Asymptotic series abound in physics. Borel resummation and resurgence theory are among the powerful tools to deal with them. The former provides a way to convert asymptotic series to numbers,
the latter reveals that different asymptotic series at different saddle points are related to each other by Stokes automorphism characterised by Stokes constants. We argue that the Stokes constants can be treated
as new invariants of the system, and in many cases can be interpreted as counting BPS states. We support this statement with examples in Seiberg-Witten theory, complex Chern-Simons theory, and topological string theory.
