1. Pickover places the discovery of knots at around 100,000 BC. He also mentions (and he was writing in 2009) that around 1.7 million non-equivalent knots with 16 or fewer crossings have been discovered.

2. His second milestone dates from 1988 when Sumners and Whittington (the latter a chemist) modelled ropes and other objects such as polymer chains, finding using purely mathematical procedures that nearly all *sufficiently long self avoiding random walks* will contain a knot (DOI: 10.1088/0305-4470/21/7/030), or more specifically that for n steps in a random walk, the knot probability goes to unity as n goes to ∞.

3. Finally, I note that Wikipedia has a whole section on knotted proteins, including trefoils. The topic of knotted proteins is a recent one, the first suggestions being in 1994!

A pentafoil knot is also reported, DOI: 10.1126/science.aaf3673, 3D Model DOI: 10.5517/CCDC.CSD.CC1KFN3R.

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