Cosmology with X-RAY galaxy cluster surveys ?
  This talk reviews the scientific motivations, the potential difficulty and
recent advances in cosmology using cluster number-counts in the X-ray band. Our
forward modelling approach shows that many of the practical and conceptual
shortcomings can now be overcome. We present recent results from the XMM-XXL
survey. The next step is to apply artificial intelligence techniques on
simulations. This allows us to bypass the unnecessarily complicated scaling
relation formalism. The net gain is to significantly reduce the number of free
parameters and to provide direct access both to the cosmological parameters and
to truly physical ingredients, such as AGN feedback. In this way, we achieve
cluster cosmology without explicit cluster mass calculation.
