Please tell me the difference between these two products.

They walked down separate paths.

I think we should try a different method.

I was really surprised by his cruelly brusque treatment.

The staff at that restaurant provided astonishingly kind treatment, and we were very satisfied.

This is my first question.

He is passionate about researching pure mathematics.

He is majoring in applied mathematics at university.

He is a world-famous mathematician.

Combinatorics is a branch of mathematics that studies combinations of things.