Physics has one quantum (or rather two quanta?) to pick with mathematics / Les mathématiques ont maille à partir avec la physique quantique (ou plutôt deux quanta à partager?)

The videos of the second Alain Connes' lecture at Collège de France for 2017 (entitled "La géométrie et le quantique") that took place last week are available now (same site as last ones mentioned in the former post).
Some slides to illustrate the title of this post:

As a teaser to the third lecture (on next Thursday 19 January) let's note that in the last six minutes of the second lecture (video "12 janvier 15h45-17h") Connes provides his general philosophy to address "quantum gravity" problems with functional integral calculation on 4D Euclidean geometries with 3D+1 Minkowski space-time "boundaries" (fitting with Hawking and Gibbons results)...