Most mathematicians, responsible for teaching solution methods for partial differential equations, would claim that an exact solution is always preferable to a numerical solution. This paper throws doubt on this view and shows, by considering a particular example, that the distinction between an exact solution and a numerical solution to a partial differential equation is not as clear as is often claimed. We demonstrate this by obtaining the exact solution for the torsion problem for a rectangular corner section. It appears the ‘exact’ solution cannot be written in closed form but necessarily involves the solution of an infinite system of linear equations which, except in certain special cases, can only be solved numerically. Thus, computing the exact solution can involve as much numerical effort as in computing the numerical solution. However, the exact solution contains algebraic ‘forms’ not present in the numerical solution which can be used to analyse special cases. This solution, which will be of particular interest to those working in the area of solid mechanics, is described in detail. The solution technique will attract the interest of those looking for non‐trivial applications of the use of Fourier series in the solution of linear partial differential equations.