General fact: 6757 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Mathematical fact: 6757 is the number of connected graphs with 10 vertices and 34 edges.
Trivia: 6757 is an unremarkable number.
Historical date: July 1st is the day in 1881 that General Order 70, the culmination of the Cardwell and Childers reforms of the British Army, comes into effect.