Mathematics professors tackle knot theory
Three University of Nevada, Reno math professors can do what a computer can’t – solve knot theory.
Swatee Naik, Chris Herald and Stanislav Jabuka plan to use a $286,000 grant from the National Science Foundation to work with other math professors around the country to study new techniques used in knot theory.
The goal of the grant is to use the money to travel and further their understanding of knot theory mathematics.
“It’s a very simple problem to explain to somebody at a high school math level,” Jabuka said. “It’s more difficult to actually solve it.”
Knot theory, which is a math problem, is part of a visual math called topology, Jabuka said. A knot is a loop that crosses over and loops through itself.
The goal of knot theory is to compare two knots by adding or removing crossings and see if both knots are similar, Jabuka said.
“For example, so far 14 is the highest number of crossings in a knot that can be compared,” he said. “Somebody might have solved a knot with 15 crossings, that’s the sort of thing the project is looking for.”
Herald said in an e-mail that he is using money from the grant to take the entire month of October to visit Paul Kirk and Charles Livingston, both experts of knot theory, at the University of Indiana.
A computer is incapable of solving knot theory question, so people have to work on the problems themselves, Jabuka said.
“In order to compare one knot to another, I might have to add millions, even billions of crossings before I can start removing them,” Jabuka said. “Computers would not know when they should stop adding crossings, so they will never ever be able to solve these equations.”
Knot theory is normally shown in two-dimensional drawings, or flat images of knots. Recent new math techniques have allowed the use of three-dimensional knots, like computer-generated images of knots and four-dimensional knots which change shape or position over a period of time
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