Fait mathématique: 1682 is the number of monoids of order 7 with 7 idempotents.
Culture générale: 1682 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Date historique: August 8th is the day in 1786 that Mont Blanc on the French – Italian border is climbed for the first time by Jacques Balmat and Dr Michel-Gabriel Paccard.