Are double negatives always wrong?

In standard written English, two negatives in the same clause cancel out, so I didn't see nothing logically means you saw something. That is why it is treated as an error in formal writing.

But the picture is more interesting than a simple prohibition.

Many languages require double negatives. In Spanish, no vi nada — literally "I didn't see nothing" — is the only correct way to say it. French, Italian, Russian and many others work the same way. This is called negative concord, and it is entirely normal in world languages.

English used to do it too. Chaucer and Shakespeare both used multiple negatives for emphasis rather than cancellation. The prohibition dates from eighteenth-century grammarians applying the logic of mathematics to language, on the argument that two negatives must make a positive.

It survives in many dialects, including African American Vernacular English and numerous regional British and American varieties, where it functions as emphasis and is understood by every speaker of those dialects without ambiguity. Linguistically it is a feature of those dialects, not an error within them — though it is not standard written English, which is what matters in formal contexts.

There is also a deliberate literary use, the litotes: understatement by negating the opposite. She's not unhappy is not the same as she's happy — it is more guarded, and that shade of meaning is the point. Not uncommon, not without merit and no small achievement all work this way.

So: avoid unintentional double negatives in formal writing, and recognise that deliberate ones are a tool rather than a mistake.