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For knot fans - there's also a code golf problem on Stack Exchange that only has one solution so far - Knot or Not? https://codegolf.stackexchange.com/q/30292



The spectacular knot homology theories such as Khovanov Homology and Heegaard Floer Homology can detect the unknot 'on the blackboard' as well. Wow!!! Actually it can detect the genus of the knot: that's an amazing theorem! I wish I understood how it worked :)




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