**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 power^{1}. 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
research^{2}. 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
organisations^{3}. 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 exists^{6}. 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
research^{8}. 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 scrutiny^{9}. 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?

- 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. - 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. - "
*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. - 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. - 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. - S. Millman, op cit.
- Such as, Hewlett-Packard's BRIMS, Microsoft's Theory Group and Cambridge Research Laboratory and NEC's Princeton Research Institute.
- For example, NSF Mathematical Sciences Postdoctoral Industrial Fellowships, the UK's Realising our Potential Awards Scheme (ROPAs) and Royal Society Industry Fellowships.
- 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.