We encourage anyone interesting in automated mathematical conjecture-making to experiment with Nico’s amazing conjecture-making program. The underlying heuristic is Fajtlowicz’s Dalmatian heuristic; the code adapts some of Patrick’s INP code and some Grinvin code. We’ve been making our own experiments. We encourage others to do the same.
Conjecture-making is a central part of the mathematics creating process. We envision a future where most mathematicians use conjecture-making programs as part of their research, at least as much as they use computers for computations today. The program conjectures relations between numerical invariants of any Sage object. We plan to add property-relation conjecture functionality at some point.