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  "body": "\n## Summary\n\nA knot invariant is a quantity attached to each [[knot|QYEAZTYGPT]] that takes the same value on equivalent knots.\nInvariants are the main tool to prove that two knots are different: if an invariant differs, the knots are not equivalent.\nExamples are the [[crossing number|SWJZ4QRF9W]], the [[knot group|AQVHM3FP0D]], [[tricolorability|KNAGK0W65G]], the [[Alexander polynomial|JKA25KDPQP]] and the [[Jones polynomial|4SPC17FPXE]].\n\n## Explanations\n\n### L1 human\n\nTo tell two knots apart, it is not enough to fail to untangle one into the other.\nInstead one computes something from each knot that does not change when the knot is moved.\nIf the two results differ, the knots are surely different.\nFor example, the trefoil can be coloured with three colours by a certain rule and the unknot cannot, so the trefoil is really knotted.\n",
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