I believe it's called scholars mate
smallest checkmate possible ever
I believe it's called scholars mate
No the Fool's Mate is a two mover, the Scholar's Mate (which a lot of people mistakenly call the Fool's Mate) is the Queen/Bishop mate in 4.

Smallest checkmate, by what metric?
Number of moves: 2.0 moves
Total units used: 1 unit
Smallest area: 1x3
Total points used: 2 points
Total points by offensive side: 1 point
Minimum point difference for offensive side: -38 points
I don't know what I'm doing.

I did keep legality in mind. (Position 1: retract -1. Qb1-b8#; position 2: retract -1. c6xNb7#; position 3: retract -1. b6-b7# Bc7-b8.)

Smallest checkmate would be with the smallest chessboard or diagram. VERY small. You'd be talking atoms or whatever makes up atoms or whatever makes up what makes up atoms, ad infinitum.

Look at this chess set: http://etikoppaka.blogspot.ro/2011/12/smallest-wooden-chess-set-in-world.html
You could deliver the "smallest" checkmate on it.
fools game