Abstract: There are 352.2 million prime knots in the 3-sphere with at most 19 crossings. In joint work with Sherry Gong, I studied which of these knots are slice, in both the smooth and topological categories. While no algorithm is known for deciding whether a given knot is slice in either setting, we were able to determine it smoothly for all but about 11,400 knots (0.003% or 1 in 30,000) and topologically for all but about 1,400 knots (0.0004% or about 1 in 250,000). In particular, we showed that some 1.6 million of these knots (0.46%) are smoothly slice (in fact ribbon) and that 350.5 million are not even topologically slice (99.54%). I’ll discuss the varied tools and techniques we used for this (many rooted in quantum topology, specifically Khovanov homology), and explain how our data is consistent with several important conjectures and suggests new ones. I'll explain how hyperbolic geometry plays an important role in these methods and discuss some surprising and unexplained patterns in the hyperbolic geometry of plausibly slice knots.