Proof and Computation in Geometry

We consider the relationships between algebra, geometry, computation, and proof. Computers have been used to verify geometrical facts by reducing them to algebraic computations. But this does not produce computer-checkable first-order proofs in geometry. We might try to produce such proofs directly, or we might try to develop a “backtranslation” from algebra to geometry, following Descartes but with computer in hand. This paper discusses the relations between the two approaches, the attempts that have been made, and the obstacles remaining. On the theoretical side we give a new first-order theory of “vector geometry”, suitable for formalizing geometry and algebra and the relations between them. On the practical side we report on some experiments in automated deduction in these areas.

• Type: Journal
• Year: 2013
• Where: ADG
• Authors: Michael Beeson
• Keywords: ADG 2013, Mathematics