For A, a common misconception is that models write out lean proofs from the start. They write/develop the Natural Language proofs, and then translate (sometimes not even the same model) to lean afterwards.

The four-color theorem appears to be case C. That was the first really long computer-assisted proof. No one has since found a concise way to do that proof, and it's been half a century now.

D. They seek disruption as way to market dominance and worldly power. It's not unfortunate, in their minds, but the means to their ends.

Disruption has been a SV buzzword for a long time now. It's not a byproduct but a strategy for your new technology product. SV has long perfected disruption and the people behind the AI products are masters at it.

How can so many who have seen it (and used it) for so long be so taken in by this well-worn tactic. Over and over, they choose what is most disruptive. They could have dealt with the mathematical output in many ways, including working with mathematicians to polish and publish; you see what OpenAI chose.

Similarly was the recent events where AI software 'broke containment' and hacked others. Obviously they could have controlled it if they valued it; they got the result they wanted. Notice how Anthropic (or were they first and OpenAI followed?) urgently publicized that their product, too, 'broke containment'. 'We're disruptive too!'