While he was publishing papers right up until the months before his death, it was in 2016 that he released one of his most talked about journal articles - a long-awaited solution to his black hole information paradox.
In other words, he'd come up with a potential explanation for how black holes can simultaneously erase information and retain it.
To understand why it was such a big deal, and what the black hole information paradox really is, we need to go back to where it all started.
Our original understanding of black holes, according to Einstein's generally theory of relativity, is that everything that crosses the event horizon - the boundary of a black hole - is lost forever. Even light can't escape its clutches, which is why black holes are called black holes (and also why it's impossible for us to actually see one).
But then in the 1970s, Hawking proposed that radiation actually can escape from a black hole, because of the laws of quantum mechanics. Put very simply, he suggested that when a black hole swallows one half of a particle-antiparticle pair, the other particle radiates away into space, stealing a little energy from the black hole as it leaves.
Because of this, eventually, black holes can disappear, and the only remaining trace would be the electromagnetic radiation they emitted - which is known as 'Hawking radiation'.
The problem is that, according to Hawking's best calculations, that radiation would contain no useful information about what the black hole ate - the information swallowed up would have been lost forever.
And that doesn't gel with our understanding of modern physics, which states that it's always possible to reverse time. In theory, at least, processes in the Universe will look the same if they're running forwards or backwards.
As Dennis Overbye explains over at The New York Times:
"The Universe, like a kind of supercomputer, is supposed to be able to keep track of whether one car was a green pickup truck and the other was a red Porsche, or whether one was made of matter and the other antimatter. These things may be destroyed, but their 'information' - their essential physical attributes - should live forever."
Hence the paradox. And it's actually a big deal not just for astrophysicists, because if the rules of quantum mechanics don't hold up for black holes, then what's to say they apply to the rest of us?
But in 2016 Hawking proposed a solution to the problem - black holes might actually have a halo of 'soft hair' surrounding them, which are capable of storing information.
That 'hair' isn't actually hair - as you might have already assumed - but is actually low-energy quantum excitations that carry with them a signature pattern of everything that's been swallowed up by the black hole, long after it evaporates.
"That pattern, like the pixels on your iPhone or the wavy grooves in a vinyl record, contains information about what has passed through the horizon and disappeared," wrote Overbye at the time.
To come to this conclusion, Hawking identified two underlying problems with his original assumptions, which is why he says his original calculations - which suggested that the information inside a black hole would be lost forever - were wrong.
Those two assumptions were that the vacuum in quantum gravity is unique, and that black holes have no quantum 'hair'.
That's getting a little complex, but what you need to know is that Hawking has since revised his calculations, and is fairly sure that black holes have 'soft hair' haloed around them.
This hypothesis was peer-reviewed and published in Physical Review Letters, and researchers are claiming that, while there's more work to be done, it's a promising step towards solving the information paradox.
"It is important to note that this paper does not solve the black hole information problem," wrote physicist Gary Horowitz from the University of California, Santa Barbara, in an accompanying commentary.
"First, the analysis must be repeated for gravity, rather than just electromagnetic fields. The authors are currently pursuing this task, and their preliminary calculations indicate that the purely gravitational case will be similar," he added.
"More importantly, the soft hair they introduce is probably not enough to capture all the information about what falls into a black hole."
His criticism is that it's still unclear whether all the information swallowed up by a black hole really can be transferred to the soft hair - rather than just an energy signature of everything that's been lost.
But he admitted: "It is certainly possible that, following the path indicated by this work, further investigation will uncover more hair of this type, and perhaps eventually lead to a resolution of the black hole information problem."
And that would certainly be a red-letter day in physics. Because we'd be one step closer to understanding some of the biggest enigmas in the known Universe - the weirdness that are black holes.
What does that mean for the rest of us? As Hawking explained in a talk in 2015: "[Black holes] are not the eternal prisons they were once thought. If you feel you are trapped in a black hole, don't give up. There is a way out."
And there might just be a little trace of you lingering on the outside, too.
Stephen Hawking, we miss you already.
A version of this article was originally published in June 2016.