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Knots have been used since antiquity, and people have known of the various properties of certain knots for centuries. Knots were first studied from a mathematical point of view by Carl Friedrich Gauss and his student Johann Benedict Listing.
Sir William Thomson (Lord Kelvin) theorized that atoms were knots of swirling vortices in the æther. This inspired Peter Guthrie Tait and others to try to classify all possible knots believing this would be equivalent to a periodic table of the elements. After Kelvin's vortex theory became obsolete, knot theory was no longer of great scientific interest.
After topology was founded, knots were investigated from a topological point of view, and some important discoveries were made such as the Alexander polynomial and the Reidemeister moves. Knot theory received a resurgence in mathematical interest after discoveries like the Jones polynomial and William Thurston's hyperbolization theorem.
Recently, new applications for knot theory have been discovered. Knots can be useful in detecting the chirality of molecules, and in studying the effects of topoisomerase on DNA. The related theory of braids, is the mathematical basis of topological quantum computers.