Joint Colloquium: Berry -- Divergent series: from Thomas Bayes’s bewilderment to today’s resurgence via the rainbow

Following the discovery by Bayes in 1747 that Stirling’s series for the factorial is
divergent, the study of asymptotic series has today reached the stage of enabling
summation of the divergent tails of many series with an accuracy far beyond that of
the smallest term. Several of these advances sprang from developments of Airy’s
theory of waves near optical caustics such as the rainbow. Key understandings by
Euler, Stokes, Dingle and Ecalle unify the different series corresponding to different
parameter domains, culminating in the concept of resurgence: quantifying the way in
which the low orders of such series reappear in the high orders