In the category of guessing, there is the Ramanujan Machine. This project got off on the wrong foot with the research mathematics community because their initial announcement made overblown claims (such as claiming novelty for some conjectures/theorems that weren't new), but it is my belief that the general concept is sound. Along similar lines, perhaps it's time to revisit Graffiti with modern neural nets. In his paper On Conjectures of Graffiti (Ann. Discrete Math. 38 (1988), 113–118), Siemion Fajtlowicz described a computer program for generating conjectures about finite graphs. Most of its conjectures were either false, trivial, or known, but it did come up with some novel conjectures that were interesting enough for graph theorists to spend time proving them and publishing the proofs.

In the category of guided search, people have tried to use neural networks to improve the performance of SAT solvers; see for example the work on NeuroSAT. This seems like a promising area for further research.