This paper shows for the first time how neural networks can be applied to the problem of stylometry. We provide an elementary introduction to the concept of neural network and its advantages as a pattern recognition technique. We then show how to take the basic multilayer perceptron architecture and train it to recognise the writing of different authors. As a concrete example of its application, we construct a multilayer perceptron to investigate questions surrounding the purported works of Shakespeare and his young acolyte John Fletcher. The plays The Double Falsehood and The London Prodigal are found to have strongly Fletcherian characteristics, Henry VIII strongly Shakespearean characteristics, and The Two Noble Kinsmen characteristics suggestive of collaboration.