The Unknotting Problem

The unknotting issue, another one of math's largest problems that appears absurdly straightforward, is a class of related but unsolved problems. In its simplest version, it questions if it is possible to develop an algorithm to demonstrate that a particular kind of random knot is in fact unknotted. To be clear, a knot is any closed curve that exists in three dimensions and can be demonstrated to be unknotted if it exists in two dimensions and does not have any intersecting lines.

You would have to repeatedly untangle whatever knot that could be made in order to demonstrate this while making sure no lines crossed one another. The solution may be considered correct if the resultant figure can always lay exactly in a two-dimensional plane. However, this is something that mathematicians have been trying to do for a while, but no such method has ever been discovered.