> hardware is a lot more likely to be mathematically proven

Maybe that's a nitpick, but I would say it's fundamentally impossible to mathematically prove anything at all about a physical system. You have to assume some model to do the proof and have no way of ever "proving" (what would that even mean?) that model.

I guess you're referring to the fact that verification and formal methods are used in hardware more often than software. This is due to commercial reasons: you can't just reprogram a million chips once they leave your fab.