Where are the opportunities for UK industry to gain a competitive edge through the exploitation of mathematics and computing? Over 50 top industrialists have now helped to answer this question. In this document, their vision of the challenges facing industry over the next 10 years has been matched to the expertise of the science base to produce the UK's first ever industrial roadmap for mathematics and computing.

Leading industrialists shaped the roadmap through a series of interviews, during which six scientific themes emerged as being of prime importance to industrial competitiveness: simulation, multidisciplinary design, uncertainty and risk, data, complex systems, and market behaviour.

Interviewees were drawn from all sectors of the economy and more than 95% of the industrialists who were asked to contribute volunteered their time - testament in itself to the widespread recognition that the UK's mathematical resources have a vital role to play in wealth creation.

By connecting the six themes with the relevant mathematical and computational methods, the roadmap shows the ever-increasing potential for coupling industry and the science base to best mutual advantage. The roadmap reveals that there is a sharp contrast with the general pattern of collaboration between industrial and academic researchers over the past 30 years, which has been concentrated heavily in the theme of simulation.

The vision for the future is one of innovative collaborations, assembled to address the multi-thematic challenges of the modern economy and spanning a vastly wider range of mathematical and computational expertise than at present. These collaborations, supported through initiatives such as the Smith Institute, will create completely new mathematical frameworks for addressing the most important industrial challenges.

Mathematics is the most versatile of all the sciences. It is uniquely well placed to respond to the demands of a rapidly changing economic landscape. Just as in the past, the systematic application of mathematics and computing to the most challenging industrial problems will be a vital contributor to business performance. The difference now is that the academic community must broaden its view of mathematics in industry and its expertise must be managed in more imaginative ways.

Mathematics now has the opportunity more than ever before to underpin quantitative understanding of industrial strategy and processes across all sectors of business. Companies that take best advantage of this opportunity will gain a significant competitive advantage: mathematics truly gives industry the edge.