On Albert Lautman from nLab page :
[Lautman influenced: Deleuze, Badiou, Fernando Zalamea, Jean Petito, David Corfield]
“Lautman detects some specific features of advanced mathematics that are not given in elementary mathematics:
a) the complex hierarchisation of various theories, irreducible to systems of intermediate deduction;
b) the richness of the models, irreducible to linguistic manipulation;
c) the unity of structural methods and of conceptual polarities, beyond the effective multiplicity of models;
d) the dynamics of the creative activity, in a permanent back-and-forth between freedom and saturation, open to the Platonic division and the Platonic dialectic;
e) the mathematically demonstrable relation between what is multiple on a given level and what is singular on another, through a sophisticated lattice of mixed ascents and descents.
Lautman on the abstract world of mathematics and the sensible world of physics as both participating in the same dialectical structure.
I have _some_ reconciliation with Plato from a neurological POV … I should say cognitive science – but I’m working on bridging that further–