  We give a survey of our joint ongoing work with Ali Chamseddine, Slava
Mukhanov and Walter van Suijlekom. We show how a problem purely motivated by
"how geometry emerges from the quantum formalism" gives rise to a slightly
noncommutative structure and a spectral model of gravity coupled with matter
which fits with experimental knowledge. This text will appear as a contribution
to the volume: "Foundations of Mathematics and Physics one century after
Hilbert". Editor: Joseph Kouneiher. Collection Mathematical Physics, Springer
2017
