A Simple Way To Measure Knots Has Come Unraveled
SMRTR summary
A tangled mathematical puzzle that has confounded experts for nearly 150 years has finally unraveled. Two mathematicians have disproven a century-old conjecture about knots using a collection of overheated laptops and remarkable persistence.
"When the paper was posted, I gasped out loud," said Allison Moore of Virginia Commonwealth University, describing her reaction to Mark Brittenham and Susan Hermiller's groundbreaking discovery.
The mathematicians tackled the "unknotting number" problem - a measurement of how many crossing changes it takes to untie a mathematical knot into a simple loop. Since 1937, mathematicians believed the "additivity conjecture": when combining two knots, the unknotting number should equal the sum of the individual knots' unknotting numbers.
Using a network of computers they called their "sneakernet," the University of Nebraska duo analyzed millions of knot diagrams over a decade. Some computers didn't survive the mathematical marathon. "There was one that actually sent out sparks," Brittenham noted. "That was kind of fun."
Their persistence paid off. They discovered that two knots with unknotting number 3, when combined, could be untied in just 5 steps instead of the predicted 6.
The result reveals the stunning complexity of a seemingly simple question: how hard is it to untie a knot?
SMRTR provides this summary for quick context. The original article belongs to Quanta Magazine.
Read the original article