Automated Geometry Theorem Proving for Human-Readable Proofs

Abstract

Geometry reasoning and proof form a major and challenging component in the K-121 mathematics curriculum. Although several computerized systems exist that help students learn and practice general geometry concepts, they do not target geometry proof problems, which are more advanced and difficult. Powerful geometry theorem provers also exist, however they typically employ advanced algebraic methods and generate complex, difficult to understand proofs, and thus do not meet general K-12 students’ educational needs. This paper tackles these weaknesses of prior systems by introducing a geometry proof system, iGeoTutor, capable of generating human-readable elementary proofs, i.e. proofs using standard Euclidean axioms. We have gathered 77 problems in total from various sources, including ones unsolvable by other systems and from Math competitions. iGeoTutor solves all but two problems in under two minutes each, and more importantly, demonstrates a much more effective and intelligent proof search than prior systems. We have also conducted a pilot study with 12 high school students, and the results show that iGeoTutor provides a clear benefit in helping students learn geometry proofs. We are in active discussions with Khan Academy and local high schools for possible adoption of iGeo-Tutor in real learning environments.