[AstralStorm]

You do this by involving mathematical proofs at every stage. That is expensive, but sometimes done.

Strict functional languages are a step in the right direction. As are verifiers as done in Rust.

[BlackFly]

Some use cases and bugs are not amenable to proof. For example, how do you mathematically prove that your rendering engine is cutting off the bottom of the g of your new font?

Not all requirements of a system can be expressed a priori. I think proofs will never be enough to make a bug free system. Working as intended is a very frustrating response to a perceived bug for a user.