Appears in collection : Probability and Geometry in, on and of non-Euclidian spaces / Probabilités et géométrie dans, sur et des espaces non-euclidiens

Take a polynomial of degree n with coefficients +/ - 1 taken randomly, independently. What is the probability that it is irreducible over the rationals? This question is still open, but a lot of progress happened around it in recent years. We will survey some of this progress, including joint work with Lior Bary-Soroker, Dimitris Koukoulopoulos and David Hokken.