Professor Hibbert graduated MA, DPhil from Oxford University in Mathematics. In 1967, he joined the Department of Applied Mathematics in Queen's University Belfast as a postdoctoral fellow, and was subsequently appointed Assistant Lecturer (1968), Lecturer (1970), Reader (1980) and Professor of Applied Mathematics (1992). He was Head of the Applied Mathematics Teaching Department for 1989-1998 and 2004-2008, Director of Education in the School of Mathematics and Physics for 2005-2008 and Head of the Theoretical and Computational Physics Research Division for 2001-2004. He chaired the government working party which drew up the proposals for the Mathematics curriculum in the Northern Ireland Common Curriculum.
He is a Fellow of the Institute of Mathematics and its Applications (1998), the American Physical Society (2002) and the Institute of Physics (2003), and was elected Member of the Royal Irish Academy in 2000.
He has given many invited conference talks and seminars overseas, and has been on the international scientific committees of a number of conferences. He chaired the local and scientific committees of the triennial Atomic Structure and Spectra conference held in Belfast in 2001.
His research interests include the calculation of accurate atomic data: energy levels, oscillator strengths, transition rates, hyperfine structure and photoionisation cross sections. The aim of the research is to determine accurate data and to develop uncertainty limits, by a study of convergence, so that users of the data - astrophysicists and plasma physicists - are aware of the likely bounds on the calculated results. He has also worked on photoionisation of atoms and ions and the photodetachment of negative ions, including pioneering work on hollow atoms.