A computer-assisted proof that e is rational
Résumé
Computers are increasingly being used to help researchers write up mathematical proofs, sometimes by automatically writing out parts of it. In this paper we present different computer-assisted approaches and provide some use cases. Using the Mixed-Integer Linear Programming (MILP) approach, we demonstrate that $e$ is rational, contrary to what has already been proved by hand and with interactive proof assistants. This is the opportunity to dive into the numerical instabilities problems and to discuss limitations of MILP solvers. These tools have some advantages over other approaches, so we propose to explore methods to verify the solutions obtained. To this end, we develop a Julia package to automatically check whether solutions meet the initial requirements or not.
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