What significant leap in knot theory followed the initial attempts by Thomson and Tait?

Answer

Development of powerful polynomial invariants like the Jones polynomial

Although Lord Kelvin and Peter Guthrie Tait made foundational contributions by attempting to create comprehensive knot tables based on physical models to test the vortex theory, their early classification attempts were eventually surpassed by more abstract mathematical tools. A major advancement occurred much later, in the 1980s, with the development of powerful polynomial invariants. Chief among these is the Jones polynomial. These polynomials serve as concise signatures for a knot, offering a calculation-based method for comparison that is significantly more effective and less reliant on manipulating physical models or struggling with difficult-to-calculate invariants like the crossing number. This development marked a definitive transition into the modern, abstract discipline.

What significant leap in knot theory followed the initial attempts by Thomson and Tait?

Related Questions

What motivated Lord Kelvin and Peter Guthrie Tait's study of knots?Knot theory emerged as a branch of which abstract mathematical field?What mathematical descriptors are sought to distinguish non-equivalent knots?What allowed two knot diagrams to represent the same mathematical knot?What significant leap in knot theory followed the initial attempts by Thomson and Tait?Which physicist connected quantum field theories to topological invariants like the Jones polynomial?What distinguishes the analytical "knot system" from prehistory knot tying?What specific area of study was Johann Benedict Listing noted for in early topology?What was the immediate purpose of cataloging knot configurations by Kelvin and Tait?Besides quantum gravity, what current area applies knot mathematics to physical structures?
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