What do fishermen, sailors, and mathematics have in common?  They all have an interest in knots, which have been used at least since the beginning of history.  Primitive, Egyptian, and Greek societies used knots extensively.  We know this through surviving artwork and archaeological records.  One interesting legend about knots involves the Persian king Gordius; he dedicated a special wagon to Zeus.  He proceeded to tie the pole of the wagon to its yoke, creating a knot so complex as to be seemingly impossible to untie.  Then the oracle of Zeus pronounced that whoever could untie the knot could be the king of Asia.  After many attempts to untie the knot, Alexander the Great  cut the knot with his sword, and announced that he would rule Asia with his sword.

Mathematics has found that knots are not always possible to untie without cutting them, like Alexander the Great opted to do.  Studying knots in mathematics began about 100 years ago, when scientist Lord Kelvin theorized that all atoms were simply knotted vortices in ether, a fluid which filled all space.  This prompted scientists to try to classify all knots, in order to understand atoms better.  When Kelvin's theory was invalidated by the atomic revolution, knot theory went by the wayside in most fields.  Consequently, knot theory was thought to be fairly unhelpful to other fields for many years.  However, some mathematicians continued to study knots, and in the 1980's, knot theory was discovered to have useful results in the fields of molecular biology.  DNA, scientists postulated, sometimes tangled into interestingly shaped knots, which, if understood could lead to revolutionary discoveries about the mechanisms of DNA replication.

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kMain menu       1. History              2.Intro               3.Invariants     4.Composition   5.Conclusion