Marston
Conder DSc FNZMS FRSNZ
Marston Conder is a Professor of Mathematics at the University of Auckland, and a Co-Director (with Vaughan Jones) of the NZ Institute of Mathematics & its Applications (NZIMA).
His research interests are in algebra, geometry and combinatorics. and especially the application of combinatorial and computational group theory to the analysis and construction of discrete objects with maximum symmetry. He has published about 70 papers in international journals and refereed conference proceedings.
After a Masters degree at the University of Waikato, Professor Conder obtained a DPhil degree from the University of Oxford, where he won the Senior Mathematical Prize and Johnson Prize in 1980.
He held a postdoctoral fellowship at the University of Otago in 1981, followed by a Royal Society (UK) Research Fellowship at the University of Tuebingen (Germany) in 1982, and a Fellowship from the Alexander von Humboldt Foundation in 1987. He has held other visiting positions at Madrid, Oxford, Singapore, St Andrews (UK), Sydney and Waterloo (Canada).
He was President of the NZ Mathematical Society from 1993 to 1995, co-founder and initial convenor of the NZ Mathematical and Information Sciences Council (now a standing committee of the RSNZ) in 1994, and is a co-founding Director of the NZ Mathematics Research Institute. He participated as a lead expert in the MoRST Review of New Zealand's Scientific Knowledge Base in 1996, and was a member of the TEAC Research Working Group (2000-2001). At the University of Auckland he was Head of the Department of Mathematics from 1996 to 1998, and served a term as Deputy Vice-Chancellor (Research) from 1999 to 2001.
He is a member of the Editorial Board of the NZ Journal of Mathematics and a member of the Marsden Fund Council (and convenor of its Mathematical & Information Sciences panel). He is also currently chairing a Working Group for the NZ Ministry of Education, charged with helping design a Performance Based Research Fund (PBRF) for tertiary education institutions in NZ.
He won a Prince & Princess of Wales Science Award in 1989, the NZ Mathematical Society's Research Award for 1993, a Claude McCarthy Fellowship in 1995, and 3-year Marsden Fund grants in 1995, 1998 and 2001. He was elected a Fellow of the Royal Society of NZ in 1998, and awarded a DSc by the University of Oxford in 1999.
Marston Conder University of Auckland
NZ Education Review Nov 27 2002 p 11
I was very pleased to be asked to write an opinion piece for Education Review on the state of mathematics in New Zealand.
Although mathematics and statistics pervade our education system, underpin almost all contemporary developments in science and technology, and impinge on much of our everyday lives in various ways, mathematics is not a subject that has traditionally attracted a lot of publicity - certainly not in comparison with medicine and biology or information technology for example.
To an extent that is now changing. Many say that mathematics is entering a golden age worldwide. Helped by rapid advances in the capacity and availability of computers and other technological tools, the range of visible applications of mathematics has mushroomed over the last few decades. We now see smart cards and other secure access protocols based on number theory, error-correcting codes (in CD players and satellite transmissions) based on linear and abstract algebra, option-pricing systems based on differential geometry, and genetic and linguistic analysis based on combinatorics, to name just a few.
Also several long-standing problems in mathematics have been resolved. The most famous of these would have to be "Fermat's Last Theorem", one of the greatest challenges in mathematics for the last two centuries (despite the ease of describing it and the fact that it was called a theorem for so long before anyone published an acceptable proof).
Fermat's Last Theorem states that equations of the form x^n + y^n = z^n have solutions in which x, y, z and n are positive integers (whole numbers) only when n is 1 or 2. This claim, although easy to state (and not too much harder to understand), was made by Fermat over 350 years ago, but finally proved to be true only in 1994, by Andrew Wiles (of Cambridge and Princeton universities), using some very sophisticated arguments from several different branches of mathematics.
A number of books have become best sellers, including at least two on Fermat's Last Theorem. Also movies like "A Beautiful Mind", "Enigma" and "Good Will Hunting", and plays such as "Arcadia", "Proof" and "QED", and even works of fine art (containing complicated but aesthetically pleasing formulae), are beginning to raise the profile of mathematics, and mathematicians. (Unfortunately some of these unfairly compound a perception that mathematicians are eccentric or psychologically unbalanced ... although perhaps we do have more than our fair share of eccentrics!)
What of mathematics in New Zealand? Well, we have good news and bad news.
Good news is that in mathematical research and for some aspects of our tertiary education system, we can foot it with the best in the world.
Many of New Zealand's mathematical scientists are international leaders in their area of expertise, who choose to forego closer location to the concentration of activity in their subject (and the much higher salaries they could earn at universities in the US or Europe), in favour of this country's lifestyle and the place they call "home". The quality of their work and their international standing were recognised in the selection and establishment this year of the New Zealand Institute of Mathematics and its Applications (NZIMA), as one of the country's five Centres of Research Excellence announced in March.
The NZIMA is forging ahead with specialist research in a number of areas, with particular support in 2003 for programmes in bioengineering (mathematical modelling of cellular function), logic and computation, numerical methods for evolutionary problems, and phylogenetics (the analysis of genealogic tree structures, with applications in biology and linguistics), and ongoing work in other important areas such as discrete geometry, medical statistics and geothermal modelling.
Our mathematics graduates are snapped up by universities overseas. This isn't necessarily because of the breadth or depth of what these students know - although that helps a lot - but often because NZ students have a reputation for creativity and innovation, willingness to have a go at anything, and sometimes downright raw cunning. There's something of our inventive spirit and the "number 8 wire" approach (perhaps born out of our pioneering history) that makes our graduate students and researchers succeed on the world stage.
Our greatest success so far would be Vaughan Jones, born in Gisborne and educated in Auckland, who studied for his doctorate in Geneva and went on to win a Fields medal (regarded by many as the equivalent of a Nobel Prize for Mathematics) in 1990, and a string of other awards and honours since then. Vaughan is now a professor at the University of California at Berkeley, but returns to New Zealand one or two times each year to interact with local mathematicians here and to stimulate future excellence. He was made a Distinguished Companion of the NZ Order of Merit in this year's Queen's Birthday Honours List, and is co-Director of the NZIMA.
Bad news is that this excellence is constrained from filtering through the tertiary education system and beyond.
Pass rates, retention rates and class sizes for most university courses in mathematics and statistics are awful. Some of this is due to low (or non-existent) entry standards, and some due to inadequate resourcing. Government tuition subsidies for mathematics and statistics are set at the lowest funding category level (the same as for arts and commerce courses), about half of those or computer science, geography and psychology (which are subsidised at the same rate as chemistry and physics), and much less than those for agriculture and engineering.
What this means in practical terms is that mathematics students don't get the one-on-one interaction with their teachers that is so important for understanding and learning difficult but fundamental concepts and processes, and get very limited access to computer-assisted learning environments. It also means there's a gap that many students don't get to cross, between the theoretical knowledge gained in a pure classroom environment and the deeper understanding and the ability to apply that knowledge in different contexts, both of which are so necessary for their future lives and employment. I think there's an obvious question here about whether that's appropriate for building a knowledge-based society and economy in this country.
Part of the problem here is a traditionally low appreciation of the value of the mathematical sciences in New Zealand society. The level of investment by business and industry in research and development is very low by world standards, and some would suggest that's the main reason we've fallen behind recently in OECD rankings on key performance indicators for economic growth.
Also we don't celebrate academic success as much as we do for business and sport (for example), and worse, it often seems there's a kind of perverse pride shown by individuals in their relative lack of achievement in mathematics. I think we can learn - and many people are now beginning to learn - from the positive example being shown to us by recent new immigrants from other cultures in these respects. The NZIMA is helping to a small extent by supporting the training of a New Zealand team sent each year to compete in the International Mathematical Olympiad (IMO). How many readers know that a young student, Simon Marshall from Wellington, won New Zealand's first ever gold medal at the IMO this year?
Now to mathematics in our schools, and to a large extent I rely on advice on this from expert colleagues in our Mathematics Education Unit such as Bill Barton - so that what I say won't entirely represent the views of an ivory-tower academic!
It seems we do quite well in international assessments of our students' mathematical ability (such as the TIMSS and PISA tests), although because of differences in curriculum from country to country these do not tell us much about the state of mathematics in NZ, but only how well students understand the sort of mathematics dealt with in these tests. Also there is a long 'tail' in mathematical performance, with few Maori, Pacific and low-income background pupils scoring highly. There is an urgent need to strengthen the teaching of mathematics in low-decile schools, so that young people from all walks of life have the skills needed to participate in a knowledge economy.
There will always be quibbles with the choice of curriculum, involving balance of topics and coverage keeping up-to-date with contemporary developments. Generally, however, the picture of mathematics presented in curriculum documents is of a potentially open subject in which creativity and excitement can be found at all levels. Highly technical but important aspects are included (and not played down), and varied applications are evident. More importantly perhaps, we have seen healthy but subtle moves away from concentration on facts, towards increasing importance on mathematical processes.
We do have some problems, however, with the implementation of the curriculum. There are some fantastic teachers in the system, and a number of recent numeracy initiatives and teacher development strategies are in place that are increasing both teacher confidence and the levels and depth of mathematics being learnt and understood (by teachers and students). But on the other hand, we have a far-too-large number of teachers who are not well trained in mathematics, with many being graduates in other scientific disciplines (rather than mathematics), and many who are falling back on processes which are little more than "learn a recipe and apply it".
More significantly, I believe we are facing an enormous potential problem in secondary schools as a result of the new assessment system. A large number of my colleagues see the curriculum being subverted by a qualifications system which is breaking up the subject into discrete units (under an apparent but loopy assumption that learning pieces of mathematics is immediate and long-lasting). This system is placing more emphasis on skills to be mastered, and less on the wider context of the subject, understanding of overall concepts, and the various inter-relationships between branches of the subject (and its applications).
As I said earlier, we have good news and bad news. Much of the good news is really excellent. Much of the bad can (and should) be improved.