Background
Tait came up with his conjectures after his attempt to tabulate all knots in the late 19th century. As a founder of the field of knot theory, his work lacks a mathematically rigorous framework, and it is unclear whether the conjectures apply to all knots, or just to alternating knots. Most of them are only true for alternating knots. In the Tait conjectures, a knot diagram is reduced if all the isthmi have been removed.
Read more about this topic: Tait Conjectures
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