Chinese Mathematicians

 

Chinese mathematicians in US say they have cracked century-old fluid mechanics puzzle

Two young Chinese mathematicians working in the United States, along with an international collaborator, may have solved a century-old problem in fluid mechanics – an area of study that is critical to many engineering fields including hydraulic systems, the design of dams and bridges, and aerodynamics.

In a paper published on March 3 on arXiv, an open-access platform for preprint papers that are yet to be peer reviewed, the trio said they had resolved “Hilbert’s sixth problem” by proving the mathematics of fluid mechanics.

The study was co-authored by Deng Yu, an associate professor of mathematics at the University of Chicago, along with Ma Xiao and Zaher Hani, both from the University of Michigan’s Department of Mathematics.

The breakthrough has triggered discussion on social media, especially in China.

“They solved the century-long problem and brought Hilbert’s sixth problem in the narrow sense to a successful conclusion,” Maths Five Group, an account run by five Chinese PhD students of pure maths in Germany and France, commented on Chinese social media on March 5.

At the intersection of physics and mathematics, researchers ask whether it is possible to establish physics as a rigorous branch of mathematics by taking microscopic laws as axioms and proving macroscopic laws as theorems. Axioms are mathematical statements that are assumed to be true, while a theorem is a logical consequence of axioms.

Hilbert’s sixth problem addresses that challenge, according to a post by Ma on Wednesday on Zhihu, a Quora-like Chinese online content platform.

In 1900, David Hilbert, a German mathematician and one of the most influential of his time, famously presented 23 problems at the International Congress of Mathematicians. The sixth one was intended to reduce to a system of basic axioms, or truths, those branches of physics in which mathematics was prevalent.

According to an article published on Fanpu, a Chinese platform that specialises in popularising basic sciences – especially physics and mathematics – the key to Hibert’s sixth problem is to derive fluid mechanics equations from microscopic Newtonian mechanics. Deng’s team set out to tackle this challenge.

Deng and Ma, both Chinese-born, showed outstanding mathematical talent at a young age.

Deng, the study’s first author, grew up in Shenzhen in southern China. He won the gold medal in the 2006 International Mathematical Olympiad and was admitted to the prestigious Peking University the following year to study mathematics.

In 2009, midway through his undergraduate studies in Beijing, Deng transferred to the Massachusetts Institute of Technology (MIT), where he received his bachelor’s degree two years later. He then earned his PhD from Princeton University in 2015.

As for Ma, according to a social media account maintained by alumni of the University of Science and Technology of China (USTC) in Anhui province, he was admitted in 2015 under a special training programme for talented students named after early 20th century mathematician Hua Luogeng.

After receiving his bachelor’s degree from USTC in 2018, Ma also headed to Princeton for graduate studies and received his PhD in 2023.

With reference to the team’s latest paper, the Fanpu article pointed out that even experts in the field of partial differential equations “need a long time to study and review before they can make an evaluation”.

It added that although their results were still awaiting a long peer-review process, the opinion of the academic community was “generally optimistic”.

Last month, Chinese mathematician Wang Hong – an associate professor at New York University’s Courant Institute of Mathematical Sciences – solved an “infamous” geometry problem called the “Kakeya conjecture within three dimensions”.

Wang and her collaborator Joshua Zahl, an associate professor at the University of British Columbia, also presented their milestone findings in a preprint paper on arXiv on February 24.

“With Professor Wang’s breakthrough on Kakeya and now the solution of Hilbert’s sixth problem, this year can be said to be a year of miracles for the Chinese mathematical community,” the Maths Five Group commented on social media.

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