## Section: New Results

### Proofs that $e$ and $\pi $ and transcendental

Participants : Sophie Bernard, Laurence Rideau, Yves Bertot, Pierre-Yves Strub [IMDEA Software, Madrid] .

In the previous year, we developed formally verified proofs that $e$ and $\pi $ are transcendental. This year we cleaned up these proofs to obtain a common lemma that applies in both cases with simple hypotheses. In parallel, P.-Y. Strub streamlined the library on multivariate polynomials which plays a significant role in the case of $\pi $. This work has been published in [11] .

In the future, we will probably extend this work to more general proofs of transcendance.