The automation of mathematical reasoning, with applications to reasoning about the correctness of computer software and hardware; and the automatic construction, analysis and evolution of representations of knowledge, also called ontologies. His research combines artificial intelligence with theoretical computer science and applies this to practical problems in the development and maintenance of computing systems.

Alan Bundy is a fellow of several academic societies, including the Royal Society, the Royal Society of Edinburgh and the Royal Academy of Engineers. The major awards for his research, include the IJCAI Research Excellence Award (2007) and the CADE Herbrand Award (2007). He was awarded a CBE in 2012. He was Head of Informatics at Edinburgh (1998-2001) and a member of: the Hewlett-Packard Research Board(1989-91); the ITEC Foresight Panel (1994-96) and both the 2001 and 2008 Computer Science RAE panels (1999-2001, 2005-8). He was the founding Convener of UKCRC (2000-5), a member of the Scottish Science Advisory Committee (2008-12) and a Vice President and Trustee of the British Computer Society with special responsibility for the Academy of Computing (2010-12).

His research has entailed the building of a number of problem solving programs for different branches of mathematics, namely number theory, algebra, mechancis, ecological modelling and logic/functional programming.  He is the author of a book on the automation of mathematical reasoning, the editor of three books on artificial intelligence and joint author of one book on ecological modelling and one on the social impact of knowledge-based systems.  He has been the sole or joint holder of 56 major grants from EPSRC, SERC, Alvey, ESPRIT and ESRC and is the sole or joint author of over 250 published papers and books.