[hsn915]

Covered in the video/article.

I'll post the relevant paragraphs, all quoted directly (verbatim) from the blog post:

Physicists knew about this puzzle since the 1960s or so, but initially they didn’t take it seriously. At this time, they just said, well, it’s only when we look at the black hole from the outside that we don’t know how reverse this process. Maybe the missing information is inside. And we don’t really know what’s inside a black hole because Einstein’s theory breaks down there. So maybe not a problem after all.

But then along came Stephen Hawking. Hawking showed in the early 1970s that actually black holes don’t just sit there forever. They emit radiation, which is now called Hawking radiation. This radiation is thermal which means it’s random except for its temperature, and the temperature is inversely proportional to the mass of the black hole.

This means two things. First, there’s no new information which comes out in the Hawking radiation. And second, as the black hole radiates, its mass shrinks because E=mc^2 and energy is conserved, and that means the black hole temperature increases as it evaporates. As a consequence, the evaporation of a black hole speeds up. Eventually the black hole is gone. All you have left is this thermal radiation which contains no information.