MathFIT - Mathematics for IT

The MathFIT Consultation Document

The following document was circulated within the research community in spring 1996.

Mathematics for IT (MathFIT): A Proposed New EPSRC Programme


As part of its continuing support for the health of both IT and Computer Science and Mathematics, the EPSRC is considering developing a programme to foster and improve the links between the two disciplines.

A steady pull-through of new research in mathematics is considered to be essential for the sustained development of Information Science, and ultimately its success in supporting the engineering and application of Information Technology in industry and commerce. For Mathematics too, there are advantages to strengthening links with the IT community. Recognition of the underpinning role and the relevance of much of pure mathematics for IT can provide a strong drive for mathematical research, not restricted to narrowly defined or directed programmes.

Initial consultation by EPSRC and the London Mathematical Society (LMS) has suggested that there are many pressing opportunities for bringing the communities together in a joint programme, driven by both industrial and scientific need, and for laying the groundwork for substantial collaboration in future generations. This document is intended to serve as the basis for further consultation with the two communities on the requirement, direction, and priorities for a possible EPSRC programme to stimulate and direct inter-disciplinary links in areas of research, training and information exchange.

This proposed programme is broadly modelled on the successful LOGFIT initiative mounted by the former Science and Engineering Research Council, which was responsible for encouraging mathematical logicians and their students to address their skills to problems arising in IT.


In recent years, questions in information science and engineering have provided the spur for much of the new work in the relevant areas of pure mathematics, which in turn has led to real technological advance. For example:

Applied mathematics has a long tradition of interaction with computer science, through the development of numerical procedures. Here we are concerned with the interplay between pure mathematics and computer science, which has traditionally centred around areas in logic, category theory and discrete mathematics. In recent years new connections between mathematics and computer science have emerged from such unexpected quarters as algebraic topology, differential geometry, dynamical systems and operator algebras.

These new developments hold the promise of bringing new insights and powerful mathematical tools to bear on problems in computing, and are already attracting the attention of the industrial community through work at the Hewlett Packard Basic Research Institute of the Mathematical Sciences at Bristol. At the same time such problems have opened new avenues of exploration for pure mathematicians.

By way of example, the January 1994 issue of the IEEE Transactions has articles on interactive communication, cellular telephone systems, detection, random sequences, convolutional codes, public-key cryptosystems and authentication. The mathematical areas concerned include probability theory, finite group theory, finite fields, algebraic geometry, linear algebra, and polynomial rings.


The aims of the proposed programme are:


This is seen as a science led programme; however, an initial consultation suggests that the following descriptions are suggestive of mathematical areas and applications in which new developments are either already appearing, or are strategically important:

This list is by no means exhaustive, and other areas identified by the community may be added in the future.

One aim of Mathfit is to create a climate in which new connections can emerge supporting new applications and industries. In this way, appropriate mathematical support may be provided for IT initiatives in line with Foresight and in pursuit of EPSRC's mission, while at the same time stimulating the emergence of new initiatives from the academic resources of the country.


An EPSRC mechanism is proposed, which would be co-ordinated jointly by the Mathematics and IT & Computer Science Programmes of EPSRC. Programme managers would draw on the advice of the two communities for guidance and peer review as appropriate. The programme will make full use of the mechanisms available under EPSRC in order to achieve the above aims. These may include:

Duration and Scope

There is a wealth of talent and expertise in mathematics in the UK, and a continual stream of gifted students renewing that talent and potential. While the mathematics of physical processes and materials is well-established in the undergraduate curriculum, this is not the case for those aspects of pure mathematics that is increasingly applied in the discrete world of IT today. This initiative is intended as support for those mathematical areas that have not traditionally been seen as directly applicable to technology and engineering but which are now beginning to demonstrate significant relevance.

It is proposed that this programme should run for 3 years in the first instance, but there is considerable scope to strengthen these links and to establish them as a permanent and thriving aspect of mathematical and computational research in the UK, a situation which would be of great import for the foundations of present and future information technologies.

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Editorial Control: Professor I.A. Stewart. Page last changed: 28 June 2000.
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