alt Hacker NewsOne 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.
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>Lean doesn't solve the problem of verifying that a formal theorem actually states what we think it states rather than something else.
With all honesty, if a tool existed that did that we would have solved maths. Or at least we would have solved human communication. In both cases it would be the most studied thing in the world, so I don't know where this belief would come from
Are there, in general, ways to do that? Sorry if this sounds like a troll question, but I struggle to think of how one would verify that a formal statement matches the accepted understanding other than painstakingly going through the definitions with experts from both sides.