In 1953 Mordell asked whether one can represent 3 as a sum of three cubes in any way other than 13+13+13 and 43+43 -53. Mordell’s question spurred many computational investigations over the years, and while none found a new solution for 3, they eventually determined which of the first 100 positive integers k can be represented as a sum of three cubes in all but one case: k=42. In this talk I will present joint work with Andrew Booker that used Charity Engine’s crowd-sourced compute grid to affirmatively answer Mordell’s question, as well as settling the case k=42. I will also discuss a conjecture of Heath-Brown that predicts the existence of infinitely many more solutions and also explains why they are so difficult to find.
This video is part of the Number Theory Web Seminar series.
