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OED: Noun.
1. Clearness of understanding or insight; great mental penetration; discernment.
2. Keenness of sight.
(OED, 2nd Ed, accessed through U of MN Libraries)

Taubes: “Less easy to imagine, though, is how anyone avoids this fate, particularly if we believe that the balancing of intake and expenditure is maintained not by some finely tuned regulatory system… but, rather, by our conscious behavior and our perspicacity at judging the caloric value of the foods we eat” (298).

Sentence: The mathematician’s great perspicacity allowed him to understand and solve the famous problem.