An Upper Bound on Reidemeister Moves

 

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Graham’s number is famous for being the largest number to have ever shown up in a proof. The true story is more complicated, as I discovered by asking Graham. But here’s a much smaller but still respectable number that showed up in knot theory:

It’s 2 to the 2 to the 2 to the 2… where we go on for 101,000,000 times. It appears in a 2011 paper by Coward and Lackenby. It shows up in their upper bound on how many steps it can take to wiggle around one picture of a link until you get anothe...