Associate Professor Vincent Tan’s work gets a spotlight by NUS for International Day of Mathematics

Most of Assoc Prof Vincent Tan’s work is theoretical in nature, but stems from real-world needs and has applications in areas such as machine learning and biology.

Associate Professor Vincent Tan (DesCartes Program, WP3): Discovering the elegance of mathematics

As a kid, Assoc Prof Vincent Tan gravitated toward puzzles that, though challenging, had particularly elegant solutions. He couldn’t have known it at the time, but this eye for elegance would be a major driving force behind his career.

In school, Assoc Prof Tan’s excellent track record in mathematics and science won him a scholarship to study engineering at Cambridge University. In his third year, taken by the “elegance of the algorithms and theorems in signal processing”, he decided to specialise in electrical engineering as it was “the most mathematical of the engineering disciplines”. He went on to pursue a PhD degree in electrical engineering and computer science from the Massachusetts Institute of Technology.

He returned to Singapore to do part of his post-doctoral training at the Agency for Science, Technology and Research (A*STAR) and later took on a tenure-track position as an Assistant and then Associate Professor at the Department of Mathematics and the Department of Electrical and Computer Engineering (ECE) at NUS. Along the way, however, his passion for elegance would bring him to one of his biggest career moments.

All forms of electronic and wireless communication occur over channels that are inherently noisy and, as a result, have fundamental limits on the amount of information that they can transmit. In 1948, American mathematician Claude Shannon defined this maximum amount of information—known as the capacity—which has since served as a theoretical target for research groups to strive for.

 “While elegant, Shannon’s channel capacity is a so-called asymptotic notion,” Assoc Prof Tan explained, adding that very long codes are needed to achieve it, which can be highly impractical in real-world settings.

With fellow ECE Associate Professor Marco Tomamichel, Assoc Prof Tan significantly extended Shannon’s theory to “provide a more refined benchmark for communication engineers and code designers”. Their work has already served as a benchmark for new families of codes and could lead to better communications technologies in the future.

As with elegance, this drive for applicability also underpins much of Assoc Prof Tan’s career. “Most, if not all, of my work is theoretical and mathematical in nature,” he said. However, his research questions almost always stem from real-world needs and potential applications.

Mathematics, after all, is the foundation on which the applied sciences are built on. Citing ChatGPT as an example, he elaborated, “The inner workings of ChatGPT is machine learning, and specifically generative models. The amount of mathematics that goes into designing such a complex model that can give us such high-quality text is simply mind-boggling!”

In fact, mathematics is also responsible for safeguarding our transactions when we use our credit cards. They rely on secure data transmission enabled by “the practical difficulty of factoring a large number into prime numbers,” Assoc Prof Tan explained.  

“Thus, an area as esoteric as number theory has immense practical applications,” he said. “Mathematics is all around us.”

Source: NUS News