This is an announcement for the paper "On uniformly differentiable mappings" by Eva Pernecka. Abstract: We are concerned with the rigidity of $\ell_\infty$ and $\ell_\infty^n$ with respect to uniformly differentiable mappings. Our main result is a non-linear analogy of the classical result on the rigidity of $\ell_\infty$ with respect to non-weakly compact linear operators by Rosenthal, and it generalises the theorem on the non-complementability of $c_0$ in $\ell_\infty$ due to Phillips. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46T20 Submitted from: pernecka@karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1503.03536 or http://arXiv.org/abs/1503.03536