We study probability density functions that are log-concave. Despite the space of all such densities being infinite-dimensional, the maximum likelihood estimate is the exponential of a piecewise linear function determined by finitely many quantities, namely the function values, or heights, at the data points. We explore in what sense exact solutions to this problem are possible. Joint work with Alexandros Grosdos, Alexander Heaton, Kaie Kubjas, Olga Kuznetsova, and Georgy Scholten.