Re, k and π : a conversation on some aspects of mathematical modelling

Re and k discuss π's approach to what we understand by a mathematical model; how it may have certain generic properties and how hierarchies of related models arise in connexion with a given physical situation. Joined at this point by π, they continue to talk about the way in which models are formulated and prepared for solution. This preparation involves such things as the choice of the most suitable dimensionless variables, reduction to the smallest number of equations, proving uniqueness and discovering the shape of the solution. In conclusion, some aspects of the presentation of the results are discussed. The abbreviated names of Reynolds, Boltzmann and Pythagoras have been used only to denote the engineer, natural scientist and mathematician taking part in the discussion; there is no allusion to the points of view of the historic figures.