Abstract
This paper presents a brief review of how industrial mathematics, inspired by the Oxford Study Group activity, organized itself in Europe, gave rise to the European Consortium for Mathematics in Industry, the series of European Study Groups with Industry, and to new modes of productive contacts between industry and applied mathematicians in academia.
1. Introduction
The interplay between the real and the abstract, between the specific and the general, has always been a fertile soil from which much mathematics, both very applied and very pure, can grow.
As the nation-states making up the European mainland moved out of the shadow of the great wars of the twentieth century, industries accelerated the pace of research, development and innovation. In that process, an increasing need was seen for mathematical solutions to intricate problems, in computation, in optimization or other technological challenges, often of considerable complexity.
A key role emerged for mathematicians having an understanding both of the real-world situation in which the problem is posed and of the wide range of choices for the abstractions which may permit a mathematical attack on the industrial problem.
The diversity of mathematical disciplines makes it nearly impossible for an individual to be familiar with research in all mathematical areas. Co-operation and information flow are increasingly necessary, not just across disciplines, but also across borders.
2. European Consortium for Mathematics in Industry
The continuing success throughout the 1970s and early 1980s of the Oxford Study Groups with Industry [1] suggested to European applied mathematicians, a number of whom had already participated in the Oxford Study Groups and had close ties with the organizers, that a new mathematical subdiscipline was in fact emerging and that individual countries in Europe would benefit from a transnational collaboration around this subject.
The creation of European Consortium for Mathematics in Industry (ECMI) is the result of pioneering efforts by a number of talented and visionary individuals on both sides of the English Channel. Rather than a detailed, person-centred, historical account, this report is a brief sketch of structure and origins, in the Scandinavian sense of Ingen nævnt, ingen glemt (‘None mentioned, none forgotten’).
In 1986, the ECMI was founded at a meeting in Neustadt-Mussbach, in (then West-) Germany. A detailed account of this meeting can be found in the first newsletter of ECMI [2]. See also the more personal account in Capasso [3].
In the minutes of the meeting, the aim of the Consortium was described:
— To promote and support the use of mathematical modelling, simulation and optimization in any activity of social or economic importance.
— To educate Industrial Mathematicians to meet the growing demand for such experts.
— To promote European collaboration in industrial mathematics.
It was agreed that there was a shortage of applied mathematicians in European industry and that multi-national cooperation was the way forward. It was also agreed that it was a common European interest to have shared standards for education in industrial mathematics, shared experiences with industry cooperation (see figure 1).
No single European country is likely to have sufficient expertise of mathematical knowledge, whereas ECMI can provide a comprehensive coverage of mathematical skills and their diverse applications.
First ECMI Brochure, 1994 [3].
Home page [4] of the Consortium with the (in 2016 re-designed) ECMI logo, top left. The home page contains a list of the current members of the governing structure of ECMI, a contact list of ECMI teaching centres, a listing of past activities, announcement of upcoming activities, contact information for SIGs and selected news and announcements from member sites. (Online version in colour.)
(a) European Consortium for Mathematics in Industry organizational structure
The Consortium has four organizational bodies: The ECMI Board, including the President, the Vice-President, the Treasurer and a few other members. This body oversees ECMI activities on a regular basis and proposes plans and new ideas to the Council. The Board meets at least on a semi-annual basis. The ECMI Council is the main governing body and has representatives from all the countries which has an institutional membership or individual membership (or both) in ECMI. The Council meets at least annually. The ECMI Educational Committee oversees the central educational aspects of ECMI and advises the Council on potential new teaching centre members. The ECMI Research and Innovation Committee is focused on new trends in research connected with industrial mathematics.
The Consortium members collaborate in several areas: Education, Modelling weeks, Special Interest Groups (SIGs), Publication and Study Groups. ECMI currently have about 100 institutional members.
(b) Education: the European Consortium for Mathematics in Industry master degree
The aim of the ECMI Educational programme in industrial mathematics has been from the beginning to develop mathematical and computational skills enabling students to solve industrial problems and developmental tasks in innovative ways. Various implementations of the ECMI educational programme are available at ECMI Teaching centres, now in a number of countries. See figure 2.
The development of ECMI teaching centres. (a) in 1987 and (b) in 2017. At each site, the students can build a master degree in industrial mathematics, certified by ECMI. Upon completion of an ECMI-certified master programme, a student receives an ECMI diploma. (Online version in colour.)
Typically, this is in the form of a 2-year master programme (comprising 120 European Credit Transfer and Accumulation System (ECTS) [5]) that can be entered after a bachelor degree in mathematics or applied mathematics. The courses must be given in English. Each ECMI Teaching centre issues an ECMI Degree Certificate in addition to the standard degree certificate from the university. The recommended background to enter the ECMI Educational Programme is a Bachelor degree: 180 ECTS of undergraduate study at university level.
Fundamental skills to be taught in the ECMI Educational Programme are:
— modelling and analytical skills,
— knowledge of numerical methods,
— skills in programming and simulation, experience with mathematical models in industry and/or economy,
— ability to handle large amounts of data by integrating mathematical, numerical and statistical methods, and
— teamworking, cooperation, communication with, and presentations for, mathematicians and engineers.
To this end, two separate study lines have been identified: one, Technomathematics, contains Scientific Computing, Optimization and Mathematical Statistics as its roughly 60 ECTS course requirement. Technomathematics covers subjects related to modelling of technical subjects as encountered in mechanics, pharmacy, electronics, chemistry, physics, bioengineering, civil engineering, biotechnology, etc. The other study line focuses on Economathematics, where more discrete mathematics and computational methods coursework fill the 120 ECTS requirements. Economathematics is intended to cover problems where planning and scheduling are central, operation analysis, quality control, statistics, distribution management, financial decision processes, cryptology and data communication.
(c) European Consortium for Mathematics in Industry modelling weeks
The common situation is that mathematics is called in to assist with the solution of problems that arise from other fields. For this reason, a mathematician often has to be a member of an interdisciplinary team [3].
Collaborative mathematics, problem-solving teamwork, though not sufficient for doing good industrial mathematics, has nevertheless become a very popular and effective part of the education of industrial mathematicians. It also is an excellent opportunity for training students how to pool their modelling skills in a group effort and discover the universal nature of mathematics. One of the most successful regular events in the framework of ECMI is the modelling weeks.
ECMI has been running annual modelling weeks for students every summer since 1988. Students attending come from ECMI member universities all over Europe to spend a week working in small multinational groups on projects which are based on real life problems. Each group is led by an ECMI instructor who introduces the problem, usually formulated initially in non-mathematical terms, and then guides the students towards a solution during the week. The students present on the final day their results to the other groups and afterwards write up their work as a joint report.
Attendance at a modelling week is an integral part of the ECMI certificate and of many of the masters courses run at ECMI teaching centres.
(d) European Consortium for Mathematics in Industry conferences
Bi-annually, since the mid-1980s, ECMI has conducted a scientific conference aiming to enforce the interaction between academy and industry and encourage contacts between industry and young researchers in industrial mathematics. These conferences have become one of the principal fora in Europe where significant advances in industrial mathematics are presented. They are attended by prominent figures from business, science and academia who discuss the use of innovative mathematics to industry. They also encourage industrial sectors to propose challenging problems where mathematicians can provide insight and innovative ideas.
The first conference of the series was in 1986, and the upcoming 2018 ECMI conference is scheduled to be held in Budapest, Hungary.
(e) European Consortium for Mathematics in Industry related publications
ECMI publishes ‘The European Consortium for Mathematics in Industry’ a sub-series of the Springer-Verlag ‘Mathematics in Industry’ book series [6].
The Journal of Mathematics in Industry is a high-quality journal that brings together research on developments in mathematics for industrial applications, including both methods and the computational problems they entail. Here, industry is understood as any activity of economic and/or social value. Here, industrial mathematics is a subject area which actually results in improvement of industrial processes and works to resolve the major challenges presented by economic and ecological industrial challenges.
In addition to these, ECMI also publishes an annual report of activities and an online newsletter.
(f) European Consortium for Mathematics in Industry Special Interest Groups
The concept of SIGs was created to promote collaborative cross-national research on specific topics in mathematics for industry within Europe. The aim is to enable researchers from both academia and industry having similar research interests to work together and submit proposals to the European Union or to other funding bodies for grants. ECMI in this aspect can act as a catalyst in the formation of such a group by offering advice about the expertise available within Europe, by posting information on the web pages and by circulating information about events to all members. ECMI also offers a small amount of financial support (on the order of XXXXXXXX 2000) towards setting up a new SIG.
Currently (2017), SIGs exist around the following topics:
— shape and size in medicine, biotechnology and materials science,
— liquid crystals, elastomers and biological applications,
— digital factories,
— numerical weather prediction,
— slow granular flows,
— computational finance,
— nanostructures for photovoltaics and energy storage,
— big data.
3. European Study Groups with Industry
In the late 1990s, several European universities decided that, in addition to ECMI activities, and because of a now well consolidate ECMI collaboration, the time had come to begin to conduct Study Groups with Industry also on the European mainland. The acronym acquired an ‘E’ (for European) preceding ‘SGI’ (see figure 3).
‘Bridges are built with mathematics and steel’. This image of the mile-long ocean span of the Great Belt Bridge between Zealand and Fuen was created by the mathematician M. Schou and served for a number of years as the poster image for the Danish Study Groups with Industry. (Online version in colour.)
The first such non-UK Study Group was the 1998 European Study Groups with Industry (ESGI) Danish Study Group, ESGI-32. The organizers followed quite meticulously the well-established Oxford format for such events: the Monday morning problem presentation by the companies; the formation of groups around the problems. A number of experienced British applied mathematicians attended, serving both as catalysts and engines for the process. One of the problems was famously not solved (though not for lack of work); this later became known as the ‘LEGO problem’, an algorithmic question of optimal construction of structures like LEGO models [7–9].
The Danish Study Group was followed within a few months by a similar event in Holland. Since then, not only have Denmark and Holland continued to organize annual ESGI, but a number of other nations, e.g. Portugal, Italy, Bulgaria and Russia, have organized Study Groups as well. The running count of ESGI will pass 130 sometime in 2017 [10].
Many universities encourage conducting Study Groups with Industry. Yet the academic reward system in general makes the time and effort put into locating industrial problems, organizing a Study Group, and especially in writing of reports, not so attractive for some mathematicians compared to ‘normal’ academic research work. A Study Group report, even if it has taken a similar amount of effort and skill, does now weigh as much in the CV as a ‘normal’ academic research paper. Research time is valuable, and taking a full week out of the calendar to work on an industrial problem of unknown depth can be hard, especially for career-minded younger academics. This is an important but not fully resolved issue. It has also been a spur for new (and shorter) collaboration formats.
4. Innovative industrial mathematics formats
With increasing university focus on relevance to the surrounding society, increasing pressure on companies to be at the cutting edge of production optimization and innovation, a need has been seen to go beyond annual study groups and have exchanges of ideas on a shorter time scale and in even less formal settings.
(a) Rapid response team (DK)
As the network of industrial mathematics expands, situations arise where a company is in need of mathematical input on a time scale shorter than the 1-year interval between the annual study groups. To meet this need, we have in Denmark experimented with a concept known as the rapid response team—‘rejseholdet’ copying the name of a television drama about a police squad. The idea is simply to be able to respond to a request at short notice, involving a few (two or three) experts, using a small amount of time, say, 1 or 2 days on the problem. The company should then have an answer to their most pressing questions, an assessment of the most productive way forward, estimate of the time and effort needed for a thorough solution. If one is lucky, a brief specialized solution.
We have carried out a small number of these rapid response events. The companies have been pleased with the outcomes. From an organizational point of view, the effort of first clarifying the issue, then finding the appropriate experts, then convincing them to take time away (during term) from their academic duties to work on this problem, even for a day, is substantial.
In the best of all worlds, taking part in the rapid response team should carry its own reward. In the real world, we find that even regular study group attendees need extra convincing, simply because their calendar mid-term is very full. Monetary rewards are in practice relatively small, and the tax issues, and legal issues associated with this are not so attractive. The most successful academic ‘carrot’ we have come up with (after negotiating with the Department Management) is that time spent in a rapid response effort will secure additional travel funds to the individual from the department, thus permitting the rapid response team member to attend at least one conference which would otherwise have been excluded due to lack of travel funds. Still, in spite of company satisfaction and departmental approval, we have decided to keep the rapid response events at a small number, and instead try to convince eager companies to be patient and wait for the upcoming study group to have their problem worked on.
(b) Breakfast meetings (NL)
In Holland, a series of breakfast meetings with industry has been conducted, mainly at various departments at the Technical University of Eindhoven. A number of company representatives were invited to come to the university for a brief and early morning meeting. These were persons with an all-round knowledge of their company and the technical and innovation challenges faced by the company. Breakfast was served. During the breakfast, faculty members gave ‘elevator pitches’, five-minute explanations of their current research and their view of potential applications.
After these pitches, informal discussions and introductions were encouraged. The aim was to facilitate new contacts that might lead to joint research projects, possibly after a Study Group treatment, possible collaboration around EU or other fundraising or places for students as interns. The entire event lasted less than an hour and a half; it did not dominate the day calendar for participants, neither industrial nor academic. These meetings have been generally successful and are being carried out on a fairly regular basis.
5. Final remarks
As part of the ambitious EU Horizon2020 research programme, a 2016 effort known as Online Consultation on Mathematics turned the tables and asked mathematicians to provide innovative ideas and proposals how emerging mathematical subjects might find use in society. The report [11] concludes that there is now a high degree of awareness of the role of both existing and new mathematics in innovation:
Mathematics is recognised today as essential for addressing the major challenges in science, technology and society. Faced with the abundance of data on social, technical, economic, ecological, and technological systems, new and sophisticated mathematical tools are required for these data to help us tackle pressing societal challenges and provide us with the necessary technological advantage.
From small beginnings, the ECMI has grown into a solid multi-national community organization with the aim to stimulate industrial mathematics practice and education. As more countries began to consider themselves part of the European scientific community, ECMI standards became a means to create in those countries much needed contact between universities and emerging industries.
Study Groups with Industry have expanded from the UK onto mainland Europe (and in various other forms around the globe), and the format, echoed in modelling weeks, also serves as a training platform for students. Innovative new formats experiment with additional cooperation between industries and universities.
Competing interests
I declare I have no competing interests.
Funding
I received no funding for this study.
Acknowledgements
The author is deeply indebted to Dietmar Hömberg, Wil Shilders, Stephen O’Brien, Jens Gravesen, Henrik Gordon Petersen, Christian T. Veje, Kamil Kulesza and many members of the Oxford industrial mathematics community for discussions and guidance towards assembling material for this paper. The author also thanks the referees for constructive remarks and suggestions.
Footnotes
A contribution to the special feature ’Mathematics in the modern economy’.
- Received February 4, 2017.
- Accepted April 3, 2017.
- © 2017 The Author(s)
Published by the Royal Society. All rights reserved.
Volume 473, issue 2201
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