[FOM] Resources on the empirical foundations of mathematics

[Ben Crowell]

>I have also read that some theoretical physicists have theorized that
>space-time may be discrete (i.e., not continuous) at a sufficiently
>small, sub-atomic scale.

A good popular-level book on this is Three Roads to Quantum Gravity
by Lee Smolin. Apparently there are some people who think topos
theory may be relevant to solving the quantum gravity problem, and
he goes into that a little. There also seems to be some interest among
string theorists in synthetic differential geometry.