Keller's conjecture <https://en.wikipedia.org/wiki/Keller's_conjecture> proposed that if Euclidean space R^n were tiled by n-dimensional cubes any which way, then there must be some pair of n-cubes that share a common (n-1)-dimensional face. This is intuitively true in dimensions 2 and 3, but was proved true in dimensions up through 6 by Oskar Perron in 1940. To the surprise of many people, Lagarias & Shor (1994) found a counterexample in dimension 10. This immediately leads to counterexamples in all higher dimensions as well. Soon after a counterexample was found in dimension 8, showing it was also false in dimension 9 and leaving the only dimension where it was open being dimension 7. A team of four people — Joshua Brakensiek, Marijn Heule, John Mackey, and David Narváez — used a computer program to search for counterexamples in dimension 7, and in October 2019 they found one: <https://arxiv.org/abs/1910.03740>. There a nice article about it in Quanta magazine: <https://www.quantamagazine.org/computer-search-settles-90-year-old-math-problem-20200819/>. —Dan