Mathematical demonstrations are as airtight as is a hand proof that software will run correctly when you are not allowed to compile it. In other words, there is no such thing as proof.

With that established, useful conversation needs to posit the existence of a shared reality, accepted by all participants. That means that a childlike refusal to accept the outside world can render anyone utterly immune to outside input.

Some people mistake this childishness for profound wisdom. I do not. On the opposite extreme I don't accept the blind acceptance of conventional belief systems as wisdom either. Instead I try to hit the middle ground, accept a shared reality so that communication is possible, but attempt to remain aware of what has been accepted as well...

Cheers,
Ben