[pdonis]

He proved both. He and Penrose proved theorems that showed that, under certain assumptions, the area of a black hole's event horizon can never decrease. But he later showed that quantum fields near the horizon can violate some of the assumptions that are required for the area theorem, so when those quantum effects are taken into account, black holes can radiate and this can cause the area of their event horizons to decrease.

[kibibu]

So he proved "if x then y", then later proved "!x"

[knzhou]

Well, perhaps, but in physics we like to think of our field as containing many separate, logically independent models of reality. Yes, "x" probably isn't true in our universe, but it is true in an exceptionally good model for our universe, and that's what makes it an important result. It's like how the round Earth is wrong, but way less wrong than the flat Earth.

[nightcracker]

No. x -> y && !x does not give !y, it just gives nothing.

He proved y under some set of assumptions, and then later !y under another set of assumptions. So he proved a -> y && b -> !y.

[xamuel]

But, given x->y, if you prove !y, you can conclude !x, so in a sense kibibu is right (possibly requiring "proved" to be read as "indirectly proved"), and we should give them the benefit of the doubt.

[pdonis]

> given x->y, if you prove !y, you can conclude !x

But given x -> y, if you prove !x, you can't conclude anything. And kibibu said !x, not !y.

[kibibu]

Yeah, I interpreted:

> quantum fields near the horizon can violate some of the assumptions that are required for the area theorem

as !x

[aeternum]

I don't think it is correct to say he proved both. A more correct statement would be something like "Stephen Hawking proved that the area of a black hole’s event horizon cannot decrease within the realm of classical mechanics".