This study is an attempt to clarify the nature of mathematical proof and brings into question many of the fundamental beliefs that we hold with regard to mathematical proofs. This study by necessity is a discussion of the philosophy of mathematics since the notion of proof is closely tied to our fundamental concepts in mathematics. Throughout this study there is an underlying criticism of the Formalist approach to mathematics, and more specifically, a criticism of the 'New Maths' introduced worldwide in the 1960's. The introduction of the New Maths saw a much greater emphasis on rigour in secondary mathematics, in algebra and trigonometry as well as the traditional geometry. This stress on rigour came about because it was believed that rigorous proof was the most important characteristics of modern mathematics. This study accepts the point that the secondary school curriculum should reflect modern mathematical theory and practice but rejects the notion that this is best achieved through a strict rigorous approach.