The Homfly polynomial is a mathematical invariant used in the study of knots and links in topology. It generalizes the Alexander polynomial and the Jones polynomial, providing a way to distinguish between different knot types. The polynomial is defined for oriented links and can be computed using a specific recursive formula based on the crossings in a knot diagram. This polynomial is particularly useful because it can capture more information than its predecessors, allowing mathematicians to analyze the properties of knots more effectively. The Homfly polynomial is named after its developers, HOMFLY, who introduced it in the 1980s, contributing significantly to knot theory.