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Asking ‘why’ while doing maths
Author: Afdeling Navorsingsontwikkeling, Division for Research Development
Published: 04/11/2019

​​The story goes that physicist Albert Einstein lamented not having a solid enough mathematical grounding with which to fully explain some of the ideas he was working on in later life. This Einstein anecdote made such an impression on Prof Cang Hui that as a student he pursued mathematics further, rather than physics, a subject he had excelled in since childhood. The decision turned out to be a win for the field of biology and ecology. Hui has since added much mathematical thought to environmental complexities such as climate change, pollination dynamics and other chunks of Big Data with a biological or ecological twist.

To that more than 200 papers, two books, eight chapters and 12 PhD students successfully supervised attest. In 2011 Hui received an Elsevier Young Scientist Award. Based on his h-index, the B2-rated researcher counts among the top 10 researchers in mathematics in South Africa.

Hui joined Stellenbosch University (SU) in 2004 as a postdoctoral researcher and is currently a core member of the Centre of Excellence for Invasion Biology. Since 2014 he has been appointed as the South African Research Chair in Mathematical and Theoretical Physical Biosciences in the Department of Mathematics and is also affiliated to the African Institute for Mathematical Sciences (AIMS, Muizenberg).

He is also the next speaker in the Division of Research Development’s Forward with Research Impact lecture series and will be talking about mathematical games between plants and their mutualists on Wednesday 5 November at 13:00 at the SU Museum.

The Einstein moment

Hui, the youngest of two children, was born in Xi'an in northwest China in 1977, the year in which the Chinese Cultural Revolution ended. His parents were academically minded but because of the political climate of the day did not have the opportunity to pursue studies.

Hui, on the other hand, did. From an early age, he was interested in how physics could help explain to him how the world works. He became a member of the Chinese Physical Society at age twelve.

“I really enjoyed physics, and the kind of questions it could answer. It was not only about how it could be used to calculate things, but how it could also be used to explain things using the equations,” he remembers.

He read about Einstein’s lamentations while preparing for his matriculation test in 1994, at a time when he was contemplating whether to further his studies in physics or mathematics – both subjects that he excelled in.

He tells more about the excerpt from the writings of another physicist, Arnold Sommerfeld, at the time of Einstein’s 70th birthday, that so influenced himi: “Einstein complained that if he could choose again, he’d have chosen maths first, because his lack of knowledge in the field hindered him from formulating certain things later in life better.

He wasn’t going to make the same mistake as Einstein: “I told myself that if I really wanted to understand the physical world, I firstly had to prepare myself mathematically.”

He never did go back to pure physics, but these days he counts quite a few physicists among his network of collaborators in Europe, North America, China, Australia, and here in South Africa.

A different mindset

Hui describes himself as an applied mathematician by training who has the mindset of not only wanting to formulate or compute things.

“I also want to understand a system and what drives its dynamics,” he explains.

He graduated with a degree in applied mathematics from Xi’an Jiaotong University in 1997 and received an Excellent Undergraduate award. In his final year, he had the good luck that his end-of-year project on epidemiological models with time-variant differential equations was supervised by a renowned biomathematician, Prof Zhien Ma. In the process, he became intrigued with the idea of complex systems, and how these operate.

After completing his MSc in Applied Mathematics in 2001 by modelling metapopulation dynamics in realistic landscapes, Hui was awarded the title of Excellent Postgraduate at Lanzhou University. His PhD in Mathematical Ecology followed at the same university in 2004, this time on the spatial and dynamic complexity found in metapopulations, and how they persist.

During his PhD project, he joined the China Eco-Economy Society to get first-hand experience of the field of biodiversity. He took part in projects by the National Natural Science Foundation of China that took him to river basins and alpine wetlands. His contribution to these projects even saw him winning prizes from his local provincial government.

Studying the environmental side of bio-mathematics wasn’t his first choice, however. During his first years of study, he very much wanted to go into brain science because he viewed it as the “ultimate complex system”. Luck was however not on his side, and as a second choice he started looking at ecological systems and biodiversity.

With the benefit of hindsight, Hui now says: “Today I think that ecological systems are even more complicated than our brains. Our neural networks, once connected, cannot change much and become nearly fixed by the age of seven. Ecological systems, on the other hand, can have numerous numbers of species interacting with and co-adapting to each other

Complex systems

Hui thinks of complex systems in terms of a game with multiple players all wearing the hats of the groups or species they belong to. All are playing the game in such a way that it benefits themselves without the mind of their group. The end results of each of these interactions are quite difficult to keep track of, and to explain.

“Biology and the natural sciences are about life itself. To try and understand it, you need more than just physical explanations or physics. You have to ask how certain phenomena emerge through complex systems. And that’s where maths come in,” he explains quite philosophically.

His academic life of using and creating new models therefore lies on the interface between mathematics and biology. His interests have over the years broadened to proposing models and theories by which to explain emerging patterns in whole-organism biology. When fine-combing ecological data about a particular system or species, he is constantly trying to find out the function and meaning of each species within in a system, and how these influence the many other parts.

One of his students is currently modelling the distribution of African dragonfly species, to get a sense about their future movement in light of climate change. Another is modelling the interactions of species within forests, as part of a major larger international collaboration project. On the local front, he is about to embark on a ten-year-long project looking at the interactions taking place on a species level in a one hectare plot of fynbos in the Jonkershoek Nature Reserve.

“If you think mathematically to formulate a biological system, you first ask what is happening. You also have to understand how, and only then you can ask why,” explains the father of two pre-schoolers who likes seeing how they experience the world as they grow up.

He reckons that in the era of Big Data all research teams worth their salt should have a strong mathematical mind as part of the team.

“Data is no longer the bottleneck when it comes to research. It is about how you are going to use the data, and what you are going to focus on,” he explains. “We need informatics to handle all the gigs of data being collected. We need modellers and biomathematicians to work with it, and to improve our understanding of a system.”