Best of the best

2009-02-23 00:00

IT’S official. Pietermaritzburg is home to some of the finest scientific minds in the world. Among these are mathematician Michael Henning and biologist Steven Johnson — both on the local campus of the University of KwaZulu-Natal — who late last year received an A-rating from the National Research Foundation.

Their rating brings to five the number of A-rated academics at UKZN. The others are professors Pat Berjak (cell biology), Rob Gous (animal and poultry science) and Michael Chapman (English).

The A-rating is given to researchers who are “unequivocally recognised by their peers as leading international scholars in their field”. Many of South Africa’s top universities promote themselves to staff and students on the basis of their tally of rated academics.

For 44-year-old Henning, the A-rating is the fulfilment of an 18-year-long goal. Specialising in graph theory — a major area of combinatorics and discrete mathematics loved by problem-solvers — Henning has published over 250 peer-reviewed papers since 1991, which is a notable achievement considering it can take up to two years for a paper to be reviewed because some are so complicated that they have to be digested in small bits.

Today, Henning is one of 25 to 30 graph theorists in South Africa and part of an international community of pure mathematicians looking for “open” or unsolved problems and seeking “beautiful proofs” for their solutions.

Although he doesn’t look for applications for his work, Henning says graph theory can be used in the planning of such prosaic systems as traffic-light networks, mail delivery and rubbish collection routes.

Attracted by graph theory because “it’s easier to get into than other types of maths where it may take a couple of years just to explain the problem”, Henning says an unsolved or “open” problem in graph theory is easy to state, but may still take years to solve without any guarantee of a solution.

He cites the famous example of Fermat’s Last Theorem, a maths problem which confounded mathematicians for about 350 years and which was finally proved in 1995 by Princeton’s Professor Andrew Wiles — after a lifelong fascination with the problem and seven concerted years of secret work.

And then there are problems for which the answers are known, but there is no known mathematical proof, like the four-colour map problem which dates back to 1852. According to Henning, every planar map of connected countries can be coloured using four colours in such a way that countries with a common boundary segment (not just a point) receive different colours. “It is amazing that such a simply stated result resisted proof for one-and-a-quarter centuries, and even today it is not fully understood,” says Henning. “In 1976, Appel and Haken announced that they had verified the Four Colour Problem. However, 1 200 hours of computer time were required to perform extensive computations on a part of their ‘proof’ and cannot be checked by humans.”

Maths is the opposite to fishing for the “big one”, says Henning. “We require tiny proofs for mathematical theorems which should be expressed as simply and elegantly as possible. To solve a problem is the first step. Then you move on to provide the ‘beautiful proof’ following the dictum of G. H. Hardy that there is no permanent place for ugly mathematics.”

According to Henning, you don’t need expensive equipment to do maths. “Your biggest expense is flying overseas to attend conferences to keep abreast of the latest developments and to work with other mathematicians. Working in a team speeds up the problem-solving process and enhances the research experience.”

Henning’s first contribution to the prestigious Journal of Graph Theory was the product of a discussion with a colleague during a flight from Boston to Chicago. “We didn't write a thing down. We just talked through the issues and wrote it up when we arrived at the other side. It’s the purest form of research since it comes from the mind. All you need is time.”

Although he has a reduced teaching load this year, research time for Henning is always a challenge, which explains why his next goal is to be awarded an NRF chair — a fully sponsored research position which will allow him to focus squarely on research.

Currently, he’s co-authoring two books on graph theory. Other goals are to retain his A-rating, which is reassessed every five years, work in a university for at least another 20 years, and to plough through his “top 20” list of maths problems he’s “dying to solve”.

Where does he source the strength to see a research problem to the end? “For me, the strength comes from within. Christ in me, my hope of glory. One does not create mathematics. One discovers it,” he says.

This year is set to be a busy year for Steve Johnson who holds the South African research chair in evolutionary biology sponsored jointly by the NRF and the Department of Science and Technology. Johnson has been invited to speak in Zurich, London and other cities where the 200th anniversary of Charles Darwin’s birth and the 150th anniversary of the publication of The Origin of Species are being celebrated.

“It’s a good year in which to hold such a chair,” says the 41-year-old botanist. “And while my A-rating is significant, the chair has already put me in the fortunate position of being able to focus on my research.”

Johnson’s field is pollination biology, the study of interactions between flowers and their pollinators. “I look at how new plant species can arise as a result of selection imposed by their pollinators. I am also interested in documenting how important these animals are for plant conservation,” says Johnson. It’s a multidisciplinary field which spans botany, entomology and the chemistry of floral scents. “Our research helps to explain how plants evolve, because the adaptations of flowers are a critical part of that process.”

South Africa is an exciting place for an evolutionary biologist. Outside of the South American tropics where infrastructure is relatively underdeveloped, Johnson says South Africa is one of the richest “outdoor laboratories” in the world, offering 23 000 species of plants and a wide diversity of animal species.

The country also attracts international attention from biologists because the interaction between South African plants and their animal pollinators is “unusually specialised”, meaning one plant species can have a single pollinator, which also makes it more vulnerable to extinction.

Thus Johnson’s work has important ecological and conservation implications, highlighting how plants are disturbed by changes in the environment, and human activities such as forestry and agriculture.

“You can see it in the KwaZulu-Natal midlands where orchids and other wild flowers inevitably end up in small patches of grassland surrounded by sterile plantations of exotic trees,” says Johnson. “A vicious circle is set up because populations of pollinators, such as bees, will decline and then the plants and vice versa.”

Specific interactions, however, present fertile ground for evolutionary biologists. “The more specialised the interaction, the more dramatic tend to be the adaptations,” explains Johnson. “So while it’s upsetting to see how some fantastically evolved species are hanging on in small populations, there is still a chance to study their spectacular patterns of floral evolution.”

One of Johnson’s special interests which gives him a “link with Darwin” is the South African orchids. Darwin was fascinated by the pollination of orchids and found them to be highly effective in illustrating adaptation processes. “I’m following in the footsteps of Darwin in a sense,” says Johnson.

Orchids are “unusually complex, specialised flowers” most of which have single pollinators. They harbour a life-giving fungus in their roots and most can’t be potted. “This means the only hope for their conservation is to ensure that their habitats remain intact,” says Johnson.

Through an upcoming book, The Cape Orchids, co-authored by William Liltved, he hopes to “bring to the attention of the public the intricate biology of these orchids”.

The book will be his second foray into writing and publishing for an audience beyond the academy. In 1999, Johnson co-authored Table Mountain: A Natural History with Anton Pauw, which was richly illustrated with their own photographs and earned awards from both the universities of KZN and Cape Town.

Johnson’s pollination research has multiple applications, including the field of agriculture where maximising seed production is often critical. He has recently established a state-of-the-art laboratory, frequently visited by international scholars, to research the chemical communication between flowers and insects. For Johnson, it takes his group to the cutting edge of international research. It also helps in his mission “to grow the next generation of university teachers and encourage students to view academic study and evolutionary biology in particular as an attractive career path”.

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