The magic of mathematics
Published on 30 Mar 2022

Professor Phillip Yam (Croucher Scholarship 2001, Croucher Scholarship 2003) is an enthusiastic advocate of mathematics and its power to benefit society, which he has shared through his involvement in the Croucher Science Week since 2017.

“I always dream of using maths to help explain different phenomena, not only in physics, but also in economics, finance, and engineering,” said Yam, Professor in the Department of Statistics, Assistant Dean (Education) in the Faculty of Science, Chinese University of Hong Kong (CUHK), and Co-Director of the university’s Quantitative Finance and Risk Management Science Programme.

Since his schooldays, Yam has adopted an unorthodox approach to learning and problem solving, combining attending formal lessons with his own personal trial-and-error-based self-study and research.

He recalls how his interest in mathematics was triggered by a simple summer vacation assignment while at kindergarten. Yam was given the visual spatial puzzle of trying to cut a round cake into seven pieces, using three straight cuts on the top only, probably his first experience of what he calls “thinking out of the box”.

“Normally, of course, we just cut the cake into six equal segments. When I took a minibus one day, I slid forward on my seat and almost fell when it stopped abruptly. I was only five or six years old but immediately it made me realise I just had to laterally shift down one of the horizontal cuts, just like myself falling down, to make the seventh segment appear in the middle of the cake,” he said.

On completion of secondary school, Yam took a Bachelor‘s degree in Actuarial Science at the University of Hong Kong (HKU), where the courses broadened his horizons from physical science to economics, finance, and even social sciences such as psychology.

His time at HKU also helped him gain a new mathematical perspective to view the real world. He believes that mathematics bridges empirical laws and observations that may not seem intimately connected and helps unify them under one single theory to explain their mechanisms.

Yam fears that current students might not be sufficiently encouraged to explore wider questions or to think beyond the boundaries of exam curricula.

“It was fascinating to see that so many issues in these apparently diverse fields could be appropriately described by partial differential equations [PDEs] and random systems. This is exactly the magic of mathematics, namely the unreasonable effectiveness of mathematics,” he said.

After graduation, Yam was strongly encouraged by Professor Patrick Ng, then head of Mathematics at HKU, to broaden and consolidate his advanced mathematical knowledge through attending Part III of the Mathematical Tripos at the University of Cambridge.

Yam received his first Croucher Scholarship for this master’s degree, which is widely acknowledged as one of the most challenging postgraduate curricula in the world. Having obtained a MASt degree with Distinction together with the E. M. Burnett Prize in Mathematics from Cambridge, he received his second Croucher Scholarship award, and continued to pursue a DPhil in Stochastic Analysis at the University of Oxford.

At Oxford, Yam was supervised by the renowned mathematician Professor Terry Lyons, former President of the London Mathematical Society. This led Yam to work on the theory of rough paths (directly linked to a 2014 Fields Medal and 2021 Breakthrough Prize awarded to Austrian-British mathematician Sir Martin Hairer). The theory focuses on robust and regular solutions of controlled differential systems driven by very irregular paths, such as well-known Brownian motion.

When Yam heard about the Croucher Science Week he was keen to become involved. “I had been the beneficiary of two Croucher awards and just wanted to reciprocate in some way to The Croucher Foundation and to Hong Kong society while learning and sharing something new related to mathematics,” he explained.

Yam received a science communication training in 2017 in presenting engaging complex scientific topics to audiences of different ages and backgrounds, and he started delivering science presentations to primary and junior secondary school audiences in 2018. “I wanted to trigger the interest of the youngsters. I used to have the ambition and now I have a mission,” he said.

He found that another benefit from participating in the programme was the opportunity to interact closely with scholars from unrelated fields and disciplines. It was stimulating to be outside his comfort zone of seminars and conferences in which he only encountered familiar colleagues and those working in closely related fields.

Yam’s areas of interest go beyond rough path theory. He has co-authored the first monograph on mean field games, along with a series of top-tier journal publications on the topic. A mean field game is a sophisticated yet tractable PDE model for interacting behaviour of individuals from various systems commonly found in different disciplines of engineering, natural, and social sciences.

“Mean field games explain quantitatively via PDEs the massive interactive dynamic behaviours of a society,” explained Yam, who is currently focused on how mean field theory can apply to the understanding and improvement of the effectiveness of deep learning.

Deep learning is an important artificial intelligence (AI) technology that mimics the workings of the human brain using layered neural networks to process data for use in detecting objects, recognising speech, translating languages, and decision-making.

A sub-branch of machine learning, deep learning involves the learning of many hidden characteristics at once, drawing from less organised data and without human intervention. Deep learning and AI in general are extremely popular topics in engineering and science, offering an ideal opportunity to engage with school students. 

In a landmark victory for AI, in 2016, South Korea’s Lee Sedol, a world champion of strategic board game Go, lost four out of five games to his computer opponent, Google’s AlphaGo.

“All AI technologies are based on maths and statistics, related to optimisation and dynamical systems,” Yam said. “You can feel the power of AI through AlphaGo, a magnificent combination of computer science, mathematics, and statistics.”

To communicate some of these sophisticated principles and demonstrate the power of mathematics to children as young as eight years old, Yam used a combination of AI and pop music. During each presentation, he played two similar-style music audio clips of pop songs – one composed and performed by the Beatles and the other created by AI.

The students were asked to distinguish which track was composed by a human being and which by AI. Many of them were puzzled and did not know, the experience demonstrating the capability of AI and the power of mathematics and statistics behind it.

“We can’t get into the details of the sophisticated mathematics and algorithms with the younger students, but we can link very powerful AI to the maths and stats behind it,” he said.

Yam also likes to explore the limitations of AI and underlines that, for all its power and potential capability to replace many human daily functions, it may enhance but not totally replace the value of human imagination and creativity. AI cannot yet create new advanced mathematics or ideas, so Yam tries to convey to students that creative problem solving, questioning, and thinking out of the box are more important than ever.

Another key message he likes to convey to school students is to find their own interest and pursue it without hesitation because knowledge, unlike money, will remain with them forever.

Professor Phillip Yam is a faculty member in the Department of Statistics at Chinese University of Hong Kong and Co-Director of the university’s Quantitative Finance and Risk Management Science Programme, and is also Assistant Dean (Education) in the Faculty of Science at CUHK. He holds a Bachelor’s degree in Actuarial Science and an MPhil degree from the University of Hong Kong. He obtained a Master of Advanced Study (MASt) degree in Mathematics, Part III of the Math Tripos, from the University of Cambridge. He also received a DPhil degree in Mathematics from the University of Oxford.  He was awarded two Croucher Scholarships in 2001 and 2003 for his studies at Cambridge and Oxford respectively.

Extended Reading:

  1. Prof. Phillip Yam’s personal profile (The Croucher Foundation): https://scholars.croucher.org.hk/scholars/phillip-yam
  2. Prof. Phillip Yam’s personal profile (The Chinese University of Hong Kong): http://www.sta.cuhk.edu.hk/scpy/