Towards Intuitive Reasoning in Axiomatic Geometry
This work addresses the challenge of teaching axiomatic geometry to students by reducing the burden of formal proof construction, though it is incremental as it builds on existing automated theorem proving tools.
The paper tackles the problem of time-consuming lemma proving in synthetic geometry by using the interactive theorem prover Elfe, which leverages automated theorem provers to handle intermediate lemmas, enabling students without formal mathematics experience to learn axiomatic geometry more easily.
Proving lemmas in synthetic geometry is often a time-consuming endeavour since many intermediate lemmas need to be proven before interesting results can be obtained. Improvements in automated theorem provers (ATP) in recent years now mean they can prove many of these intermediate lemmas. The interactive theorem prover Elfe accepts mathematical texts written in fair English and verifies them with the help of ATP. Geometrical texts can thereby easily be formalized in Elfe, leaving only the cornerstones of a proof to be derived by the user. This allows for teaching axiomatic geometry to students without prior experience in formalized mathematics.