I think this point is odd. If you could really come up with a proper solution (a correct essay in this case) faster than to verify it then why not produce the correct solution directly instead of verifying.
And if you argue, but I don't want a different correct essay but I want this one verified my answer is that the corrected essay without flaws is also a different one.
I think where the line of argumentation in the article derails is that the author confused finding a solution with coming up with any odd candidate that could be a solution. The former is serious effort, the latter is trivial. Their Sudoku example is the former, their article example the latter
P vs NP, of course, but also the halting problem and Rice's theorem: non-trivial semantic properties of programs are undecidable.
In other words, if you say "this is the solution to that sudoku puzzle", that's easy to verify. "This sudoku puzzle has a solution" is almost certainly much harder to verify. "Here's a program that can solve any sudoku puzzle - impossible (in general).
I've been saying this for years. Especially related to predictions like "AGI in N years".. no, it will come a different speeds per domain. All proportional to the scale of verification.
Verifiable domains are usually math and code. Games also fit the bill. But for real world tasks there is the 1B people using AI, we verify, the signal is there implicit in the chat logs.
b0gb•6mo ago
aleph_minus_one•6mo ago
> https://en.wikipedia.org/wiki/TFNP
"TFNP is the class of total function problems which can be solved in nondeterministic polynomial time", i.e. we don't consider decision problems (as for NP), but total functions.
This class contains quite some interesting subclasses, such as PLS (solution can be found via Local Search), PPA (solution exists because of a Parity Argument), PPP (solution exists because of a Pigeonhole Principle), PPAD (solution exists because of a Directed Parity Argument), CLS, ...
In interesting article which explains this topic quite well is https://inference-review.com/article/when-existence-is-ineff...