A student who dropped out of school for poor math wins this year’s Fields Medal

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Text/Yang Jingfengse

Source: Qubit (ID: QbitAI)

When I was young, I was bad at math and dropped out of high school to become a poet.

Later, I worked as a reporter for livelihood studies. At the age of 24, I accidentally listened to a class given by a Fields Medal winner. Suddenly, I was connected to the second line of Ren Du and began to study mathematics.

This is the legendary experience of the new Fields Medal winner Xu Xinger – entering the mathematics world for 15 years and reaching the highest podium.

Some people say that it is as impossible as a person picking up a tennis racket at 18 and winning Wimbledon at 20.

It is worth mentioning that this is another Asian scientist who has won this honor after Qiu Chengtong, Tao Zhexuan and Wu Baozhu.

15 years of sharpening a sword

The reason for this award is that he introduced the ideas of Hodge’s theory into combinatorics and proved several conjectures.

Including the Dowling–Wilson conjecture for geometric lattices, the Heron–Rota–Welsh conjecture for matroids, the strong Mersen conjecture, and the development of Lorentz polynomials.

The most well-known work is that he developed a new way of thinking, explaining and proving the Heron–Rota–Welsh conjecture (hereinafter referred to as the Rota conjecture).

The Rota conjecture was proposed in 1971, and the research object is the combination object of “matrix”.

In simple terms, take a graph composed of points and lines as an example, color the vertices of a graph, and two adjacent points have different colors. With a specified number of colors, the probability of coloring can be calculated by a characteristic polynomial equation.

The Rota conjecture predicts that the coefficients of the characteristic polynomial of any matrod are always log-concave.

It is worth mentioning that the other two collaborators, one who gave up mathematics because of being a chef, and the other is a senior rock music lover, ended up solving a world-class problem by accident.

It was for this work that he became an instant hit, and soon received the title of a long-term researcher at the Institute for Advanced Study (IAS) in Princeton.

Before him, only three young scientists had been awarded the title.

Two scientists, including Wu Baozhu, won the Fields Medal.

So at that time, at the age of 34, he was already recognized as the favorite winner of the Fields Medal.

It’s hard to imagine that such a big cow-like life experience would happen to a mathematician who was halfway through his career.

In fact, at the beginning of his mathematical journey, even with Fields Medal winner Hironaka Hironaka (1970 winner), he was still not seen by the rest of the academic world.

After completing his master’s degree in this school, he applied for more than a dozen doctoral programs in the United States.

Unfortunately, the research experience is really mediocre, and the postgraduate courses are also mediocre. Even if there is a recommendation letter from a big cow, American universities are not impressed, and traditional strong schools are even more rejected. In the end, he only got one offer – UIUC.

But soon, things came to a turning point.

Perhaps it was because he became a monk halfway through, so from the very beginning, his thinking was different from that of ordinary mathematicians.

In the first semester, he discovered that he could use the singularity theory, that is, the knowledge he learned in Hironaka Heisuke, to prove many properties of graph theory.

Among them is a famous conjecture, the Reed conjecture, which can also be said to be a special case of the Rota conjecture. The two are very similar, but the subjects of the studies are not identical.

One is a graph and the other is a matrix.

Before that, he didn’t even know the existence of this conjecture.

He posted the proof process online, and the University of Michigan invited him to give a presentation.

At that time, a mathematician, Mircea Mustaţă, gave high praise, and later became Xu Xianer’s doctoral tutor.

In a way, the report is beautiful and clear; it hits the spot right off the bat.

It’s rare for someone who’s just starting out in graduate school to make such a clear report.

After the meeting, the University of Michigan immediately invited him to transfer. So he came to Michigan for a Ph.D. in 2011, less than two years after he came to the United States.

At this time, after having proved Reed’s conjecture, he began to move on to the next battlefield, that is, the advanced version of Reed’s conjecture – Rota’s conjecture.

After his Ph.D. at Michigan, he worked as a researcher at IAS, Stanford University, and is now a professor of mathematics at Princeton University.

To this day, he also returns to South Korea to study every summer, which is the origin of everything.

6 years in university

In 1983, Xu Xinger’s parents gave birth to him when he was a graduate student in California, USA.

When they were 2 years old, the family returned to South Korea, where his father taught statistics at Korea University and his mother taught Russian at Seoul National University.

According to Quanta Magazine, school was a pain for Xu Xianer because he couldn’t concentrate in class and couldn’t learn anything.

On the contrary, he likes to read books by himself. He has read all 10 volumes of a biological encyclopedia, and has also touched a mountain near his home.

Mathematics is also a less interesting thing for it. He chose to copy the answers to the practice questions his father gave him.

When my father knew it, he tore up the answer, and he went to the bookstore to copy the answer.

A bad math score in elementary school made him “rotten” completely.

In the blink of an eye, at the age of 16 years old, the “emotional” Xu Xianer chose to drop out of school to write poetry:

I literally cry when I hear good music. “

I knew I was smart, but couldn’t prove it with grades, so I started writing poetry.

At the time, he wrote something about nature and his own experiences, and wanted to finish it all within two years before going to college.

However, he found that the writing process was a bit painful and depressing, and he just liked the aura he had after becoming a great poet, plus he could not support himself by writing poetry,

After careful consideration, I still went back to school to finish high school and take the university entrance exam.

Xu Xianer was 19 years old when he entered Seoul National University, which is not too late, but he still felt very confused: he didn’t know what he wanted to do, and he didn’t know what he was good at.

He chose to major in astronomy and physics because he wanted to be a science reporter, but ended up skipping classes frequently and retaking multiple courses.

I’m probably lost.

At the age of 24, his classmates had already graduated, but he had not yet, and he abruptly read the sixth year.

But it was a coincidence, “Fortunately, he hasn’t graduated yet,” and he met Hironaka, a Fields Medal winner who came to the school to visit and give lectures.

Because he wanted to make this big celebrity his first interview, he took his algebraic geometry class.

Unexpectedly, he was attracted by the teacher’s charm, and he found that the course itself was also very interesting: not as “smart” as ordinary undergraduate courses, but rather “simplified”.

Open up, the math seal is lifted!

He increasingly felt that mathematics was so interesting and different from writing poetry:

In mathematics, you will not pay too much attention to yourself, and you can freely find “beauty outside yourself”, and this beauty is an objective and real thing that can open your heart more than writing.

At the same time, unlike the period when he was quite a poet, studying mathematics also prevented him from always seeking external approval.

In this way, Xu Xianer became the most active student in Guangzhong Pingyou’s class——

At that time, after a few weeks in a class of 200 students, there were only five students left, and he persevered until the end.

Guangzhong Pingyou saw Xu Xun’er’s potential, and he was also swept away.

In this way, Xu Xinger and the teacher ate together, exchanged mathematical ideas, and especially learned Hodge’s theory from him.

Even when Hiroyuki Hiromaka returned to Japan, Xu Xianer also followed.

ps. Interestingly, Xu Xianer took the initiative to go to Hiro Naka Pingyou for lunch at first, mainly hoping to ask some of his personal information as interview material. As a result, Hiro Naka Pingyou always shifted the topic to mathematics.

However, Xu Xianer pretended to understand, and the professor recalled the incident later, saying that he really didn’t remember that he didn’t understand at all.

Obsessed with math, living off frozen pizza for months, wife giving birth and still solving problems

In fact, in addition to the “twisted” mathematical enlightenment experience mentioned above, Xu Xianer also has some interesting episodes.

Many who have worked with him describe him as very humble and down to earth.

When he learned that he won the Fields Medal, he said that he was really happy, but in his heart he would doubt whether he was really so good?

When interviewed by Quanta Magazin reporters, he found that he actually speaks slowly, uses his words carefully, pauses frequently, and expresses himself in a very peaceful, calm way.

Here’s what another collaborator had to say about him:

Xu Xianer is a person who is not easily excited. If you talk to him about calculus for 5 minutes, you will think that this person may not even pass the qualifying test.

But in fact, he was taking a deeper look at some seemingly simple concepts that later turned out to be useful.

In life, Xu Xianer prides himself on being a person who can tolerate repetition and maintains the same routine every day.

He has very few things in his office and often works in the noisy children’s section of the public library, where quiet places make him doze off.

Obsessed with math, he doesn’t want to waste time cooking, and has been living off frozen pizza for months.

After graduating from my doctorate, I moved to catch up with the winter, and there was no blanket at home.

He thought the shopping center was too far away and was a waste of time, so he bought ten pieces of cloth + a huge staple at the nearby drugstore and made himself a blanket.

…

So much so that the girlfriend he met when he was studying for a master’s degree in South Korea came to see him and found that his “survival skills were so worrying”, he hesitated to marry him.

After getting married, he was still doing math problems when he gave birth to a child…

Fortunately, after the birth of the child, Xu Xianer “converged” a lot, and he can also put down time to play with the child and do housework.

What doesn’t change is that Xu Zhener can only concentrate on work for a few hours a day.

His wife described him: “Others work for an hour, take a 5-minute break, he spends an hour doing other things, and then concentrates for 5 minutes, 10 minutes.”

Another female mathematician won this year

The wonderful story of Xu Xianer, a mathematician, is over. The other three mathematicians who won the award with him today are also worthy of attention.

The first was James Maynard, a professor at the University of Oxford, whose research direction was number theory.

Citation: The 2022 Fields Medal has been awarded for contributions to analytic number theory, which have resulted in significant progress in the understanding of the structure of prime numbers and the Diofen diagram approximation.

I believe that many of them are already familiar with him. He has won the Cole Award, the “highest award in number theory”, and even Tao Zhexuan, another Fields Medal winner, sighs with his method of proving the twin prime conjecture.

The second is Professor Hugo Duminil-Copin from the University of Geneva, Switzerland/Institut d’Advanced Sciences in France, whose research direction is probability theory.

Reason for award: For solving long-standing problems in the probability theory of phase transitions in statistical physics, especially in the three- and four-dimensional domains.

The last is Maryna Viazovska, a Ukrainian mathematician at the Swiss Federal Institute of Technology in Lausanne.

She is the second female mathematician in history to win this award (the first was the 37-year-old Iranian mathematician Maryam Mirzakhani in 2014), and her research direction is the same as Xu Xinger, which is combinatorial geometry.

Citation: For her proof that the E8 lattice provides the densest packing under the same sphere in 8-dimensional space, and for further contributions to related extreme value and interpolation problems in Fourier analysis.

Finally, so far, a total of 64 mathematicians have won the Fields Medal, most of them are Americans and Europeans, and there are very few Asian winners:

So far, there are 11 people who are well-known besides our Professor Yau Chengtong (awarded in 1982), including Vietnamese mathematician Wu Baozhu (2010) and Chinese mathematician Tao Zhexuan (2006).

The latter two have won gold medals in the same IMO competition at the same time.

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