Andrew Sutherland: Sums of three Cubes (NTWS 002)
Channel: Number Theory Web Seminar
Date: 2023-04-11

Abstract: In 1953 Mordell asked whether one can represent 3 as a sum of three cubes in any way other than 1^3+1^3+1^3 and 4^3+4^3 -5^3.  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

Number Theory Web Seminar: https://www.ntwebseminar.org

Original air date: 
Thursday, May 7, 2020 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 8:30pm IST, 11pm China Standard Time, (+1) 1am AEST, (+1) 3am NZST)