王虹自述：对专业和职业的选择以及挂谷猜想
字幕摘录
| 时间 | 英文 | 中文 |
|---|---|---|
| 0:22 | Sometimes I just walk around the mountain flowers and trees and plants. | 有时我只走在山花 树木和植物周围 |
| 0:28 | It clears my mind and makes me more calm. | 它能让我清醒,让我更冷静. |
| 0:33 | I just sort of let my thoughts wander and think about whatever comes to my mind. | 我只是有点让我的思绪徘徊 思考我的想法。 |
| 0:42 | Mathematics is a way for me to understand the world. | 数学是我了解世界的方法 |
| 0:47 | It's something that I could try to think very hard and understand from the axioms and the basics. | 我可以试着从逻辑和基本原理中 仔细思考和理解 |
| 0:56 | What I understand, what I don't understand, what needs to be understood. | 我理解的,我不明白的, 需要被理解的。 |
| 1:03 | The first math problem that I was interested in was when I was five or six. | 我感兴趣的第一个数学问题 就是我五六岁的时候 |
| 1:09 | If you have seven points in the plane, and then if three points in a row, | 如果你在飞机上有7分, 如果连续3分, |
| 1:15 | and how many rows can you find? | 还有你能找到多少行? |
| 1:17 | I feel quite happy when I figure out the answer. | 当我找到答案的时候,我觉得很快乐 |
展开字幕全文（55 条）
| 序号 | 英文 | 中文 |
|---|---|---|
| 1 | Sometimes I just walk around the mountain flowers and trees and plants. | 有时我只走在山花 树木和植物周围 |
| 2 | It clears my mind and makes me more calm. | 它能让我清醒,让我更冷静. |
| 3 | I just sort of let my thoughts wander and think about whatever comes to my mind. | 我只是有点让我的思绪徘徊 思考我的想法。 |
| 4 | Mathematics is a way for me to understand the world. | 数学是我了解世界的方法 |
| 5 | It's something that I could try to think very hard and understand from the axioms and the basics. | 我可以试着从逻辑和基本原理中 仔细思考和理解 |
| 6 | What I understand, what I don't understand, what needs to be understood. | 我理解的,我不明白的, 需要被理解的。 |
| 7 | The first math problem that I was interested in was when I was five or six. | 我感兴趣的第一个数学问题 就是我五六岁的时候 |
| 8 | If you have seven points in the plane, and then if three points in a row, | 如果你在飞机上有7分, 如果连续3分, |
| 9 | and how many rows can you find? | 还有你能找到多少行? |
| 10 | I feel quite happy when I figure out the answer. | 当我找到答案的时候,我觉得很快乐 |
| 11 | I feel like I have a clearer understanding of the subject. | 我觉得我对这个问题有更清楚的理解。 |
| 12 | My parents gave me a lot of freedom to do whatever I want. | 我父母给了我很多自由来做我想做的事 |
| 13 | They allowed me to go to bookstores and pick some interesting math books and try to solve the problems. | 他们让我去书店 选一些有趣的数学书 试着解决问题 |
| 14 | My mom tried to teach me English, and my dad is a teacher in mathematics. | 我妈妈试图教我英语, 我爸爸是一个数学老师。 |
| 15 | When I went to college, suddenly mathematics became difficult. | 当我上大学时,数学突然变得很困难. |
| 16 | It took effort and discipline to actually learn it, and it took many years. | 花了很多努力和纪律才真正学会了它,花了很多年. |
| 17 | I felt a little discouraged, and I did an internship in architecture in Paris. | 我感到有些沮丧,我在巴黎做了一个建筑实习。 |
| 18 | After this internship, I decided that I should spend my most creative years in mathematics, | 经过这次实习,我决定,我应该 度过我最有创意的数学岁月, |
| 19 | and if it didn't work out, then I would re-evaluate my choice after five years. | 如果失败了 我会在五年后重新评价我的选择 |
| 20 | After that, I stopped worrying about whether I'm good at math or not. | 之后,我不再担心我是否擅长数学. |
| 21 | I work in Fourier analysis and geometric measure theory. | 我从事傅里叶分析和几何测量理论. |
| 22 | We see fractal sets in our daily life. | 我们在日常生活中看到分形装置。 |
| 23 | For example, the snowflake, if you keep zooming in, | 例如,雪花,如果你继续放大, |
| 24 | then you see some structures that are quite similar to the bigger structure. | 然后,你可以看到一些结构 与更大的结构相当相似。 |
| 25 | In some of the math problems that we work on, the structures are so natural | 我们研究的一些数学问题 结构很自然 |
| 26 | that it felt that they had been there waiting for us to discover for a long time. | 感觉他们在那里 等待我们发现很长时间。 |
| 27 | I am a professor of mathematics at NYU Koran Institute of Mathematical Sciences | 我是纽约大学古兰经数学科学学院的数学教授 |
| 28 | and a permanent professor at the IHES. | 和IHES的终身教授. |
| 29 | During COVID, I ran into a task block post on the Kaikea set conjecture. | COVID期间,我遇到一个任务 块柱 在凯凯亚套装猜想。 |
| 30 | We decided to try to write down some details of this outline | 我们决定试着写下这个大纲的一些细节 |
| 31 | in the very special case of sticky Kaikea sets. | 在非常特殊的情况下,粘性凯凯卡套。 |
| 32 | So we have to spend a long time to overcome this, | 所以我们得花很长时间来克服这些 |
| 33 | and in the end, we were more convinced that this is going to be solved. | 最后,我们更确信,这个问题将得到解决。 |
| 34 | In 1917, Kaikea asked the following question. | 1917年,凯凯亚提出如下问题. |
| 35 | If we rotate a needle in 180 degrees, what is the smallest area it sweeps out? | 如果我们在180度旋转一根针, 它所扫射的最小区域是什么? |
| 36 | Surprisingly, Bessicovitch showed two years after in 1919 | 令人惊讶的是,贝西科维奇在1919年的两年后就出现了 |
| 37 | that there exists a way of rotating the needle in 180 degrees, | 有一种方法可以旋转 180度的针, |
| 38 | such that the area it sweeps out is as small as you want. | 以至于它所扫荡的区域 和你想的一样小 |
| 39 | Bessicovitch's example showed that this set could have zero volume or zero area. | 贝西科维奇的例子表明,这个集可能具有零音量或零面积. |
| 40 | A Kaikea set is a set that contains a unit line segment in every direction. | Kaikea集是一个包含每个方向的单元线段的集. |
| 41 | The question is how small a Kaikea set could be. | 问题是Kaikea的装置可能很小 |
| 42 | The Kaikea set conjecture states that any Kaikea set should have maximal dimension. | Kaikea设定猜想指出,任何Kaikea设定应具有最大维度。 |
| 43 | Joined with Josh Zao, we showed that any Kaikea set in the three-dimensional space has dimension three. | 我们和Josh Zao一起表明,三维空间中的任何凯凯亚设定都有三维. |
| 44 | If there exists a count example to the Kaikea set conjecture in higher dimensions, | 如果Kaikea设定在更高维度上的猜想存在一个计数例子, |
| 45 | then some functions, for example, the solutions to the linear Schrodinger equation might be surprisingly large. | 例如,线性Schrodinger方程的溶液可能非常大。 |
| 46 | Another conjecture is about first and third sets, which are more general than Kaikea sets. | 另一种猜想大约是第一和第三套,它们比凯凯亚套集更为笼统. |
| 47 | So instead of containing a unit line segment in every direction, | 而不是每个方向都包含一个单位线段 |
| 48 | it contains subsets of unit line segment of fixed dimension in any direction. | 它包含任何方向固定尺寸的单元线段的子集。 |
| 49 | In New York, there is a beautiful botanical garden. | 纽约有一个美丽的植物园. |
| 50 | The greenhouse is very humid. | 温室非常潮湿. |
| 51 | It reminds me of the climate of Guilin. | 这让我想起桂林的气候. |
| 52 | Every time when I come back home, I feel rejuvenated. | 每次回到家,我都会感到恢复活力. |
| 53 | And often I will go for a walk with my parents in the park. | 我常常会和父母去公园散步 |
| 54 | Guilin is a very beautiful and relaxed city. | 桂林是一个非常美丽和放松的城市. |
| 55 | Sometimes it's nice to explore other things than math. | 有时探索数学之外的其他事物也不错. |
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