Professor Ray Hill

School of Science, Engineering and Environment

Photo of Professor Ray Hill

Contact Details

Newton Building Room LG10

Please email for an appointment.

Current positions

Honorary Professor of Mathematics


I obtained my BSc (First Class Honours) in Mathematics from the University of Manchester in 1967. I gained an MSc (1968) and PhD (1971) in Mathematics from the University of Warwick, under the supervision of Professor Sandy Green. After working for two years as a Temporary Lecturer at the University of Nottingham, I was appointed Lecturer in Mathematics at the University of Salford in 1973. I was promoted to Senior Lecturer in 1985, to Reader in 1992, and to a Personal Chair in 1999. I took early retirement in 2000 and now have an appointment at Salford as Honorary Professor.

I have published over 50 research papers on group theory, finite geometry, coding theory and combinatorics. My book “A First Course in Coding Theory” (Oxford University Press, 1986) has sold over 12,000 copies. Since 2002, this book has been the core text for the Open University Master’s Module “M836 – Coding Theory”.

I have given over 60 conference talks, including main invited speaker at the British Association for the Advancement of Science (1980 and 1989), Fortieth British Mathematical Colloquium (1988), Second IMA Conference on Cryptography and Coding (1989), Fifteenth British Combinatorial Conference (1995), and many overseas conferences. I have given invited seminars at over 30 universities, including Oxford (three times), Cambridge, and Massachusetts Institute of Technology.

My external appointments include Membership (1983-87) and Secretary (1984-87) of the British Combinatorial Committee, Editorial Board of “Serdica” (1994-2004), Editorial Board of “Designs, Codes and Cryptography” (2003-present), Member of Organizing Committee for a series of International Workshops on Optimal Codes held in Bulgaria (1995, 1998, 2001), Member of Organizing Committees for IMA Conferences “Applications of Finite Fields” and “Applications of Combinatorial Mathematics” (1994), and EPSRC Panel Member (1998).

I supervised PhD students John Mason, David Newton, Karen Traynor, Phil Greenough, Pawel Lizak, Chris Jones, Jehangir Karim and Chris Love.

I have had the pleasure of collaborating with many distinguished mathematicians, such as:

  • Ivan Landjev (Bulgarian Academy of Sciences), who spent two years with me at Salford , first as a Royal Society Visiting Fellow, then as an EPSRC funded Visiting Fellow, working on optimal code problems.
  • Emil Kolev (Bulgarian Academy of Sciences), who was also a year-long Royal Society Visiting Fellow.
  • Elwyn Berlekamp (MIT), with whom Jehangir Karim and I solved a famous long-standing problem of Ulam (how to win a game of “Twenty Questions” against a liar).
  • Thann Ward (University of Virginia), who has worked with me at Salford on a number of short visits. Together with Ivan Landjev and Simeon Ball, Thann and I have carried out some novel research on multi-arcs in finite geometries and their links with codes.
  • Tatsuya Maruta (University of Osaka), who spent a year (and several shorter visits) with me at Salford, and who has greatly extended my initial work on extendibility of codes.
  • Leo Storme (University of Ghent), with whom, together with other collaborators, we have made progress on cap problems in finite geometry.

My main research career has centred on coding theory and finite geometry, and particularly on the interplay of these two topics.

Since my early retirement in 2000, I have branched into a quite new direction, namely the use (or misuse) of probability and statistics in criminal trials. I worked for the defence teams of mothers such as Sally Clark, Angela Cannings and Trupti Patel, who not only suffered the tragic sudden unexplained deaths of two or more babies, but were then, on the basis of flawed statistical evidence, accused of their murder. My work towards proving the innocence of these mothers has led to publications in medical and statistical journals, as well as invitations to speak at mathematical, statistical, medical and legal conferences and seminars. The work has attracted a fair amount of media coverage and has also been commended by Sir Herman Bondi in a letter to “Nature”, by Barry Lewis in his presidential address as President of the Mathematical Association, by Angela Saini in an article “Justice you can count on” in New Scientist (24 October 2009), and by Sir Mervyn King in his Inaugural Lecture (on probability) as Governor of the Bank of England.  My papers (listed below) on this topic are available in electronic form on request from

  • “Cot death or murder – weighing the probabilities”, Developmental Physiology Conference, June 2002.
  • “Multiple sudden infant deaths – coincidence or beyond coincidence?”, Paediatric and Perinatal Epidemiology, 18 (2004), 320-326.
  • “Reflections on the cot death cases”, Significance2 (2005), 13-15.


I am currently supervising a final year project on Cryptography.

Research Interests

Coding theory, Finite geometry, Combinatorics, Group theory, Probability and Statistics.

Qualifications and Memberships

  • BSc in Mathematics, University of Manchester, 1967.
  • MSc in Mathematics, University of Warwick, 1968.
  • PhD in Mathematics, University of Warwick, 1971.
  • Member of London Mathematical Society.
  • Member of Institute for Combinatorics and its Applications