The answer is in the concluding paragraph. >It began as an applied area of mathematics, with Thomson attempting to use knots to understand the makeup of matter

The answer is in the concluding paragraph. >It began as an applied area of mathematics, with Thomson attempting to use knots to understand the makeup of matter. As that idea faded, it became an area of pure mathematics, a branch of the intriguing and still unpractical domain of topology. Basically because they're interesting. A better headline will've been something like "knot landscape in mathematics" since it covers the knot theory history and advancements.