alt Hacker News> but I would like to understand the problem, too
But why should it be the case that this is always possible?
It's entirely reasonable that the set of useful mathematical proofs is a proper superset of human intelligible useful proofs.
In fact, to argue the contrary would imply there is something incredibly remarkable about human cognition.
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No, it doesn’t imply that.
Just that the set of proofs a human can interpret and the set of statements a human can understand overlap; conversely, you require that the statements/theorems humans can understand be a larger class than the proofs they can understand.
To me, it’s not obvious which of those should be true:
- can we only understand theorems for which we comprehend their proof?
- or can we understand theorems despite not comprehending the proof structure?
Within the mathematics community, opinions differ. But you’re elevating your perspective on that question into a law, without any evidence.
> It's entirely reasonable that the set of useful mathematical proofs is a proper superset of human intelligible useful proofs.
If you can't explain something in a way that a child could understands it, you don't fully understand it either.