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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.
Tait's Flyping Conjecture states that the number of crossings is the same for any diagram of an Alternating Knot. This was proved true in 1986.
See also Alternating Knot, Flyping Conjecture, Jones Polynomial, Knot
References
Tait, P. G. ``On Knots I, II, III.'' Scientific Papers, Vol. 1. London: Cambridge University Press, pp. 273-347, 1900.
Thomson, W. H. ``On Vortex Motion.'' Trans. Roy. Soc. Edinburgh 25, 217-260, 1869.