I doubt many pure mathematicians would be okay with totally subordinating all exploratory mathematical investigation to specific practical problems, and the field would look very different both in terms of how it's organized and what output it produces were it run that way.
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It sounds like you've answered your own question of:
And you're really just quibbling about scheduling.
Whether humans will be involved or not is an entirely different debate.
I doubt many pure mathematicians would be okay with totally subordinating all exploratory mathematical investigation to specific practical problems, and the field would look very different both in terms of how it's organized and what output it produces were it run that way.