El 17° problema de hilbert

En 1900, en Paris, David Hilbert, invitado a dictar una conferencia, propone 23 problemas abiertos de matemáticas [10]. La solución de estos problemas era difícil: podemos citar, por ejemplo, los trabajos de Montgomery, Zippin y Gleason para resolver el 5º, aquellos de Julia Robinson y Matijasevich para el problema 10 y la respuesta negativa de Nagata al problema 14

Towards an Intelligent Tutor for Mathematical Proofs

Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs. We characterize the particularities of the domain and discuss common ITS design models. Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453