One of the most important theorems that played a role in smashing mercantalism was that of the specie-flow mechanism, the chief proponent of which was David Hume. It should be noted that Richard Cantillon formulated the theorem first. But Cantillon's work was not published until after Hume wrote on the subject. Mark Thornton has an interesting paper claiming that Hume may have had access to Cantillon's work nonetheless. I will definitely write about that paper at some point.
Also significant in smashing mercantalism was Hume's work with the quantity theory of money (although Hume's formulation was inferior to that of Cantillon's) and his insight that money was a "lubricant" of prosperity, not a "fuel", as well as his insights regarding the importance of commerce in general.