We survey five mathematical discovery programs by looking in detail at the discovery processes they illustrate and the success they had. We focus on how they estimate the interestingness of concepts and conjectures and extract some common notions about interestingness in automated mathematical discovery. We detail how empirical evidence is used to give plausibility to conjectures, and the different ways in which a result can be thought of as novel. We also look at the ways in which the 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. We conclude with some hints on the use of interestingness measures for future developers of discovery programs in mathematics.