When the Stirling numbers of the second kind were introduced by James Stirling in 1730, it was not combinatorially; rather, the numbers ${n \brace k}$ were defined via the polynomial identity $$ x^n = \sum_{k=1}^n {n \brace k} x(x-1)\ldots (x-(k-1)). ~~(\star) $$ Most modern treatments of the Stirling numbers introduce ${n \brace k}$ combinatorially, as the number of ways of partitioning a set of size $n$ into $k$ non-empty blocks, and then (combinatorially) derive identities such as ($\star$).

While preparing for some upcoming talks on topics related to Stirling numbers, I realized that I have no idea who it was who first observed that the numbers ${n \brace k}$ defined by ($\star$) have a combinatorial interpretation.

The earliest reference I can find is in W. Stevens, Significance of Grouping, Annals of Eugenics volume 8 (1937), pages 57--69 (available at http://onlinelibrary.wiley.com/doi/10.1111/j.1469-1809.1937.tb02160.x/abstract). This seems to predate any mention of ``Stirling numbers of the second kind'' on MathSciNet.

I imagine that this is a question that has been thoroughly researched --- does anyone know of a reference?