 12 | in reality I haven't written any of the papers. | 事实上,我还没有写任何论文。 |
| 13 | I'm a professor of mathematics at the University | 我是大学的数学教授 |
| 14 | of Chicago. | 芝加哥大学 |
| 15 | I mainly work in the field of PDEs, partial differential equations, and also kind of | 我主要从事PDEs, 部分微分方程, 以及某种 |
| 16 | in connection with probability. | 关于概率。 |
| 17 | The questions I work on mainly concerns how do you see these real | 我所研究的问题主要涉及 你怎么看待这些真实的 |
| 18 | phenomena like fluid waves from microscopic pictures of interacting tiny particles. | 诸如微镜照片中的流体波 相互作用的微小粒子 |
| 19 | I grew up in Shenzhen in China. | 在中国深圳长大. |
| 20 | When I was in sixth grade, I was working with my dad | 我六年级的时候 和爸爸一起工作 |
| 21 | on a particular question about finding patterns in a particular sequence, and I remember we | 关于一个特定的问题 寻找特定序列的规律 我记得我们 |
| 22 | spent a few hours together to solve that, and at the end we were really happy that we could | 花了几个小时 一起解决这个问题, 到最后,我们真的很高兴 我们可以 |
| 23 | solve this question, and that was perhaps the earliest thing I could remember while I get | 这个问题的解决, 这可能是最早的事情 我可以记得 当我得到 |
| 24 | excited about mathematics. | 兴奋的数学。 |
| 25 | I started learning Go when I was maybe about six. | 我六岁的时候就开始学走 |
| 26 | The game of Go | Go的游戏 |
| 27 | is really about analyzing the positions of the board and really having an accurate idea about it | 真正重要的是分析董事会的立场 并真正有正确的想法 |
| 28 | before you make your move. | 在你行动之前 |
| 29 | In some sense it was maybe closer to the idea of thinking about math | 从某种意义上说,它也许更接近 思考数学的想法 |
| 30 | metal questions and having an idea of the question before you start really working on it. | 在你真正开始着手研究之前 有个问题的想法 |
| 31 | I seriously played it for a few years. | 我认真玩了几年 |
| 32 | I even thought of going for professionals, but in the | 我甚至想找专业,但是... |
| 33 | end I wasn't successful, so I gave up and I turned to the math competitions. | 最后我没成功 所以我放弃了 转向了数学比赛 |
| 34 | I went to the IMO in | 我去了海事组织 |
| 35 | Slovenia in 2006 and got a gold medal. | 2006年斯洛文尼亚获得金牌. |
| 36 | I started to think maybe I really have some talent in this | 我开始觉得 也许我真的有些天赋 |
| 37 | field and maybe I should really try to pursue this field. | 和也许我应该真的 尝试追求这个领域。 |
| 38 | Consider a billiard ball. | 考虑一个台球。 |
| 39 | It moves | 动了 |
| 40 | in a straight line, collides with other billiard balls, changing velocity, and keeps moving. | 在一条直线上,与其他台球相撞,改变速度,并不断移动. |
| 41 | Simple. | 简单 |
| 42 | But what if we have trillions of such tiny balls constantly colliding with each other? | 但如果我们有数万亿个如此小的球 不断相互碰撞呢? |
| 43 | This is what happens in the hot sphere model of gases where the little billiards are the gas | 热球型的气体就是这个 台球是气体 |
| 44 | particles. | 颗粒。 |
| 45 | For such a huge system, it's practically impossible to track each individual particle | 对于如此庞大的系统来说,几乎不可能 追踪每个粒子 |
| 46 | precisely. | 没错 |
| 47 | Instead, we're interested in the statistical information of the system, overall | 相反,我们感兴趣的是 系统的统计资料,总体 |
| 48 | distribution of the particles, average velocity, and so on. | 颗粒的分布,平均速度等等. |
| 49 | This will be captured in a single | 这将会被单枪匹马抓住 |
| 50 | density function which is governed by Boltzmann's kinetic equation. | 密度函数,由Boltzmann的动量方程所支配。 |
| 51 | In a parallel picture, consider | 在平行情况下,考虑 |
| 52 | water waves which can be viewed as a system of many wave packets again constantly interacting | 水波,可以看作是许多波包的系统 不断相互作用 |
| 53 | with each other. | 与彼诸人. |
| 54 | This occurs in the physical phenomena of wave turbulence where the statistical | 在波浪暴动的物理现象中, |
| 55 | information is governed by the wave kinetic equation. | 信息受波动方程的制约. |
| 56 | With collaborators, we've successfully | 我们合作成功 |
| 57 | justified both scenarios in pseudo-architectic limits on a mathematical level. | 在数学水平上,在伪结构限制中,这两种假设都是合理的。 |
| 58 | The key challenge | 关键的挑战 |
| 59 | is that an average particle will experience arbitrarily many collisions and complicated | 平均粒子会任意经历许多碰撞和复杂 |
| 60 | dynamics as opposed to less than one collision in previous works. | 动力学,而不是以往作品中不到一次碰撞. |
| 61 | To overcome this, we introduce | 为了克服这些,我们介绍 |
| 62 | multi-layer diagrams representing the whole collision process and inventing ways to analyze | 代表整个碰撞过程的多层图和发明分析方法 |
| 63 | them effectively. | 有效。 |
| 64 | These diagrams are enormous in size but they are formed by the basic building | 这些图是巨大的,但是它们是由基本建筑形成的 |
| 65 | blocks. | 块。 |
| 66 | Each of these basic scenarios, for example, when the billiard ball has one single collision | 例如,台球发生一次碰撞时 |
| 67 | or when it has one collision that causes a second collision, is easy to estimate. | 或者当它发生一次碰撞导致第二次碰撞时,很容易估计。 |
| 68 | Then, by | 然后,通过 |
| 69 | carefully designed cutting algorithm, we can break any diagram into such building blocks which in the | 仔细设计的剪切算法 我们可以把任何图表 分解成这样的构件 |
| 70 | end guarantees a complete understanding of the diagrams and leads to the resolution of the full | 最终保证了对图表的完全理解,并导致完全解析 |
| 71 | problem. | 问题。 |
| 72 | After several thousand years, there are still a lot of mysteries about the universe. | 几千年后,宇宙仍有许多神秘之处。 |
| 73 | Our | 我们 |
| 74 | understanding of the physical universe on the mathematical level is still extremely small. | 数学层面对物理宇宙的理解仍然极小. |
| 75 | The | 那个 |
| 76 | thing that keeps me in this field is the happiness when your plan works perfectly, | 使我留在这个领域 是幸福 当你的计划完美地工作, |
| 77 | that you're able to solve the questions you're faced with. | 你能够解决你所面临的问题 |
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