Mathematical results should never be accepted or rejected by whether you "trust this guy". You should read the work, think about it, and decide for yourself whether the results are right or wrong.
That's true, but trust is the way most everything is built outside of academics.
Why do we use X framework? Well, because Mr. Deep Pockets over there is using it!
I wish we could have a more mathematical world, but it doesn't scale beyond a handful of architects and really talented engineers.
The amount of hassle and push back I get for getting 100% code coverage tells me that it's rare for people to leverage more concrete and deeper ideas to even validate their thinking. The market rewards "just ship it" way more because ultimately customers just learn to manage the shit that ships.