Branches of Mathematics
Knot Theory
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Knot theory is the branch of topology that studies mathematical knots, embeddings of a circle in three-dimensional space whose ends are joined so they cannot be undone. It emerged from nineteenth century physical speculation that atoms were knotted vortices in the ether, which motivated the first systematic knot tables in the 1880s, and it survived the collapse of that physical theory to become a mathematical field in its own right.
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Central QuestionGiven two different-looking descriptions of a closed loop embedded in three-dimensional space, is there a way, ideally a computable one, to tell whether they represent the same knot? 1 Key DebateWhether knot theory's founding motivation, Lord Kelvin's nineteenth century theory that atoms were stable knotted vortices in the ether, deserves credit as a genuine scientific origin given that the physical theory itself was entirely wrong; the systematic knot tables Peter Guthrie Tait built to catalogue possible vortex atoms in the 1880s outlived the physics that inspired them and became the field's own foundation. 1 Cross-Tradition Connections
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