Mathematics-in-Industry Study Groups—A Global Phenomenon

October 21, 2007

Enthusiasm for maths-in-industry runs high throughout the world. Shown here at the minisymposium is Tan Youngji of Fudan University, in Shanghai---the “nerve centre” of the MII programme in China.

Hilary Ockendon

The ICIAM minisymposium "Study Groups with Industry" revealed a wealth of interactive mathematical activity around the world. About thirty mathematicians who either had experience with Study Groups, or were keen to gain it, gathered to extol the joys and excitement of working in this mode and to exchange ideas concerning best practice.

The four talks illustrated the wide diversity of problems that can be addressed and the ways in which they can be tackled. The concept of a Study Group with Industry, initiated by Alan Tayler and Leslie Fox in Oxford in 1968, is central to the way in which all the speakers work. The idea is simple: Invite a number of industrial scientists to present problems that are ripe for quantitative analysis to an audience of open-minded academic applied mathematicians and mathematical scientists. The first day is devoted to problem presentation; participants then work on the problems in brainstorming workshop-style sessions for two or three days, and report back orally on the final day. Typically, there are 4–8 industrial problems and 40–80 academics, ranging from doctoral students to professors, but the formula works on almost any scale.

Something is almost always achieved, no matter how diverse or unusual the problems. Graeme Wake (New Zealand) described one meeting at which real progress was made on six out of seven challenges, which ranged from pricing washers to modelling the management of mountain vegetation. His assessment was that two problems were solved during the workshop, one was shown to be infeasible, and the other four are the subject of ongoing work.

The range of topics that maths can tackle is endless. Poul Hjorth (Denmark) described the amazing mechanical and geometric ideas needed to understand and improve the design of a scroll compressor (first patented in 1905), a problem he contrasted with the request for an algorithm to build any given design in LEGO bricks, which was conjectured to be NP-hard. The mathematics that comes out of these encounters is sometimes spectacularly novel: David Allwright (UK), describing a problem concerning the number of frequencies needed for a wireless-secure office configuration, showed that it boils down to a three-dimensional version of the four-colour problem. Although examples suggested that the chromatic number for a block of cuboidal offices might be bounded by 6, subsequent rigorous analysis by Bruce Reed (Montreal) proved that n offices could require of order loglogn/logloglogn colours for large n!

The basic Study Group formula has remained remarkably stable as it has spread throughout the world, although a number of new organizational ideas have been introduced in different countries. The speakers covered four continents, and at least thirteen countries were represented in the audience. Discussion highlighted the common features, as well as local differences and new developments in this mode of mathematics-in-industry activity. For example, Study Group organisation can benefit greatly from the support of an "intermediate institution," as described by Huaxiong Huang (Canada/
China), who drew attention to the symbiosis between the Study Group programme in Canada and the MITACS network ( He also spoke of the enthusiasm for the challenge in China, where the nerve centre for the Mathematics-in-Industry programme is Fudan University in Shanghai.

On the organisational side, the idea of "moderators" who have responsibility for ensuring that the work on a particular problem stays on track and results in a timely report has been developed very successfully in Australia and New Zealand, where a Study Group can attract more than 200 participants. The recent addition of a "student moderator" to each problem team enables students to gain hands-on experience. Indeed, the Study Group formula has a significant role in the training of doctoral students and postdocs, as well as in offering obvious employment opportunities. Any student attending a Study Group will en-gage in collaborative research in a unique way, and can greatly enhance this experience by attending one of the "modelling camps" offered as the run-up to Study Groups in several countries, including the USA, Canada, and Portugal.

Of course, the technology transfer effected by a Study Group can be accomplished with equal efficiency in other scientific communities. Medical Study Groups, where industrialists from biotech companies are complemented by medical researchers from hospitals and university departments, are now popular in the UK and elsewhere. Several large industries in Europe, the USA, and Australasia are now extending the idea, holding regular "in house" study groups and thus avoiding some of the problems that can be caused by intellectual property issues.

A spontaneous but fruitful round-table discussion at the end of the minisymposium highlighted the following issues:

1. The number of people actively involved in maths-in-industry is relatively small, in part because of the universal perception that there is scant recognition for the resulting research, which often cannot be published in the usual way. There is a need for a "performance indicator" that gives due credit for this sort of collaborative work; the current Australian Research Quality Framework, by emphasising the "impact of research," attempts to provide such a mechanism. A new initiative that may help here is the recent establishment by the Fields Institute of the electronic journal Mathematics-in-Industry Case Studies (

2. Despite a great deal of activity in maths-in-industry worldwide,* there is a need for a global forum to further publicise and collate activities and to facilitate the exchange of information. Information about Study Groups and related activities can already be found at, and moves are afoot to develop this into a larger and more globally inclusive site. Anyone who wishes to participate in or even to organise a Study Group is strongly encouraged to use this Web site.

If you want practical problems, mathematical excitement and a few days away from your desk with a congenial group of like-minded people, then go to a Study Group!

MII Study Groups:
Main Contributors to the Minisymposium
Graeme Wake, Massey University, Auckland, New Zealand
David Allwright, KTN for Industrial Mathematics, UK
Poul Hjorth, DTU, Lyngby, Denmark
Huaxiong Huang, York University, Toronto, Canada

John and Hilary Ockendon, OCIAM, Oxford University, UK

*Participants in the minisymposium identified the following countries as having some activity in maths-in-industry: Australia, Brazil, Canada, China, Denmark, Finland, Germany, India, Indonesia, Ireland, Mexico, the Netherlands, New Zealand, Poland, Portugal, South Africa, South Korea, Spain, Thailand, Turkey, United Kingdom, and the USA. We apologise for any omissions and urge anyone with additional information to send it to

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