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Comment by cubefox

One thing I didn't know until recently was that Lean doesn't solve the problem of verifying that a formal theorem actually states what we think it states rather than something else.

In some cases that's not an issue, because the formal statement of the theorem is very simple. E.g. for Fermat's Last Theorem, which can be formally expressed with "(x y z : ℕ+) (n : ℕ) (hn : n > 2) : x^n + y^n ≠ z^n". But in other cases it might be much harder to verify that a formal statement actually matches the intuitive informal statement we want.

Of course, Lean or similar languages still offer the huge potential of verifying that a formal statement is provable, even if they don't help with verifying that the formal statement matches the intended informal statement in natural language.

parent cubefox 1 year ago

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