Taivi (AI tutor)¶

Taivi is an AI-powered mathematics tutor that guides learners through Socratic dialogue. Instead of handing out solutions, Taivi asks targeted follow-up questions and gives step-by-step hints, so students work out the solution themselves. Taivi runs entirely on European infrastructure, is operated by European companies and complies with the GDPR. Use is voluntary, and dialogue data is used only in anonymized form, to improve the tutor and for research.

Taivi is currently available in two versions.

Taivi for courses such as OMB+ and HM4mint¶

In such courses, Taivi is built directly into the MUMIE platform. It knows the learner's current, personalized exercise and the course content. To keep its feedback mathematically reliable, it combines large language models with symbolic mathematics: a language model assesses each learner's answer, and a powerful computer algebra system checks it as well.

Taivi for university courses¶

Taivi for arbitrary university courses is embedded via LTI (Learning Tools Interoperability) in local learning management systems such as Moodle or ILIAS. It is connected as a stand-alone LTI tool and needs neither the MUMIE plugins nor a MUMIE course. It is a multi-component agentic AI application whose components include a retrieval-based (RAG) system grounded in the learning material of the specific course, so its explanations and hints draw directly on the lecture notes, exercises and other materials students already work with. In particular, it uses the notation and terminology of the course in question. This version has been in use since the winter semester 2026/27 in the Linear Algebra course at RWTH Aachen University.