Summary of Key Points
At the 2026 International Congress of Mathematicians, two alumni from Peking University's class of 2007, Wang Hong and Deng Yu, both won the Fields Medal (the highest honor in mathematics) – marking the first time in history that mathematicians from the same country and the same class have achieved this distinction. Wang Hong solved the century-old geometric problem known as the "Hanging Valley Conjecture," while Deng Yu provided a crucial proof for Hilbert's Sixth Problem. Academician Shing-Tung Yau believes that China will become a mathematical powerhouse in the next 5-10 years, but he also pointed out the limitations of the current education system on fostering innovative thinking.
1. Historical Breakthrough: Why is it so remarkable that two alumni from the same university and class won the Fields Medal?
The Fields Medal is considered the "Nobel Prize" of mathematics, but it is even more prestigious, awarded every four years to young mathematicians under the age of 40 (with a maximum of four recipients globally). Both Wang Hong and Deng Yu were born around 1990 and are alumni of Peking University's class of 2007. This is the first time in history that two individuals from the same country and class have received the award simultaneously! This is not coincidental; it indicates that China's cultivation of mathematical talent has evolved from focusing on individual geniuses to producing a cluster of outstanding mathematicians, demonstrating a qualitative leap in our basic science education.
2. Wang Hong’s “Hanging Valley Conjecture”: What’s the use of solving a century-old geometric problem?
The Hanging Valley Conjecture is a geometric challenge that was posed in 1917. Simply put, it asks whether it is possible to use a finite area in three-dimensional space to allow a needle to rotate 360 degrees and cover all directions. It had already been proven impossible in two dimensions, but the solution in three dimensions remained elusive. Wang Hong’s team provided a proof in a 127-page paper, which not only solved this geometric problem but also has implications in various fields such as signal processing (how to improve mobile phone signal transmission) and combinatorial geometry (optimizing the arrangement of objects). This discovery offers new mathematical tools and opens up additional research directions.
3. Deng Yu’s Contribution to Hilbert’s Sixth Problem: A bridge from the microscopic to the macroscopic world
Hilbert’s Sixth Problem was posed in 1900 as part of the effort to mathematize fundamental physical theories. Deng Yu provided a crucial proof connecting microscopic particles with macroscopic phenomena. For example, we know that gases are composed of molecules (microscopic), and gas diffusion is a macroscopic phenomenon, but there was no rigorous mathematical evidence explaining how the movement of microscopic particles leads to macroscopic behavior. Deng Yu’s proof fills this gap, which is essential for physics and engineering applications (such as engine design and weather forecasting), allowing for more accurate predictions using precise mathematical models.
4. Shing-Tung Yau’s Vision: Why can China become a mathematical powerhouse?
Academician Yau cites two reasons:
- Comprehensive coverage of fields: Twenty-eight years ago, Chinese mathematicians focused on only a few areas; now, achievements are being made in number theory, algebra, geometry, and all other fields.
- Abundant talent: Chinese children around the age of 12 possess talents and cognitive abilities comparable to their European and American counterparts, and there is a large pool of potential candidates. If even one-third of them become successful mathematicians, it would be a tremendous asset for the country.
5. The Concerns about Education: Why do “standard answers” stifle innovation?
Academician Yau emphasizes that the essence of mathematics lies in the existence of multiple solutions to problems – one problem could have ten different approaches, each potentially leading to new branches of mathematics. However, the current education system only allows for one standard answer. Students become accustomed to finding the optimal solution within a predefined framework, which prevents them from developing the ability to ask new questions and explore new avenues of research. For instance, in math problems, teachers often limit students to using a single method, preventing them from thinking creatively. Original innovation requires this kind of unstructured thinking.
This news report highlights the achievements of these two mathematicians but also reveals the potential for China to become a mathematical powerhouse. However, to truly achieve this goal, the issue of “standard answers” in education must be addressed. After all, innovation is about breaking with conventional approaches, not following them rigidly.