Making Sense of Proof by Contradiction [pdf]

Proof by contradiction is a standard logical technique taught in mathematics: to prove a statement P, you assume P is false and then derive a logical contradiction, concluding that P must be true. This PDF, by mathematics educator Colin Foster, addresses a common pedagogical problem — many students find the method confusing, arbitrary, or unsatisfying because they struggle to see why a false assumption "proves" anything. The paper discusses ways to teach the method more intuitively, often using everyday analogies (e.g., proving someone cheated by showing that if they hadn't, the evidence would be impossible). Foster is a well-known figure in UK maths education (associated with the Mathematical Association and the University of Nottingham). The piece appears in the *Scottish Mathematical Council Journal*, a practitioner-focused publication for teachers. For the general reader: this is not about new mathematical discoveries but about how to make a foundational logical tool make sense to learners.