The Insane Math Of Knot Theory

most of us tie our shoelaces wrong there are two ways to tie a knot in your shoelaces in one you go counterclockwise around the loop and in the other you go clockwise these two methods look almost identical but one of these knots is far superior to the other it doesn't loosen or come untied nearly as easily to understand why we need to delve into knot Theory this is a whole branch of mathematics that aims to identify categorize and understand every possible knot that could ever exist so far we have discovered the first 352 million 152 252 knots each one has its own particular properties and characteristics I think it's fascinating that there's something like a periodic table for knots out there but it's not pure math not theory has turned out to be remarkably useful it is core to the structure of proteins and DNA it's leading to new materials that could be stronger than Kevlar it's even used to develop medicines that save millions of lives all of this just from trying to understand the humble not [Music] so what is a knot well in our everyday lives we see knots like this or this but if you're trying to rigorously study knots you want to be able to pull them apart so you can really see what's going on the problem is knots like this are held together only by tension and friction so if you pull on them too hard they fall apart so in order to capture the knot on the Rope mathematicians got the idea to connect the two ends and now well you can tease the knot apart to study it but it will never fundamentally change so in not Theory all knots exist on closed Loops this means the simplest knot you can have is just a circle like this now admittedly this is not much of a knot which is why it is called an unknot here is another knot again it's made of a single piece of rope that forms a closed loop here is another two knots are only different if you can't make one into the other without breaking the loop this is the simplest knot after the unknot it is called the trefoil and you can see that there's no way for me to turn this back into a circle unless I actually ...