Untangling the beautiful math of KNOTS

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Suppose you have two tangled knots. How can you tell whether they are the same knot or different knots? Welcome to Knot Topology. A knot is a nice embedding of a circle into three dimensional space, up to "ambient isotropy" where you can wiggle it around but not cut it. We can project this onto a plane to create a knot diagram. Then, two knot diagrams represent the same knot if and only if there is a sequence of Reidermeister moves between them. We next explore various knot invariants like the simpler tricolorability and then expand to the Alexander Polynomial and ultimately compute this polynomial for the trefoil knot.

The software I used to make all the knots is called https://knotplot.com/

0:00 Mathematical Knots
0:33 Knot Diagrams
1:48 Reidermeister Moves
4:24 The equivalence problem
6:05 The idea of Knot Invariants
6:27 Tricolorability
9:12 Alexander Polynomial
14:37 Future direction in Knot Topology
16:01 Brilliant.org/TreforBazett

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