Appendix 4

Basic Research in Mathematics
Collaboration between Academia and Industry

Working Paper for the Discussion Meeting at
The Isaac Newton Institute on 4 November 1997

Jeremy Gunawardena
BRIMS, Bristol, England

September 16, 1997

Mathematics is unique among the sciences in the depth and breadth of its contributions to humanity. It provides the infrastructure for all the exact sciences, some of the social sciences and all traditional engineering. This is supported by a corpus of pure mathematical knowledge of elegance, versatility and power1. The roots of the subject go back to antiquity but its great flowering took place in parallel with the first industrial revolution and the development of industrialised societies in the eighteenth and nineteenth centuries.

A second industrial revolution is now taking place, fuelled by development in computing, communications, finance and bioscience, as societies evolve from energy-based to information-based. Concomitant political and economic changes are altering the environment for basic research. Governments have changed the criteria for public funding of research, greater emphasis being placed on relevance, technology transfer and wealth creation. Lower defense spending, following the ending of the Cold War, has reduced another major source of research funding. Universities are struggling to prepare their students for a challenging job market while attempting to maintain their commitment to basic research2. What is emerging from this are Grand Challenges for mathematical science and new equilibria in the balance of basic research between governments, universities and industry.

Examples of these Grand Challenges include (1) the development of a mathematical infrastructure for computer engineering (2) the provision of universal access to the Internet and its services (3) the physics and engineering of electronic devices as feature sizes shrink to atomic dimensions. These are not merely technological challenges: they require fundamental progress in several areas of mathematical science.

There is a distinguished tradition of industrial mathematics represented by the Society for Industrial and Applied Mathematics (SIAM) and its affiliated organisations3. While this will remain vital, the new industrial developments have begun to draw upon new areas of mathematics, including some hitherto regarded as pure (algebraic geometry, number theory, logic, etc), and have begun to throw up problems which lack adequate mathematical formulation in the first place 4.

Sustained collaborative research by engineers, mathematicians and others, both industrial and academic, seems essential to tackle Grand Challenge problems. There is a precedent for such research from the early days of telecommunications: the commercial and engineering challenges of providing universal access to the telephone stimulated fundamental developments in probability theory and other areas of mathematics 5. The development of the World Wide Web present us with challenges of a similar scale and complexity, if not yet solutions of the same stature.

There are few modern environments in which such challenges can be successfully tackled. Much of the telecommunications work mentioned above was conducted at AT & T Bell Laboratories in a monopoly commercial environment which no longer exists6. Industry has only recently begun to experiment with new environments which attempt to merge academic and industrial philosophies and modes of operation 7.

The lack of organisational structures in matched by a lack of people. Many of the Grand Challenges of the second industrial revolution are not on academic research agendas or course curricula and there are consequently few people motivated to study them. Industry has been slow in articulating these challenges and in clarifying their intellectual depth and difficulty, a precondition for attracting the brightest academic talents. In recent years funding mechanisms have emerged which directly encourage collaboration in basic research8. Despite this development, the idea of collaborative research remains uncomfortable to many on both sides of the academic-industrial divide. It is not always career-enhancing for an academic mathematician to spend time in industry. Postdoctoral students are particularly vulnerable to this pressure, which is unfortunate, since they are at a stage when the stimulation of new ideas could have the greatest impact. Mobility across the academic-industrial divide remains sluggish.

It is used to be taken for granted that mathematics was vital to society. This could be attributed, at least in part, to its immense contribution to the first industrial revolution. In recent times, in keeping with much else, the subject’s role in society has come under searching scrutiny9. If it is to maintain its accustomed status in the future, can it afford not to be at the forefront of the second industrial revolution?


  1. The abstracts of programmes at the Isaac Newton Institute, available in the Institute's information pack, give an idea of the scope of the subject. For its technological impact in the USA see James Glimm (editor), "Mathematical Sciences, Technology and Economic Competitiveness", Board on Mathematical Sciences, National Acadmey Press, 1991.
  2. Congressman George E. Brown, "Challenges Facing Mathematics in the Twenty-first Century", Notices of the AMS, 44:576-579; 1997 A. Jackson, "Downsizing at Rochester", Notices of the AMS, 43:300-306, 1996; R. S. Rosenbloom and W. J. Spencer, "The Transformation of Industrial Research", Issues in Science and Technology, Spring 1996.
  3. "SIAM Report on Mathematics in Industry", available from the Society for Industrial and Applied Mathematics; J. R. Ockendon, "The Moving Interface between Mathematics and Industry", Proceedings ICIAM-95.
  4. We know how to predict the stress in a girder but not the minimum redundancy needed to achieve a specified MTBF in a computer system, a problem first articulated by von Neumann but still awaiting an appropriate theoretical framework: J. von Neumann, "Probabilistic logics and the synthesis of reliable organisms from unreliable components", in C. E. Shannon and J. McCarthy (editors), Automata Studies, PUP, 1956.
  5. By, among others, Bode, Erlang, Heaviside, Kolmogorov, Nyquist, Rice, Shannon and Wiener: S. Millman (editor), "A History of Engineering and Science in the Bell System: Communications Sciences (1925-80), AT & T Bell Laboratories, 1984.
  6. S. Millman, op cit.
  7. Such as, Hewlett-Packard's BRIMS, Microsoft's Theory Group and Cambridge Research Laboratory and NEC's Princeton Research Institute.
  8. For example, NSF Mathematical Sciences Postdoctoral Industrial Fellowships, the UK's Realising our Potential Awards Scheme (ROPAs) and Royal Society Industry Fellowships.
  9. Mathematics is not mentioned as a core area in "Towards the Fifth Framework Programme: Scientific and Technological Objective", European Commission Working Paper COM(97)47.