>That would cost an arm-and-leg,
Without being able to provide any evidence, I'm quite sure (that is, I hypothesize) that if a theorem is clearly stated, such as in the case of formal proof assistants, we'll soon reach a point where we'll have a distributed network in which people are able to 1) provide economic incentive for somebody to provide a given proof, 2) somebody else to potentially offer a better proof which will computationally be accepted (verified by some algorithm that prefers one proof over another by some sort of metric), and therefore 3) have a system in which the validity of a computer algorithm, which has been stated as a conjecture, can be mathematically created and verified in a decentralized fashion.
>it would need to be done by someone who actually understands both the theory of proving algorithm corectness and the algo in question
If the theorem is stated clearly, no further understanding is needed. But of course they'd need the understanding of providing the right axioms and definitions, which are as limited as possible, to state their conjecture. That, I think, will be the point at which the purpose of the mathematician will shift from providing proofs, towards discovering interesting and coherent conjectures, as the proving of those will turn into a kind of rat-race, and ultimately merely a computational challenge.
Anyways, I'm just rambling about some things that have been on my mind recently. Don't take me too seriously.