Finding Structure in a Noisy World

For world-renowned mathematician Professor Hà Văn VŨ, the beauty of mathematics lies not in abstraction, but in its quiet presence everywhere. His work, spanning combinatorics, probability, and random matrix theory, might sound remote from daily experience, yet its fingerprints are all around us: navigation apps, recommendation engines, search algorithms, and the foundations of machine learning. His arrival at HKU marks both a professional turning point and a personal return to Asia. 

 

Rather than viewing mathematics as an esoteric pursuit, Vũ sees it as something woven into the fabric of modern life. “Probability is the mathematics of uncertainty,” he begins. “Large language models are essentially learning probability distributions from data. Combinatorics, meanwhile, is the mathematics of structure and efficiency.”

To the layperson, these fields can feel remote, but Vũ describes them as the foundation beneath countless modern systems: search engines, navigation tools, recommendation algorithms, and communication networks. Before an algorithm can optimise a network or interpret a data pattern, the mathematics of that structure has to be understood. “In everyday life, the impact of these areas of mathematics is often invisible, but they are everywhere,” he says with a gentle shrug, as if stating the obvious.

It is this combination of modesty and clarity, a belief that complex ideas can and should make intuitive sense, that has shaped much of his career, from early breakthroughs to his recent move to Hong Kong.

 

Some mathematicians become known for depth, others for breadth; Vũ is unmistakably both. His career is defined not only by the problems he has solved, but by the way he approaches them. Among his best-known achievements is the proof of the Circular Law, a problem that sat unsolved for more than fifty years. The symmetric case had been settled by Nobel Laureate Eugene WIGNER in the 1950s, but the non-symmetric version resisted classical methods. To solve it, Vũ and his long-time collaborator Terence TAO ventured across mathematical landscapes seldom brought together: numerical analysis, combinatorics, and additive number theory.

“It was an exciting and rewarding journey across very different mathematical worlds,” he recalls. “It involved learning new techniques, making unexpected connections, and gradually watching the pieces of the puzzle come together.”

This breakthrough, along with solutions to problems such as the Erdős–Folkman conjecture, the Four Moment Theorem, and advances in random graph theory, earned him international acclaim, including the SIAM Pólya Prize and the Fulkerson Prize, two of the highest honours in his fields.

Yet the way he speaks about these achievements is disarmingly modest. For Vũ, the real reward is the moment of clarity that emerges after long uncertainty, the instant when disparate ideas align, and something previously opaque becomes suddenly, beautifully comprehensible. In his words, it is the experience of “watching the pieces of the puzzle come together” that keeps his curiosity alive.

 

While many academics pivot toward application-driven research in the era of AI, Vũ sees deeper foundational questions emerging, particularly around noise. “Real-world data is noisy,” he says. “I want to understand how that noise changes the output of the most important algorithms in practice. When decisions are made using only noisy observations of the ground truth, how accurate and reliable are those decisions?”

These questions, deceptively simple, touch the heart of modern society’s greatest technological challenges. As models grow more complex and data grows more abundant, the reliability of algorithmic decision-making becomes ever more crucial: in healthcare, finance, infrastructure, and beyond.

In his view, this is where fundamental mathematics becomes indispensable. “In the era of AI and big data, fundamental mathematics will become even more important, not less,” he says. Many industry leaders echo this sentiment, he notes, pointing out that as AI automates routine coding, deep mathematical understanding becomes the real differentiator.

“This is an especially exciting period,” he reflects. “The way we learn and conduct research may change substantially.”

 

Vũ describes his early months at HKU with the freshness of someone still settling into new rhythms, albeit as a scholar whose standing and accomplishments are already firmly established. Hong Kong’s proximity to Hanoi allows him to continue supporting educational initiatives in Vietnam, while HKU’s growing strength in mathematics offers fertile ground for building something new.

“HKU is widely recognised as one of the leading universities in Asia,” he says. “I hope we can build a strong and visible school of probability and combinatorics, one that attracts outstanding students from around the world.”

His vision extends well beyond his own field. He speaks enthusiastically about forging closer collaborations among the computer science, engineering, and applied mathematics groups, drawing on experiences from Yale and the Yale Institute for the Mathematical Foundations of Data Science. As he speaks, ideas for joint seminars, collaborative programmes, and shared problem sessions surface effortlessly, each delivered with a quiet but unmistakable excitement.

Teaching is just as central to his mission. “Students should first understand the big picture,” he explains. “Mathematics should feel meaningful. Once that perspective is in place, we focus on building the technical foundations that will serve them for years to come.”

Throughout the conversation, this theme of the interplay between noise and structure keeps resurfacing. Whether speaking about his research, his teaching, or his hopes for Hong Kong, Professor Vũ returns again and again to the same quiet conviction: that beneath the apparent disorder of modern life lies a deeper order waiting to be understood. And at HKU, he is ready to help uncover it.