  We present the first double-resummed prediction of the inclusive cross
section for the main Higgs production channel in proton-proton collisions,
namely gluon fusion. Our calculation incorporates to all orders in perturbation
theory two distinct towers of logarithmic corrections which are enhanced,
respectively, at threshold, i.e. large x, and in the high-energy limit, i.e.
small x. Large-x logarithms are resummed to next-to-next-to-next-to-leading
logarithmic accuracy, while small-x ones to leading logarithmic accuracy. The
double-resummed cross section is furthermore matched to the state-of-the-art
fixed-order prediction at next-to-next-to-next-to-leading accuracy. We find
that double resummation corrects the Higgs production rate by 2% at the
currently explored center-of-mass energy of 13 TeV and its impact reaches 10%
at future circular colliders at 100 TeV.
