# A PhD Student In The US Solved A Math Problem That Hasn't Been Solved For 50 Years In Just One Week

Monday, June 29, 2020
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In the US, a PhD student named Lisa Piccirillo solved the 'Conway knot' problem, which has not been solved for 50 years, in less than a week. Piccirillo, whose work was published in the science journal Annals of Mathematics, was appointed a faculty member at the Massachusetts Institute of Technology (MIT).

In the US, a PhD student named Lisa Piccirillo was able to solve a mathematics problem that had not been solved for exactly 50 years, having first heard of it at a seminar she attended in 2018, in less than a week, taking time out only in her spare time.

Piccirillo, who was studying for a PhD at the University of Texas when he started working on the problem called the’ Conway knot', spoke about his calculations with a relaxed attitude when talking to one of his professors at the University, Professor Cameron Gordon. Piccirillo said in a statement to Quanta that the professor's reaction at the time “suddenly started shouting ‘Why don't you get more excited?’ He was distraught, " he recounted.

## Lisa Piccirillo first heard of the Conway knot at a seminar she attended in 2018

The Conway knot problem was first raised in 1970 by British mathematician John Horton Conway, who died of coronavirus in recent months. Lisa Piccirillo first became aware of the existence of such a problem at a seminar she attended in 2018.

Piccrillo, whose work was recently published in the science journal Annals of Mathematics, was appointed as a faculty member at the Massachusetts Institute of Technology (MIT) after solving the problem.

## What is a math node?

In mathematics, and especially in graph theory, mathematical nodes, the subject of topology, are known as the fundamental elements that make up a line. To give a real-life example, the ends of a math knot are joined, the simplest knot is annular and unresolved. But the knot gets more complicated as the places it passes over it multiply.Marithania Silvero, of the Institute of Mathematics at the University of Seville, said the mathematical knots "intuitive idea is to imagine a rope. Knot theory works on deformations on this rope. In other words, we look at how we can bend this rope, bend it, fold it, stretch it. But we can't cut this rope. It is forbidden," he says.

## How did a PhD student solve the problem that hasn't been solved for 50 years?

The Conway node problem, which had previously been addressed by numerous mathematicians, had never been solved by anyone. In order to solve the problem, Piccirillo developed a similar version, known as the ‘sister knot’, which was less complex and became known as the Conway knot problem, which had 11 different transitions and twists.

Piccirillo, who managed to work on the sister knot for a while and solve it, then applied his findings on the Conway knot. Speaking to Quanta about his work, the young genius said of the process of solving the problem, “I didn't work on it in the daytime because I didn't see it as real math. I was looking at it more like a homework assignment, and I went home and did my homework," he recounts.

Elisenda Grigbsy, one of piccrillo's professors, says that when the young name began, he had no education beyond knot theory and linear algebra, but succeeded in equations, where a large number of PhD students were forced within a week.

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