Showing Chocky by John Wyndham

Matthew's parents are worried. At eleven, he's much too old to have an imaginary friend, yet they find him talking to and arguing with a presence that even he admits is not physically there. This presence - Chocky - causes Matthew to ask difficult questions and say startling things: he speaks of complex mathematics and mocks human progress. Then, when Matthew does something incredible, it seems there is more than the imaginary about Chocky. Which is when others become interested and ask questions of their own: who is Chocky? And what could it want with an eleven-year-old boy?