Phylogenetics is concerned with the problem of reconstructing the past evolutionary history of organisms from molecular data, such as DNA, or morphological characters. There is ongoing interest in the further development of the mathematics that underlies computational phylogenetic methods. Hidden from view, in the software packages used by biologists, are algorithms performing statistical inference using Markov models on binary trees. The mathematics involved represents a unique confluence of probability theory, discrete mathematics, statistical inference, algebraic geometry, and group theory. There are many important theoretical problems that arise, such as statistical identifiability of models, consistency and convergence of methods. These problems can only be solved using a multi-disciplinary approach. Phylomania brings together phylogenetic researchers with a strong theoretical leaning, with the aim of discussing some of the more pressing problems.