Well, if in future we do end up with a magical tool that can solve any formal mathematical problem on a whim, we really won’t need field of mathematics anymore as it is today.
replyThere would be no need to deliver new mathematical insights by solving problems. You would just have a magical math problem solving machine and that’s it.
What do you mean “we won’t need mathematics as it is today”?
replyTo further human understanding is itself a goal that single-handedly justifies our efforts.
Jumping straight to the “answer” and therefore missing both the understanding of the actual problem, and any useful discoveries along the way is a waste at best, and actively harmful at worst.
Physics alone is more than enough to “further human understanding”. All current mathematicians can move to other sciences, closest being fields in physics, and it will all continue to progress just fine.
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replySurely it is. Ask it to keep a list of all the promising sub paths, reprompt the collections of agents again on these after the main problem has been addressed.
Or even release a list of them and let others investigate.
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