[FOM] Geometry question

[Olivier Souan]

/Hello,
/         I would like to know of surveys in axiomatic theories of
geometries
/which do not allow for conceptions of points, lines and surfaces.

There are some interesting recent developments in that direction, in the
framework in algebraic geometry.

See Pierre Cartier, "A mad's day work : from Grothendieck to Connes and
Kontsevich. The evolution of concepts of space and symmetry", in Bulletin
(New series) of the AMS, Vol.38, 4, pp.389-408. The §3 could be of some
interest :
http://modular.fas.harvard.edu/sga/from_grothendieck.pdf

Best,

Olivier Souan
Preparing a PhD thesis on "Mathematical Platonism"
Univ.Paris 4 Sorbonne