Knot theory emerged as a branch of which abstract mathematical field?

Answer

Topology

The formal, analytical system recognized as knot theory developed specifically as a branch of topology. Topology itself is defined as the study of geometric properties that remain constant even when objects undergo continuous deformation, such as stretching or bending, provided there is no tearing or gluing involved. This characteristic aligns perfectly with the study of knots, where two diagrams represent the same mathematical knot if one can be continuously transformed into the other. While early motivations were physical (related to the aether), the methodology employed—focusing on properties invariant under deformation—cemented its identity within this abstract area of mathematics, moving it away from reliance on physical rope and toward abstract diagrams.

Knot theory emerged as a branch of which abstract mathematical field?

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