P. G. Tait undertook a study of knots in response to Kelvin's conjecture that the atoms were composed of knotted vortex tubes of ether
(Thomson 1869). He categorized knots in terms of the number
of crossings in a plane projection. He also made some conjectures which remained
unproven until the discovery of Jones polynomials:

Conjectures (1) and (2) were proved by Kauffman (1987), Murasugi (1987ab), and Thistlethwaite (1987, 1988) using properties of the Jones polynomial
or Kauffman polynomial F (Hoste et al.
1998). Conjecture (3) was proved true by Menasco and Thistlethwaite (1991, 1993)
using properties of the Jones polynomial (Hoste
et al. 1998).

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Knots." Math. Intell.20, 33-48, Fall 1998.Kauffman,
L. H. "State Models and the Jones Polynomial." Topology26,
395-407, 1987.Menasco, W. and Thistlethwaite, M. "The Tait Flyping
Conjecture." Bull. Amer. Math. Soc.25, 403-412, 1991.Menasco,
W. and Thistlethwaite, M. "The Classification of Alternating Links." Ann.
Math.138, 113-171, 1993.Murasugi, K. "The Jones Polynomial
and Classical COnjectures in Knot Theory." Topology26, 187-194,
1987a.Murasugi, K. "Jones Polynomials and Classical Conjectures
in Knot Theory II." Math. Proc. Cambridge Philos. Soc.102, 317-318,
1987b.Tait, P. G. "On Knots I, II, III." Scientific
Papers, Vol. 1. London: Cambridge University Press, pp. 273-347, 1900.Thistlethwaite,
M. B. "A Spanning Tree Expansion of the Jones Polynomial." Topology26,
297-309, 1987.Thistlethwaite, M. B. "Kauffman's Polynomial
and Alternating Links." Topology27, 311-318, 1988.Thomson,
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