Knot Theory is the study of, well, knots. Inspired by real-world examples, this unique field of mathematics specializes in the tying, untangling and categorization of theoretical knots. Picture a fastened necklace twisted in a jewelry box - the chain crosses itself at various points creating a knot. The number of times it crosses, the ability to untangle the necklace, and the uniqueness of the pattern are all key elements of knot theory. But let’s be clear, these mathematicians aren't dealing with necklaces, their knots are far more abstract.
Knot theory got its start in 1869 with Scottish mathematician William Thomson (AKA Lord Kelvin). He hypothesized that atoms were made up of a series of knots that corresponded to elements. Although this was later proved wrong, the interest in theoretical knots grew over the years, leading to practical applications across the sciences, including quantum physics, biology and cosmology.
For example, knot theory may help shed light on how the double helix in DNA unfurls before it replicates itself. Applications of the theory are also being used in cryptography, helping to create super secret encryption keys for two-way communications.
Like most scientists, knot theorists love to categorize things, which is why each knot is judged on how many crossings it has (as well as other super complex mathematical properties). At the turn of the 20th century, experts identified a whopping one million different knots that have 16 crossings.
Mathematicians are typically faced with three questions when categorizing a knot:
How many times does the knot cross itself.
Can the knot be untangled without ‘cutting’ it.
Is it a known knot (no other knot has the same crosses, twists and turns).
We know... it sounds like a bunch of scientists playing with laces. But knot theory isn’t without its drama. Earlier this year, Lisa Piccirillo, a student at the University of Texas, solved a decades-long knot conundrum in just one week. She went to class, learned about the Conway Knot Problem, did some super smart mathematics and concluded that the knot was not slice- a type of knot that exists in both 3rd and 4th dimensional space.
Tying our shoelaces never felt so complicated.
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Image by Reimund Bertrams