[Covenantor]

Ahh..."...In mathematical knot theory, you throw everything out that's related to mechanics," Dunkel says. "You don't care about whether you have a stiff versus soft fiber—it's the same knot from a mathematician's point of view...."

All well and good in the ivory tower kingdom...except that everyone who's handle ropes, cords or lines knows that material type and mechanics play very important roles in practical usage. As an example, a simple slip knot tied with a hemp rope will retain it's shape and function whereas a polypropylene, stiff and slick, will not, due to difference in amount of friction. Soak the hemp rope, tighten the slip knot and it becomes more difficult to move, plus or minus depending on need.

[DUMBGRUNT]

Knots are some intersting things, many years of climbing and many of my fellow climbers deep into knots... I retained a few fun bits.

No knot is stronger than the rope. (NOT SOME HATCHET KNOT)
Splices can be stronger than the rope.

Most knots weaken the rope, sometimes over 50%.

Most knots have been known for a long time.
IIRC about 300? Not included the now computer-generated knots. The computers took the fun out of it for some and gave it to others.