Given positive real numbers x_1,...,x_n, an old problem dating back to Schur (1918) and Siegel (1945) aims at understanding the distribution of the traces t = (x_1 + ... + x_n)/n on the positive real axis, when the polynomial (x-x_1)*...*(x-x_n) has integer coefficients and is irreducible. It turns out that there is a discrete set of isolated points and that the traces become dense in [t_0,+oo), for some threshold t_0. Finding the exact value of the threshold and classifying all isolated points below t_0 has been the subject of extensive research throughout the years. I will survey old and recent progress on this topic and mention a recent breakthrough by Alexander Smith (Annals 2024) on the determination of the threshold t_0.