Reductio ad Absurdum (Proof by Contradiction)

This is the elegant trick of proving something by assuming the opposite and showing it leads to an outright impossibility. Greek geometers wielded it to demonstrate that the diagonal of a square cannot be measured by its side—the discovery of irrational numbers—and that certain results must hold uniquely. Aristotle gave it a formal name and place in his logic, calling it "leading back to the impossible," and it remains a cornerstone of mathematical reasoning to this day.