Mathematical fact: 634 is a number n whose 5^{th} root has a decimal part that begins with the digits of n.
Trivia: 634 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Historical date: September 25th is the day in 1775 that Ethan Allen surrenders to British forces after attempting to capture Montreal during the Battle of Longue-Pointe.