The first Chinese female winner of the American Mathematics Award! She said: I am just an ordinary person

The only Chinese girl who participated in the competition in French was questioned by the examiner because she just passed the test. Now, she has won the 2024 Salem Prize in the United States for her groundbreaking research in mathematics.

Written by | Luffy

Inadvertently, Wang Yilin, who never likes to be labeled, has a label of her own: the first female Chinese winner of the Salem Prize. This is a factual statement that cannot be torn off.

Before her, only two Chinese mathematicians, Terence Tao and Dapeng Zhan, had won this award. Her achievement made her stand out in the male-dominated mathematics world.

The Salem Prize is administered by the Institute for Advanced Study in Princeton and is awarded annually to young mathematicians who have made outstanding contributions to harmonic analysis and related fields. The award citation for the Salem Prize reads: Wang Yilin won the Salem Prize for establishing deep new connections between complex analysis, probability theory, and mathematical physics, especially for his contributions to Teichmuller theory and Schramm-Loewner evolutionary theory.

At 6 a.m. Eastern Time, Wang Yilin connected with "Return to Pu". In the video, she was full of energy, wearing a casual and comfortable Morandi sweater, revealing a literary atmosphere. She spoke softly and at a moderate speed.

Wang Yilin was totally surprised to receive the award. She said, "I am just an ordinary person. I think the Salem Award is an encouraging award. This award can make young researchers who are just starting out more confident to do in-depth research."

Wang Yilin is teaching. Source: provided by me

“Don’t worry about having no friends on the road ahead”

Born in 1991, Wang Yilin grew up in Shanghai, China. She studied at the Affiliated Middle School of Shanghai International Studies University from junior high school, which formed an indissoluble bond with France.

Unlike ordinary middle schools, where the foreign language is English, the Shanghai International Studies University Affiliated High School allows students to freely choose a foreign language to learn. The 12-year-old Yilin chose French. When she was in the first year of high school, the school had a French cross-border exchange program. Many students hesitated because they thought that delaying the study of the first year of high school would affect the college entrance examination. But Yilin was different. She had a great curiosity about this strange country, so she signed up immediately and received the support and affirmation of her parents.

During this year, Yilin studied and lived with French high school students, gaining a deep understanding of French local culture and folk customs. After the exchange program ended, she returned to China to catch up on the lessons she missed in her first year of high school, and her life seemed to be back on track.

The turning point came in the third year of high school. My mother accidentally learned about the French Ministry of Education's enrollment project from a colleague and secured a place for Yilin in the selection test. The selection test consists of two rounds, a written test and an interview.

"During my exchange, I learned about the high-quality education in France, which is almost free (some schools even pay all students a salary). I thought I might as well give it a try. Because I didn't receive any math competition training in high school, and the test was competition questions, I found out that I had never seen any of the questions in the exam. I worked hard on one part, but didn't have time to look at the other part, so I could only barely pass." Yilin laughed as he recalled the past.

She thought the matter was over, but she received an interview notice. During the interview, the examiner said with a dark face, "I gave you the opportunity to interview not because you scored high, but because you were the only one who answered the questions in French. Why did your score so much lower than others?" Yilin was stunned for a moment, and she said to the examiner seriously, "I think I did quite well. These questions are new to me, at least I am confident that I answered all the questions correctly." The examiner was immediately amused. So, Yilin became one of the admitted candidates.

This year, Yilin was 18 years old, and she went to Lyon Parc High School to study in the mathematics and science preparatory class.

In 2011, she was admitted to the Ecole Normale Supérieure in Paris. This school only enrolls more than 200 students from around the world each year and is a cradle for nurturing elite talents. It has trained a group of scientific and cultural talents who have gone down in history, such as Fourier, Lebesgue, Galois in mathematics, and Jean-Paul Sartre and Michel Foucault in philosophy.

What is quite unique is that the École Normale Supérieure does not award degrees itself. Students of the school must register at a partner university to obtain a degree awarded by the partner university.

Yilin first studied geometry at the University of Paris VI and obtained a master's degree in basic mathematics. Then, she developed a strong interest in probability theory, so she went to the University of Paris XI to continue her studies and obtained a master's degree in probability and statistics. "I have always been a leisurely person. My undergraduate thesis was about analysis, and my master's degree was mainly about geometry. Others may have studied for a doctorate after completing their master's degree, but I felt that I wanted to learn more about other areas, so I turned to study probability theory."

When asked if she had expected to win the award, Yilin said she had not expected it, but she was very happy to hear the news because "the mathematics major is too specialized nowadays, and not many people are interested in and can understand the articles I wrote. I found that my work is recognized and paid attention to by everyone, and I feel like I have no worries about the future."

After the list of winners was announced, Terence Tao immediately expressed his affirmation of her work on Twitter, "Wang Yilin has revealed many new features and methods to study Schramm-Loewner evolution associated with many important random structures in the complex plane. I personally look forward to seeing how her work will advance this field in the future."

Screenshot of Terence Tao's Twitter

“I always wonder why”

So, what specific problems did Wang Yilin’s achievements solve in academia?

Phase transition is an extremely important concept in physics, which describes the change of the state of a system. For example, when the temperature reaches 100 degrees Celsius, water will turn into water vapor; and when the temperature drops to a certain value, the resistance of a superconductor will suddenly become zero. In order to describe different types of phase transitions, physicists have introduced various parameters, such as using a sharp change in density to characterize the transition of water from liquid to gas, and using a change in resistivity to explain the change in the conductivity of a superconductor. These phenomena are usually simulated using lattice point models.

In physics, phase transitions are often associated with a critical value. At this critical point, the macroscopic properties of the system will undergo discontinuous changes, so the study of this critical value is particularly important. Based on the invariance characteristics at large scales, scientists speculate that when approaching the critical state, the local area should also show similar invariance, that is, it conforms to the principle of conformal symmetry.

When using the lattice point model to analyze real problems, a natural question arises: as the grid size tends to infinitesimally small, does it correspond to a continuous limit? If there is such a limit, does it still maintain conformal symmetry?

It was not until the beginning of the 21st century that the outstanding mathematician Oded Schramm first combined the Loewner equation in complex function theory with random processes and pioneered the SLE (Schramm-Loewner Evolution) theory. He not only gave a precise definition of the scaling limit, but also proved that if the random walk on the erasure boundary (LERW) exists and is conformally invariant, it can be described by SLE. Since then, SLE has rapidly developed as a bridge connecting multiple fields such as complex analysis, random processes, conformal field theory, and statistical physics, and has gradually become one of the new research directions that have attracted much attention internationally.

Wang Yilin's work discovered a profound connection between random conformal geometry based on SLE and Kähler geometry of Teichmüller space. She found and proved that the action of SLE is exactly the same as the Kähler potential of universal Teichmüller space.

The research history of Teichmüller space is longer than that of random conformal geometry. Among them, the universal Teichmüller space is an infinite-dimensional complex manifold that contains the Riemann surface Teichmüller space as a complex submanifold. The study of its Kähler structure was originally inspired by string theory. Wang Yilin's research connects several originally distant branches of mathematics and provides a new perspective for understanding the behavior of complex systems. Therefore, her work has attracted widespread attention from probabilists, geometers, and analysts, and invitations to lectures from all over the world continue.

Wang Yilin began to engage in this research in 2015, when she went to the Swiss Federal Institute of Technology in Zurich to pursue a doctorate under the tutelage of Wendelin Werner, the 2006 Fields Medal winner.

Werner is a leader in probability theory and geometric probability. His research on SLE has enabled people to re-understand how random geometric phenomena work in two-dimensional space. He asked Wang Yilin a question, "Look at the large deviation properties of the SLE curve when it passes around a point."

Following this question, Wang Yilin thought of the large deviation of Brownian motion, so she introduced a concept called Loewner energy, which quickly solved the first question raised by her mentor. However, she did not continue to move forward in the direction envisioned by her mentor. In collaboration with Steffen Rohde, she expanded the definition of Loewner energy to quantify the roundness of simple planar closed curves, and proved the root invariance of Loewner energy, even though this invariance is not obvious from the definition.

Many people may stop at this step, but Wang Yilin has been asking why in her mind. She thinks there must be an equivalent definition of Loewner energy, which can directly show its root invariance. For at least two years during her doctoral studies, she has been looking for an equivalent definition of Loewner. Inspired by the results in random conformal geometry, she finally found a simpler equivalent definition. This new expression is very concise, and she believes that predecessors must have studied this expression. So she went to look for the research results of her peers in this area. To her great surprise, she saw the work of Leon A. Takhtajan and Lee-Peng Teo, in which the Keller potential was very close to her expression, perhaps equal?

Professor Shen Yuliang of Suzhou University has also done quite mature research in this area. She consulted Professor Shen and put forward her conjecture, and Shen Yuliang also confirmed that her conjecture should be correct. Standing on the shoulders of giants, she finally proved the equation that links SLE with Teichmüller's theory and completed her doctoral thesis.

"Because I have some background in geometry, I am more familiar with Teichmüller space and Kähler manifold than other probabilists, at least I am not afraid of them," Wang Yilin explained. "During my master's degree, I learned a very wide range of knowledge and tools, and I never thought I would be able to use them, but now they come in handy, which may be one of the reasons for my research results."

She later proved with Marco Carfagnini that the Loewner energy is indeed the action of the SLE ring measure, and in collaboration with Fredrik Viklund, she used the results in random conformal geometry to obtain results about universal Teichmüller spaces. The connection she found was later further extended to three-dimensional hyperbolic manifolds by her collaborators Martin Bridgeman, Kenneth Bromberg and Franco Vargas Pallete.

Wang Yilin said: "A research result is actually the result of multiple complex factors, including the right time, right place and right people. From the initial question raised by my supervisor, to the fact that my research on this path later deviated from my supervisor's research direction, he has always supported me in this direction. He would not insist that I come back to solve the problems he envisioned, but would escort me from the side. I also like to talk to him about my progress and my troubles. His intuition in controlling problems is always very accurate. For example, when I told him that I now have three ideas, he could tell me which one would not work."

“I’m a walnut soaker”

Facing the media's overwhelming exaggeration of "female mathematicians", Wang Yilin said that society has overly labeled women. "Learning mathematics is not easy for anyone. Often, when girls say that learning mathematics is difficult, they attribute it to their gender, and when boys say that learning mathematics is difficult, they attribute it to the fact that they haven't thought it through. In ancient times, only men could take the imperial examinations, so why didn't they say 'women are suitable for liberal arts'? (Laughs)"

Fortunately, Wang Yilin has never been disciplined by stereotypes such as "men are suitable for science and women are suitable for liberal arts" since she was a child. "I have never heard such words at home. It was not until I grew up and talked with others that I realized that girls can encounter so many obstacles in their growth process." She said, "My parents fully support me no matter what I do, and I can pursue anything I am interested in."

The open-minded family environment has cultivated Wang Yilin's confident character. She never doubts her ability. If a problem is not solved, it is not because she is not good enough, but because she is not mature enough. Wang Yilin's parents both work in an architectural firm. At first glance, this has nothing to do with mathematics. "They have never heard of the Salem Prize." But influenced by her mother's excellent aesthetic ability, Wang Yilin has been subtly influenced by the artistic atmosphere. "I always feel that mathematics and art are closely related." In her spare time, Wang Yilin always walks on the streets of Paris to visit art exhibitions, watch old movies, or go into the forest of the institute to embrace nature.

Wang Yilin's life photos丨Source: provided by myself

When talking about her study path, she explained everything as "a certain inevitability in chance", and the driving force behind it was "curiosity". She chose French because of curiosity; she took the selection test because of chance; she devoted herself to mathematics because of her interest; and she built a bridge between two unrelated directions because she couldn't let go of the question in her heart.

It is worth mentioning that Wang Yilin, who is full of curiosity, also had a strong interest in psychology when she was in junior high school, and she always dreamed of studying psychology at Peking University. After arriving in France, she often attended psychology courses.

In the past five years, Wang Yilin has worked in many famous academic institutions. After graduating with a doctorate in 2019, she served as a CLE Moore lecturer at the Massachusetts Institute of Technology in the United States; then, she worked as a postdoctoral researcher at the National Institute of Mathematical Sciences in the United States; in June 2022, she joined the Institut des Hautes Études Scientifiques (IHES) in France as an assistant professor, becoming the first holder of the prestigious assistant professor position at IHES funded by the Simons Foundation. In July 2025, she will go to the Swiss Federal Institute of Technology as an associate professor.

For young researchers, Wang Yilin believes that if they want to go far, they need to have a healthy mentality. "You explore because of your thirst for knowledge, simply because 'we must know, we will know'. Once a person is held hostage by external interests, it is easy to separate himself from his original passion and fail to fully stimulate his potential. Nowadays, many students have too many calculations about their future due to external pressure or peer pressure. I think it is a pity. I hope young people can protect the flame of curiosity in their hearts at all costs. It is more fragile than we think. Competition, pride, fear, and vanity may kill it. Follow your heart, even if you don't have worldly success, you are living your true self, of course, on the premise of having basic living security."

Wang Yilin is not a die-hard person, so she never seems to get mad. She cited the example of Alexander Grothendieck, the founding professor of IHES. Grothendieck is the winner of the 1966 Fields Medal and the founder of modern algebraic geometry. He once said that if you want to crack a walnut, don't think about using various tools to open it immediately, but put the walnut in water and wait for the walnut skin to soften, and the problem will be solved. "I am also a person who likes to soak walnuts. When the time is right, everything will be solved naturally."

Wang Yilin mentioned many mathematicians who had a profound influence on her, but she did not focus on the research results and honors these mathematicians have achieved, but on the qualities of these mathematicians. For example, William Thurston "pays great attention to understanding and is a thinker who likes to share and inspire others"; Maryam Mirzakhani "has a wild imagination, visual expression ability, and deep insight", and her mentor Wendelin Werner "not only has a very unique perspective, but is also committed to maintaining the research ecology in the field of mathematics and guiding the academic community to develop in a healthy direction."

At the end, Wang Yilin said meaningfully, "I am just an ordinary person. I think this Salem Award is an encouraging award. This award can make young researchers who are just starting out more confident to carry out in-depth research work."

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