Three high school students, along with their mentor Malors Espinosa from the University of Toronto, set out to prove a new theorem related to knots and fractals. They revisited Karl Menger’s century-old theorem about the Menger sponge and aimed to show that all knots could be found within it. Through a clever and meticulous process, the students were able to demonstrate this, leading to a groundbreaking result. The students faced challenges and setbacks in their research, but ultimately persevered and found innovative solutions. Their work not only advances mathematical knowledge but also opens up possibilities for measuring the complexity of fractals and inspiring new art forms.
https://www.quantamagazine.org/teen-mathematicians-tie-knots-through-a-mind-blowing-fractal-20241126/