My main interest is in automated scientific discovery and how this fits into the question of computational creativity. I have a grand challenge for computing research (meant to last for decades) here:

From 1996-2002, I worked in Alan Bundy's Mathematical Reasoning Group, and my main application area was mathematics. I wrote the HR program to perform automated theory formation in mathematics, then generalised this to theory formation given any (reasonable) scientific data. Theory formation involves the invention of concepts, the making of conjectures and - in domains where the axioms admit this - the proving of theorems and finding of counterexamples. The best reference for this project is the book published by Springer:

• Automated Theory Formation in Pure Mathematics

• Early days of theory formation (overview)
• How HR makes conjectures
• How HR invents concepts

• Inventing Integer Sequences
• Learning mathematical concepts
• Discovering additional constraints for CSPs
• Aiding in the setting of mathematical exercises
• Comparing automated theorem provers
• Adding to a library of theorems
• Making conjectures about computer algebra functions
• Differentiating between algebraic structures
• Generating puzzles

There are more papers about each of these topics on my publications page.

I've worked on projects to try and extend the capabilities of theory formation, including:

• Cross-domain theory formation
• Meta-level theory formation
• Multi-agent theory formation

HR can be seen as a creative AI program, and I've endeavoured to use it to explore machine creativity issues, including:

• The effect of input knowledge on the creativity of programs
• The notion of interestingness in heuristic searches
• Assessing creative programs

I'm currently involved in a number of projects, the two main ones being:

• Alison Pease's PhD to explore Lakatos style reasoning, and it's effect on the modelling of creativity in a social setting. Alison is implementing a multi-agent version of HR to test various Lakatos-style techniques for fixing faulty theorems. For a report on this project, see Edinburgh Technical report 0056.

• Roy McCasland's visiting fellowship project to apply automated theory formation to discovery in an algebraic domain known as Zariski spaces.

I'm now a member of Stephen Muggleton's Computational Bioinformatics Group, and - while I'm continuing with mathematics projects - I am also turning my attention to using HR and/or the Progol program for discovery tasks in bioinformatics. I don't have any publications on this yet, but I've written about:

• The similarities and differences of HR and Progol

If you've read this far, then you may be interested in seeing some more web pages on the HR program:

• Web pages from the original PhD project about HR (1996-1999)
• The current HR pages (still under construction, sorry)
• The NumbersWithNames program (a spin off from the work with integer sequences)
• An multi-agent version HR available online