The importance of mathematical sciences, including computational sciences, cannot be overemphasized. 'The impact of mathematics on society is pervasive and there is ample historical evidence that every area of mathematics, however abstract, has important applications. Maintaining and enhancing the historical strength of the mathematical sciences as an intellectual endeavour and as a foundation for applications are prerequisites for sustaining a knowledge-based economy’.

The Engineering and Physical Sciences Research Council (EPSRC), in its Strategic Plan, describes mathematics and computation as Foundation disciplines: ‘The mathematical sciences have an extensive range and diversity of applications in modern society. Mathematics is truly pervasive, underpinning all other research disciplines and contributing to advances made in many fields of endeavour’. Furthermore: ‘The impact of computer science and engineering across the breadth of other fields of research has been truly astounding, and there are few areas of scholarship that have not been transformed as a result’.

The mathematical sciences are disciplines in themselves, with their own vitality. But they also serve as the fundamental tool and language for science, engineering, industry, management and finance. They are inextricably linked to these ‘user’ fields and frequently draw their inspiration from them. Thus mathematics has a dual nature: it is both an independent discipline valued for precision and intrinsic beauty and a rich source of tools for the world of applications.

Mathematical sciences, like all other sciences, are pursued in a world that is changing rapidly. Both the techniques of the sciences and the needs of society are dramatically more complex than those of the past. They require new mathematical ideas and methods as well as an improved dialogue between the mathematical and non-mathematical communities, each of which needs to be more receptive to the views of the other.

The advent of computational science, which is an integral part of the mathematical sciences, is amongst the most significant developments in the practice of scientific inquiry to have taken place in the last century. Within the past two decades, scientific computing has become an important contributor to all scientific research programmes. It is particularly important for the solution of research problems that are insoluble by traditional theoretical and experimental approaches, hazardous to study in the laboratory, or time-consuming or expensive to solve by traditional means. Computer-based simulation provides a means of solving mathematical equations and predicting the behaviour of complex systems that can only be described empirically at present.

'Increasingly, simulation is taking the place of expensive and unfeasible experimental testing’. To emphasise the importance, the Office of Science and the Department of Energy in the US, state that ‘Advances in the simulation of complex scientific and engineering systems provide an unparalleled opportunity for solving major problems that face the nation in the 21st Century’.

Undoubtedly, a strong foundation in Mathematical and Computational Sciences is essential for a modern knowledge-based society. Higher education institutions, industry, business, commerce and governments around the world accept this premise. This collaborative partnership, titled ‘The Wales Institute of Mathematical and Computational Sciences’, will ensure Wales plays its role in shaping the future of these fundamental disciplines and benefit from their advances.