Analysing Mathematical Proofs (or Reading between the Lines)

We study equation solving and analyse the solutions of experienced mathematicians. We find that traditional theorem proving methods are inadequate to explain the directness of these solutions, and that the well known algorithms for polynomials etc. are inadequate to explain the wide variety of equations solved. Our analysis reveals a system of high-level descriptions, strategies and goals, which can be used to guide the search through an explosively large search space. A few of these strategies will be investigated in detail. It is hoped that this analysis will eventually be incorporated into a computer program that solves equations.