System A lunar theory is one of the high points of Babylonian mathematical astronomy. In the cuneiform tables of lunar ephemerides which tabulate many aspects of lunar motion, including the length of the synodic month, one of the columns, known as Column Φ, remained a mystery at the time of publication of the authoritative monograph, Astronomical Cuneiform Texts, Otto Neugebauer (1955). The subsequent discovery of additional cuneiform astronomical tablets and their interpretation by several scholars, including O. Neugebauer, B. L. van der Waerden, A. Aaboe and J. Britton has led to the understanding of the meaning of Column Φ and its origin based on two numerical algorithms. We will describe their research on this fascinating example of mathematical modelling from approximately 400 BCE.