Solving the Conway knot problem took mathematician Lisa Piccirillo on a journey into the fourth dimension. Here’s how she did it
5 August 2020
OVER the course of one week in 2018, Lisa Piccirillo cracked a mathematical problem that had gone unsolved for half a century. Posed by legendary mathematician John Conway in 1970, it concerns a complex geometrical object known as the Conway knot. While an ordinary overhand knot – the kind you would tie at the end of a thread – sees the string cross over itself three times, the Conway knot has 11 crossings. What Conway wanted to know is whether his knot can be formed by cutting a slice out of a more complex four-dimensional knot – or, as mathematicians put it, is it “slice”?
Piccirillo discovered that it isn’t. Her breakthrough came after finding a back door into the problem that could help mathematicians understand other four-dimensional objects. Currently a post-doctoral mathematician at Brandeis University in Waltham, Massachusetts, solving the Conway knot – along with her other research – has seen her offered a tenure-track position at the Massachusetts Institute of Technology. New Scientist spoke to her about the week she spent on the problem, her approach to mathematics and why it is time we stopped talking about geniuses.
Chelsea Whyte: How did you first become interested in mathematics?
Lisa Piccirillo: As a kid, I always liked maths and I was good at it in school. I’m from quite a rural area in Maine, and people said “if you like maths, you can become an engineer”. So I thought that’s what you do with maths, become an engineer. I went to a lot of day camps for engineering and made a lot of bridges out of popsicle sticks, and found out that …