Recent advances in quantum theory meet an explosion of different types of quantisation. Geometric quantisation that EU-funded scientists focused on speaks the language of geometry.
The geometry of classical mechanics is mainly differential geometry of finite-dimensional manifolds, fibre bundles and Lie groups. Its prominent role is due to the possibility of dealing with invariantly defined objects. On the other hand, the standard mathematical language of quantum theory had long been different from geometry.
Further details: The mathematics of quantum symmetries