> the Penrose singularity theorems in General relativity were impossible until Einstein's theory was formulated correctly with rigorous mathematics I wonder if

> the Penrose singularity theorems in General relativity were impossible until Einstein's theory was formulated correctly with rigorous mathematics I wonder if you would please justify that statement, specifically and only with respect to one of the things called the [Hawking-]Penrose singularity theorem? In particular, what was sufficiently unrigorous or alternatively missing from classical General Relativity that blocked a reasonable choice -- especially the early 1960s ones (example and commentary below) -- of such a theorem? [Penrose 1965] Gravitational Collapse and Space-Time Singularities https://doi.org/10.1103/PhysRevLett.14.57 https://doi.org/10.1103/PhysRevLett.14.57 (2.5 pages) (You can also find a copy in the usual place) (I submit the reason it took until 1964 for a Penrose singularity theorem is explained by the first two lines of [Penrose 1965]: the surprising discovery that QSO 3C 273's highly extragalactic redshift z ~ 0.16 having been published in 1963 and QSO 3C 147's z ~ 0.55 following in 1964 strongly suggested SMBH activity. In other words the underlined statement in the fourth paragraph did not follow any sort of mathematical development (ADM, for instance) but rather was motivated by one of the most provocative observations of nature I can think of off the top of my head, up there with the (also 1964) discovery of the CMB.)