Following the work of Rolf Schimmrgk, it is tempting to try to piece together the "big picture", in relating motives to black holes and emergent spacetime. In the 10D stringy picture, one considers automorphic forms on the worldsheet and constructs the Calabi-Yau varieties induced by those automorphic forms. One can also consider black holes with Siegal form partition function (modular form) and ask if the form is associated to (motives of) a compactified geometry. This is the essence of the stringy extension of the geometric Langland's program.
Hence, the "big question", in quantum gravity, is can one always re-construct spacetime geometries from number theory information? More examples are needed, but there are tantalizing hints coming from supergravity and topological string theory.