Doughnut topology offers new mathematical framework for classifying textiles

For centuries, human hands have woven, knitted, and crocheted textiles through intuition and tradition — but now mathematicians are finding that the same abstract geometry describing a doughnut also describes the deep structure of a knitted sweater. Researchers applying topology, the mathematics of shape and continuity, have developed a framework that classifies textiles not by how they look, but by how their loops and connections relate to one another at a fundamental level. This convergence of ancient craft and abstract mathematics suggests that the fabrics clothing humanity carry within the