There are certain topics in mathematics where ‘philosophy’ (in the broadest sense) is likely to intrude. Introducing negative or complex numbers is one: is mathematics discovered or invented? Another one is proof by contradiction (or contrapositive, see Kinnear & Sangwin, 2018, for a discussion of the difference).
This article first appeared in Scottish Mathematical Council Journal 51 (2021), pp. 74-77 and is reprinted in Mathematics in School with the kind permission of the Council.