It's all about the black hole existence now, stupid
Roger Penrose has done a lot in mathematical and theoretical physics – and in the popularization of these fields (popular books etc.). Twistors and Penrose tilings (2D quasicrystals) are two very serious examples, I wrote a lot about both (including a proof of the completeness of the tiling, plus some code drawing them; the 5D definition was included in my and Zahradník's textbok on linear algebra, I am pretty sure that it's the only such an undergraduate linear algebra textbook in the world LOL). Quasicrystals could have deserved a Nobel Prize by themselves because they are far more "empirical" than most people think. Don't forget the Cosmic Censorship Conjecture, wildly inspiring, partly wrong (in the strong sense), but probably right in a weak sense and equivalent to the Weak Gravity Conjecture. Then the Penrose stairs and the Penrose triangle and the annoying beatle notation for tensors etc. ;-)
Of course, while many of his great ideas (like those in the previous sentence) are closer to recreational mathematics and/or non-empirical mathematical physics, many of these contributions have greatly influenced the adult physics world.
One-half of the 2020 Nobel Prize in Physics went to Roger Penrose for the proof that black holes are really predicted to emerge almost everywhere, e.g. after the collapse of the heavy enough stars.
The other one-half of the award is divided to Reinhard Genzel and Andrea Ghez for their discovery of Sgr A*, the black hole at the center of the Milky Way. Not the chocolate, it is our galaxy. I have produced a term paper (plus a talk) about the very same Sgr A* black hole in the 1990s – being sure that it was the black hole, in opposition to some lousier physicists who had doubts – but the main names that I cited were a bit different (I did refer to Genzel twice but there was no Ghez there, the lady). I am no historian in that field so I am not quite sure why these two were chosen. But yes, some PC has played a role, as far as I can say. I think that Sgr A* remains the most important "real world black hole" that we have observed.
Penrose's price is exciting. For decades, the late Stephen Hawking complained that he wasn't getting a Nobel Prize because there aren't too many small black holes around (because he would quickly get that prize for the Hawking radiation). But it turned out an hour ago that his and Penrose's "singularity theorems" are good enough for the Nobel committee. A typical person of the 21st century Aryan Physics movement could instinctively shout: "But there is no empirical confirmation of their theoretical work!"
Well, is that statement by the Aryan Physics fan correct? It depends. The theorem implies that under some conditions and generic enough (but not quite arbitrary) initial conditions, a black hole develops in the final state. Well, have we observed a black hole? Yes, we have. Do these observations prove that the derivation by Penrose and Hawking is exactly right? No. But experiments can really never prove the theoretical work in the strongest possible way. Good theorists must know that the theorem is (at least "almost completely") right because the underlying Einstein's equations are verified "almost exactly" in some low-curvature regime and the rest is rigorous mathematics (but not straightforward mathematics; it was a very clever idea).
We have a broader issue here: black holes are damn important in modern physics. I have given dozens of (technical and popular) talks purely about black holes (plus all the papers; the other black hole Motl is Patrick Motl, an astrophysicist). Who should be rewarded for them? In the 18th century, John Michell and Pierre-Simon de Laplace argued that objects may become... something we would call a black hole... because the Newtonian gravitational field is strong enough to accelerate the emitted light back into these objects. The escape velocity is the speed of light or higher. The mass-radius relationship of these Newtonian black holes happens to agree with the 4D Schwarzschild black hole.
Now, Albert Einstein's GR was needed for black holes. Einstein didn't even get a Nobel Prize for relativity, special or general, because of some demented people such as the Aryan Physics folks and "philosophers" who were close enough to the Aryan Physics crap. But Einstein didn't actually believe that black holes were physical when Karl Schwarzschild wrote the first black hole solution, while fighting in the First World War. While he had found the right equations, Einstein didn't quite appreciate the power of locality which guaranteed that no phenomena could have prevented the black holes from forming (in many situations, including situations where the density of matter never exceeds the density of water). Others wrote other solutions, Kerr and Newman, Reissner and Nordstrom etc. But whether the "frozen stars" could really exist seemed disputed by many "reasonably intelligent" people.
In the 1960s, John Wheeler (who is no longer alive, either) invented a catchy and more accurate name for the "frozen stars", namely "black holes". A black hole is defined as an object that is black and that is a hole: light doesn't come from it (black) and you may fall into it (a hole). That name makes it clear how they behaved and that they are very different from stars and other objects "made of any material" (see my laymen completely misunderstand black holes which I wrote exactly one month ago). I think that at that time, Wheeler was already pretty sure that they should exist. At any rate, the evidence has been growing since the 1960s. Lensing, some other gravitational effects on other celestial bodies... and up to the LIGO "sound" which has been rewarded by the Nobel Prize.
The theoretical developments were even more striking. Bekenstein and Hawking invented the black hole thermodynamics in the 1970s, it was microscopically explained by totally different tools by string theory in the 1990s, and black holes became the most important players in the research of quantum gravity and "quantized spacetime geometry" etc. Many of these developments are of course deeper and harder but they're also further from the "empirical science" that Alfred Nobel wanted to reward – he decided that a refined, important physicist (or two or three) with deep new ideas should get some money as long as the discovery is a similar bombshell as the dynamite. ;-)
But it is still true that these very deep theoretical developments make the black holes more important which is why it was right to find someone who deserved the prize for "marginally empirical" yet deep contributions. Obviously, despite his publication of many stupid and hostile things etc. (which may be summarized as the fudging, famatory-de, frong, & fictitious fault-finding, fulmination, & fuss for fabricated faith, fashion, fads, and fantasies), I am happy that a theorist of Penrose's caliber finally got this award – although I am saddened that his collaborator Stephen Hawking didn't live long enough to share these pennies.
Congratulations to all, extra smiles to Roger Penrose. Yes, Penrose's name appears in hundreds of TRF blog posts (no other personal website on this planet will beat me LOL). But Penrose is still far enough from "black holes" which are closer to thousands of TRF blog posts.
Yesterday, hepatitis C earned the prize in medicine. Those heretical Swedes haven't even noticed that Covid-19 is the only disease that is allowed to be talked about. ;-)