Proof in Context

1) Wider research context
Unlike other sciences, mathematics does not rely on experiments or other empirical procedures to justify its conclusions. Instead, its primary means of justification is proof, a form of justification that relies on reasoning alone and is supposed to make plain that the proved proposition is not just true, but necessarily so. But while mathematicians tend to agree on what a proof is when presented with one, it is notoriously hard to pin down what a proof actually is. Towards the end of the nineteenth century, several scholars started to delineate what they thought was essential to proof, and as a result, they developed the first formal systems of logic. Since then, logicians have studied formal proofs as objects in their own right. And yet, ever since the dawn of modern mathematical logic, scholars from different fields have stressed that there is a significant gap between the formal and informal concepts of proof that needs to be explained.