From Doubting Her Ability to Do Math Research to Winning the Fields Medal

After this year's Fields Medal winners were announced, there was a lot of discussion in the community. Wang Hong is the third woman in history, and the first Chinese woman, to receive the award. Some reports described her with labels like skipping two grades, entering Peking University at 16, and earning a PhD from MIT, as if a path like that made winning the medal feel almost inevitable.

But after reading her deeper interviews with Quanta Magazine and other publications, I realized her path was not nearly that linear or smooth. She once doubted whether she had the ability to do mathematical research at all. During her time studying in France, she even spent half a year away from mathematics, taking architecture classes and interning at an architecture firm.

Although she skipped two grades and entered Peking University at 16, she did not get into the math department at first. Only after spending an entire year working in the library did she finally manage to transfer. Even after entering the math department, she found that the people around her always seemed to understand things faster than she did. Since Wang did not come from a math competition background, and Peking University had many Mathematical Olympiad medalists, including Deng Yu, her classmate who also won the Fields Medal this year and had won an IMO gold medal, she did not stand out as an undergraduate.

She even described that period as constantly struggling, where simply surviving felt good enough.

Later, Wang went to Ecole Polytechnique in France for graduate school. Her classroom performance in Paris was actually quite strong, but she still did not believe she was capable of doing mathematical research. So for one semester, she switched to studying architecture and interned at an architecture firm in Paris.

Looking back on that period away from math, Wang said she did not feel much pressure then, but she also did not know what her goal was. So she decided to return to mathematics. After coming back, she decided to stop worrying about whether she was good enough and focus only on deepening her understanding.

When she began her PhD at MIT, Wang chose Larry Guth as her advisor because she had heard him give a talk. In that talk, Guth explained the problems and proof methods so clearly that Wang felt she could understand part of what was going on. That gave her a lot of encouragement.

Choosing Guth as her advisor became a turning point in Wang's research career. She said what stood out most about Guth was not intelligence, but patience and empathy.

When they first started discussing research problems, Guth would often ask questions from a very deep, sometimes unexpected angle. Wang would not know how to answer right away and would simply freeze at the blackboard. Guth would not rush to answer for her or immediately move on to the next question. He would usually just smile, look at her, and wait while she thought it through.

Sometimes Wang would go to Guth with an idea she had not yet organized clearly. Those thoughts might be vague or even contradictory. Guth would not interrupt her, nor would he immediately judge whether the direction was viable. Instead, he encouraged her to say everything that was in her head. First pour out the confusion, then understand the structure inside it together.

Wang later said those conversations gradually taught her how to clarify the ideas in her mind and how to keep pushing deeper. Only when you go deep enough do you discover exactly where an idea is unreliable. That is very different from simply being told, "This direction does not work."

Through that process, Wang slowly built the confidence needed to do mathematical research. This confidence was not "I can definitely solve it." It was "Even if my current idea is still unclear, I know how to keep going."

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