Automated Theorem Proving

Suppose that we have a conjecture in plane geometry. The usual approach to settling whether it is true or not is to try to deduce the result at hand from the axioms of geometry and other statements directly derived from them. Algebraic geometry promises an alternate approach. If we can formulate the conjecture as a system of polynomials equations, then the above logic problem has been turned into an algebraic one: solving equations. The former requires the reasoning skills of humans, the latter, the computational power of software. In this way, we can hope to automate the process of theorem proving. The goal of this project is to see how well this works and to what range of theorems it applies.

Project:The second part of chapter six in your book provides a nice introduction to this topic. I have also included a number of references. Your job is to figure out how algebraic geometry comes into play. Your paper should contain an introduction to the relevant parts of algebraic geometry as well as an introduction to automated theorem proving. As a capstone, pick a theorem from geometry and prove it using these techniques.

• Wu's original paper
• Liu: some results on theorem proving