Demystifier said:
That's the citation, yes, but what Penrose has really done is proving singularity theorems. It looks as if the guys in the Nobel committee have not correctly understood what Penrose has really done.
You have to look at things in context, and not lose sight of the forest before the trees. Prior to Penrose' singularity theorem in his 1965 paper, the consensus of the discipline was diametrically opposite based mostly in a false proof by Lifshitz and Khalatnikov, not too mention a prior barrage by Einstein himself. In other words, not only was it generally seen that there was no need whatsoever for singularities in GR, but a false proof meant that searching for them was a hopeless idealistic endeavor; such false proofs are thematic in the history of physics (e.g. recall von Neumann's proof) and the only purpose they serve in the end is the obstruction of progress, but I digress.
Penrose' 1965 paper proved the first singularity theorems, but prior to this, namely in
Penrose 1963, he had already put forward the concept of conformal infinity, which lead to the definition of asymptotic flatness, which again lead to the very idea of an event horizon. The singularity theorem, especially the latter Hawking-Penrose theorem, retroactively as a corollary directly legitimized these notions, directly leading to the standard theory of black holes we have today.
In other words, the theorems didn't arise out of the blue in a vacuum but were intimately linked to his own ideas which served as the original background motivation, which possibly weren't even fully and concretely verbalized prior by Penrose, let alone properly documented.
A simple historiography shows that it was of course completely aligned with Penrose' own personal motivation, which in true classical pure mathematics fashion cared nothing about the consensus of the field, but instead was just an attempt to make concrete his own vague ideas, for their own sake and to satisfy his own curiosity regardless of what the rest of the discipline wanted; this is classic Penrose.
What Penrose did required skill and creativity, but more importantly courage and boldness, namely to directly go against the grain and say based on your intuition that some generally accepted argument or proof is wrong and then follow your own path. Instead of wasting time by showing directly showing the Lifshitz-Khalatnikov argument was wrong, he instead mathematically constructed his own theorem by using new tools, and so demonstrating that the prior argument which represented the consensus of the field was completely irrelevant (again, recall the similarity with Bell's theorem and von Neumann's proof).
Looking at the 1965 paper in isolation, it might seem somewhat mysterious when viewed outside of context of Penrose's motivations. Somewhat regrettably, viewing such matters out of their original context seems to be the default modus operandi of most scientists when evaluating such matters, because of course 'context' needs to be wholly absent in any formally polished mathematical paper, which specifically goes out of its way to not take into consideration the actual historical progression of a discovery including all failed attempts, but instead just focuses on presenting the cleaned up ahistorical finished result, as if it was deductively arrived at in that manner.
To end, Grothendieck's description of the attitude which seems to be characteristic of such once in a generation stellar mathematicians which go against the grain seems especially apt in Penrose' case, so much so in fact that Grothendieck's immortal words could've been spoken by Penrose himself, were it not for the fact of Penrose being far too humble and polite as a consequence of him being the archetype of a distinguished English gentleman:
Grothendieck said:
Since then I’ve had the chance in the world of mathematics that bid me welcome, to meet quite a number of people, both among my “elders” and among young people in my general age group who were more brilliant, much more ‘gifted’ than I was. I admired the facility with which they picked up, as if at play, new ideas, juggling them as if familiar with them from the cradle–while for myself I felt clumsy, even oafish, wandering painfully up an arduous track, like a dumb ox faced with an amorphous mountain of things I had to learn (so I was assured) things I felt incapable of understanding the essentials or following through to the end. Indeed, there was little about me that identified the kind of bright student who wins at prestigious competitions or assimilates almost by sleight of hand, the most forbidding subjects.
In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still from the perspective or thirty or thirty five years, I can state that their imprint upon the mathematics of our time has not been very profound. They’ve done all things, often beautiful things in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they’ve remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have to rediscover in themselves that capability which was their birthright, as it was mine: The capacity to be alone.
