Some tangles that look like knots are actually “the unknot”, which can be untangled into a simple loop, and a new algorithm has sped up the process of finding them
Source:
https://www.newscientist.com/article/2266995-determining-which-knots-are-not-really-knots-just-got-much-faster/?utm_campaign=RSS%7CNSNS&utm_source=NSNS&utm_medium=RSS&utm_content=home