This Mondrian math puzzle yields puzzling scores

Mathematician Gordon Hamilton presents a curious puzzle inspired by the art of Piet Mondrian: within a square canvas filled with rectangles that all have different dimensions, what's the lowest possible score when subtracting the smallest rectangle's area from the largest?

As the area of the canvas increases, the lowest score sometimes goes down, and other times up.

Below are the lowest possible scores in the series:

• 5x5: 4
• 6x6: 5
• 7x7: 5
• 8x8: 6
• 9x9: 6
• 10x10: 8
• 11x11: 6
• 12x12: 7
• 13x13: 8

Mondrian Puzzle (YouTube / Numberphile)