The true history of the Knot Theory began in the early 1800's with the work of the german mathematician, Karl Frederich Gauss (1777 - 1855), who was always interested with knots. His contribution to the Knot theory was "analysis situs", which deals with the mathematical difference between simple and complex knots. The mathematical differences between different knots in comparison to how the naked eye percieves the knot is extremely different. Until Gauss began his work, the mathematical and physical differences were almost impossible to differentiate between.
After the work of Gauss there was no real social interest in Knot Theory, until the late 1800's when English scientist, Lord Kelvin, took up an interest in the theory and began his own work. Also known as William Thomson, Lord Kelvin's greatest theory/achievement was the idea of "ether" and the chemical basis of the universe. Lord Kelvin believed that the universe was filled with an invisible and frictionless fluid, which he called "ether", and atoms were the vortex's in "ether", in the shape of knots. Thus, a table of knots would be a table of elements. Kelvin's theory was latered disproved when an interest for atomic chemistry became of social interest.
Kelvin's theory inspired Scottish physicist, Peter Tait, to undergo an intensive study to create a tabulation of different knots, in an attempt to try to understand when two knots are different. Tait's final explanation of "different" and "same" knots is still one that is used today. "Two knots are isotopic if one of them can be continuosly changed in 3 dimensional space(self-intersection not allowed) until it is identical in shape to the other." The diagram to the right is a portion of Taits' work. This table would probably be known today as the periodic table if Lord Kelvin's theory had been true, but once physicists disproved Kelvin's work, they also dismissed Tait's work. Click image for larger size. After Tait's theories were dismissed along with his 163 knot projections, other mathematicians and physicist began to become more interested in his work and his understanding of isotopic similarities in terms of how one knot could be continuously manipulated to look identical to another. This understanding of knot manipulation was summarized in a set of possible different knots. These projections are now known as the "Tait Conjectures". Research relating to the Knot theory continued but in the early 1950's with the work of Crick and Watson, the Knot theory collided with the genetic and biological world.
James Watson and Francis Crick finally uncovered, in 1953, DNA's double helix shape.It wasn't until the 1980s until scientists discovered that DNA strands can become tangled at times. This discovery led to the rise of Knot theory and the study of three-dimensional figures. |