There’s an ongoing discussion on math sites about Vladimir Voevodsky’s Fall 2010 lecture expressing doubts that math is consistent, i.e. doubts that it is not possible to deduce formally correct proofs of false statements starting from standard axioms.
Consistency links
There’s an ongoing discussion on math sites about Vladimir Voevodsky’s Fall 2010 lecture expressing doubts that math is consistent, i.e. doubts that it is not possible to deduce formally correct proofs of false statements starting from standard axioms.
Voevodsky’s original lecture
FOM discussion
mathoverflow discussion