From the world of Advanced Mathematics: Knot Theory
Studied as part of Topology, mathematical knots are closed loops in 3D-space. The core idea of Knot Theory is to classify & manipulate knots to understand complex mathematical behavior. Knots are of various types - e.g., composite, prime, ribbon, satellite, torus, trivial (unknots), etc.
Knot Theory is extensively applied in different fields like biology (e.g., understanding processes like DNA replication), chemistry (e.g., development of new molecules), physics (e.g., study of electromagnetic field lines & quantum fields), and computer science (e.g., computational topology & visualization.)
Modern research in Knot Theory aims to address its unsolved problems (e.g., Slice-Ribbon Conjecture), study its application in quantum physics, and create efficient algorithms for classifying knots & for calculating knot invariants.