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so we are on a quest to find a complete invariant for nuts in other words we want to find some mathematical object which when it measures the same thing for two different knots weamp;#39;re guaranteed for those two knots to be the same up until this point the invariance weamp;#39;ve been able to build such as the crossing number the bridge number the unknotting number the fraction for a rational tangle none of them have been perfect fractions or rational tangles completely classify rational tangles but not every knot in the world is built on top of a rational tangle similarly the numerical invariants we found for knots so far are good insofar as if I have two different diagrams of the same knot then those numerical invariants are going to measure the same but itamp;#39;s not always the case that if that numerical invariant is the same for two diagrams it doesnamp;#39;t always mean that I have the same knot right there are several different knots that have crossing number of six or
