You cannot falsify mathematics by experiment (except in the subjective Bayesian sense).
Actually, that’s technically false. The statements mathematical axioms make about reality are bizarre, but they exist and are actually falsifiable.
One of the fundamental properties we want from our axiomatic systems is consistency — the fact that it does not lead to a logical contradiction. We would certainly reject our current axiomatic foundations in case we found them inconsistent.
Turns out it’s possible to write a program which would halt if and only if ZFC is consistent. I would not recommend running this one as it’s a Turing machine and thus not really optimized (and in any case, ZFC being inconsistent is unlikely, and it’s even more unlikely that the proof of it’s inconsistency would be easy to be found with current technology), but in theory one might run one of such machines long enough to produce a contradiction, which would basically physically falsify the axioms.
Actually, that’s technically false. The statements mathematical axioms make about reality are bizarre, but they exist and are actually falsifiable.
One of the fundamental properties we want from our axiomatic systems is consistency — the fact that it does not lead to a logical contradiction. We would certainly reject our current axiomatic foundations in case we found them inconsistent.
Turns out it’s possible to write a program which would halt if and only if ZFC is consistent. I would not recommend running this one as it’s a Turing machine and thus not really optimized (and in any case, ZFC being inconsistent is unlikely, and it’s even more unlikely that the proof of it’s inconsistency would be easy to be found with current technology), but in theory one might run one of such machines long enough to produce a contradiction, which would basically physically falsify the axioms.
This is a good point. Mathematical axioms must be consistent.