A mathematical knot is a closed loop in three-dimensional space that cannot be untangled without cutting the loop. It is a concept studied in the field of topology, which is a branch of mathematics focused on the properties of space that are preserved under continuous transformations. Knots can be classified based on their complexity and the number of crossings they have. Mathematicians use various tools to analyze knots, including knot diagrams and invariants that help distinguish one knot from another. The simplest knot is the unknot, which is just a simple circle. More complex knots, like the trefoil knot, have unique properties that make them interesting for both theoretical studies and practical applications, such as in molecular biology and computer science.