On the notion of interestingness in automated mathematical discovery

We survey five automated discovery programs working in mathematics, by looking in detail at the discovery processes they illustrate, summarising the successes they’ve had and by focusing on how they estimate the interestingness of concepts and conjectures. We then extract some common notions about the interestingness of conjectures and concepts. We detail how empirical evidence is used to give plausibility to conjectures, and the different ways in which a concept or conjecture can be thought of as novel. We also detail how programs assess how surprising and complex a conjecture statement is, and the different ways in which the applicability of a concept or conjecture is used. Finally we note how a user can set tasks for the program to achieve and how this affects the calculation of interestingness.