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7月5日,有着数学界“诺贝尔奖”称号的菲尔兹奖揭晓了,这也是数学界的最高奖项菲尔兹奖揭晓了!2022年,共有4位伟大的数学家获奖。本次获奖名单中包括之前呼声最高的乌克兰女数学家Viazovska,还有一位许埈珥异军突起,成为首个获奖的韩裔数学家。
39岁的许埈珥将Hodge理论引入了组合学,成功证明了几何格的Dowling–Wilson猜想、拟阵的Heron–Rota–Welsh猜想、强梅森猜想,以及发展了洛伦兹多项式理论。(组合代数几何)
小时候数学不好、高中辍学当诗人。后来为生计学做记者,结果在24岁那年偶然听了节菲尔兹奖得主的课,突然就被打通任督二脉,开始学习,在进入数学界15年后,39岁的他登上了数学界的最高领奖台。这是2022年度新晋菲尔茨奖得主许埈珥的传奇经历。
韩国总统尹锡悦在获悉喜报之后,向韩裔美籍数学家许埈珥致贺电,祝其获得菲尔兹奖。尹锡悦表示,韩裔数学家荣获被誉为数学领域诺贝尔奖的菲尔兹奖见证韩国已迈入发达国家行列,这是为数学等基础科学献身的人们所努力的硕果。从小学到研究生在韩国就读的年轻数学家获此奖项更是令人振奋。
尹锡悦对许埈珥挑战人类智慧的极限,扩展数学基础而付出的努力和热情给予高度赞赏。他说,希望许埈珥和国内外数学家们通过活跃的研究活动,成为开启人类智慧新道路的指南针。
许埈珥是谁?
这位韩裔数学家凭什么获得菲尔茨奖?
↓↓↓ 上下滑动,查看摘要稿 ↓↓↓
Most top mathematicians discovered the subject when they were young, often excelling in international competitions.
By contrast, math was a weakness for June Huh, who was born in California and grew up in South Korea. “I was pretty good at most subjects except math,” he said. “Math was notably mediocre, on average, meaning on some tests I did reasonably OK. But other tests, I nearly failed.”
As a teenager, Dr. Huh wanted to be a poet, and he spent a couple of years after high school chasing that creative pursuit. But none of his writings were ever published. When he entered Seoul National University, he studied physics and astronomy and considered a career as a science journalist.
Looking back, he recognizes flashes of mathematical insight. In middle school in the 1990s, he was playing a computer game, “The 11th Hour.” The game included a puzzle of four knights, two black and two white, placed on a small, oddly shaped chess board.
The task was to exchange the positions of the black and white knights. He spent more than a week flailing before he realized the key to the solution was to find which squares the knights could move to. The chess puzzle could be recast as a graph where each knight can move to a neighboring unoccupied space, and a solution could be seen more easily.
Recasting math problems by simplifying them and translating them in a way that makes a solution more obvious has been the key to many breakthroughs. “The two formulations are logically indistinguishable, but our intuition works in only one of them,” Dr. Huh said.
It was only in his last year of college, when he was 23, that he discovered math again. That year, Heisuke Hironaka, a Japanese mathematician who had won a Fields Medal in 1970, was a visiting professor at Seoul National.
Dr. Hironaka was teaching a class about algebraic geometry, and Dr. Huh, long before receiving a Ph.D., thinking he could write an article about Dr. Hironaka, attended. “He’s like a superstar in most of East Asia,” Dr. Huh said of Dr. Hironaka.
Initially, the course attracted more than 100 students, Dr. Huh said. But most of the students quickly found the material incomprehensible and dropped the class. Dr. Huh continued.
“After like three lectures, there were like five of us,” he said.
Dr. Huh started getting lunch with Dr. Hironaka to discuss math.
“It was mostly him talking to me,” Dr. Huh said, “and my goal was to pretend to understand something and react in the right way so that the conversation kept going. It was a challenging task because I really didn’t know what was going on.”
Dr. Huh graduated and started working on a master’s degree with Dr. Hironaka. In 2009, Dr. Huh applied to about a dozen graduate schools in the United States to pursue a doctoral degree.
“I was fairly confident that despite all my failed math courses in my undergrad transcript, I had an enthusiastic letter from a Fields Medalist, so I would be accepted from many, many grad schools.”
All but one rejected him — the University of Illinois Urbana-Champaign put him on a waiting list before finally accepting him.
“It was a very suspenseful few weeks,” Dr. Huh said.
At Illinois, he started the work that brought him to prominence in the field of combinatorics, an area of math that figures out the number of ways things can be shuffled. At first glance, it looks like playing with Tinker Toys.
Consider a triangle, a simple geometric object — what mathematicians call a graph — with three edges and three vertices where the edges meet.
One can then start asking questions like, given a certain number of colors, how many ways are there to color the vertices with the rule that the vertices at each end of an edge cannot be the same color? The mathematical expression that gives the answer is called a chromatic polynomial.
More complex chromatic polynomials can be written for more complex geometric objects.
Using tools from his work with Dr. Hironaka, Dr. Huh proved Read’s conjecture, which described the mathematical properties of these chromatic polynomials.
In 2015, Dr. Huh, together with Eric Katz of Ohio State University and Karim Adiprasito of the Hebrew University of Jerusalem, proved the Rota Conjecture, which involved more abstract combinatorial objects known as matroids instead of triangles and other graphs.
For the matroids, there are another set of polynomials, which exhibit behavior similar to chromatic polynomials.
Their proof pulled in an esoteric piece of algebraic geometry known as Hodge theory, named after William Vallance Douglas Hodge, a British mathematician.
But what Hodge had developed, “was just one instance of this mysterious, ubiquitous appearance of the same pattern across all of the mathematical disciplines,” Dr. Huh said. “The truth is that we, even the top experts in the field, don’t know what it really is.”
许埈珥(June Huh)现在是普林斯顿大学数学系的一名教授。
他出生于美国加州,在2岁时返回韩国后,直到硕士毕业前一直在韩国就读。
他于2007年毕业于首尔大学数理科学系·物理天文学,2009年和2014年分别取得同校数理科学系硕士学位和美国密歇根大学博士学位。
可以说,顶级数学家在年轻时,往往都会在国际比赛中有着出色的表现。然而,许埈珥小时候的数学成绩却并不怎么好:「我对大多数科目都很擅长,除了数学。」
上了高中之后,许埈珥的理想是成为一名诗人,于是他真的就在上高一时辍学去写诗了。
在他进入首尔国立大学,学习物理天文学时,许埈珥甚至还考虑过自己将来去从事科学记者的工作。
直到大学的最后一年,也就是许埈珥23岁的时候,才萌生了对数学的兴趣。而更有趣的是,最初吸引到他的还不是数学本身,而是一个人。
那一年,曾在1970年获得菲尔兹奖的日本数学家广中平祐是首尔国立大学的客座教授。他当时正在讲授有关代数几何的课程,而许埈珥想着正好可以借此开启自己的记者生涯,于是就报名参加了。
一开始,这门课吸引了100多名学生。但很快的,大多数学生就发现,内容实在是难以理解,便纷纷放弃了。「大约三次讲座之后,就只剩下五个人了。」
一下课,许埈珥就会跑去找广中平祐聊天。逐渐地,两人甚至开始共进午餐。每次,许埈珥都想询问一些广中平祐的个人问题,但谈话的最后总是会重新回到数学上。
好在,两人的关系倒是越处越好。本科毕业后,许埈珥也就是顺理成章地开始跟着广中平祐攻读数学硕士学位。2009年,许埈珥在广中平祐的敦促下,申请了十几所美国的研究生院。
虽然有着一封来自菲尔兹奖得主的热情洋溢的推荐信,但许埈珥的数学背景很浅,上过的课程不多,而且成绩还不咋样。于是,除了伊利诺伊大学厄巴纳-香槟分校以外,全部拒绝了他。
不过在入学之后,许埈珥便开始崭露头角。初出茅庐的他,便证明了图论中一个悬而未决40年之久的猜想——Read猜想。
2015年,许埈珥与俄亥俄州立大学的Eric Katz和耶路撒冷希伯来大学的Karim Adiprasito一起证明了Rota猜想。
随后的故事大家也都能猜到了。凭借着对著名的「Read猜想」、「Rota猜想」等数学界难题的验证,以及他卓越的研究成果,许埈珥获得了西蒙斯学者奖、三星湖岩奖、数学新视野奖、布拉瓦尼克国家青年科学家奖等多个奖项。
算下来,许埈珥在拿到菲尔兹奖之前,只在数学这条路上走了15年的时间。再加上之前的这些经历,确实相当的传奇。
‍Hugo Duminil-Copi
是数学家也是运动达人
James Maynard
改进了张益唐「孪生素数猜想」最佳结果一举成名
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