Yeah. On a similar note, without the computer aspect, I once had a prof tell me that he did not like character theory. If I remember right, there you calculate some numbers from a group and can prove some properties about it. But you gain no understanding of why those properties hold.
That was terrible phrasing. I meant "The problem with the proof was that although it showed that FCT was true, the proof did not explain why".
Yeah. On a similar note, without the computer aspect, I once had a prof tell me that he did not like character theory. If I remember right, there you calculate some numbers from a group and can prove some properties about it. But you gain no understanding of why those properties hold.
> the proof did not explain why
So humans do/did still have a role to play
Something as simple as the FCT may have an alternative intuitive proof that humans can relate to.
I do not think it is a given that humans or algorithms can find such a proof for any given problem.
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Unless the existence of the reason is also proved.
Unless AI can explain why today.
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