For example K. Schwarzschild (1916) “assumes” a point mass with solar mass. He even clearly stated that it was “ideal mass point” which should not have been treated as a real point having a huge mass.

But perhaps this is the limitation of mathematics that such a thing could be “assumed” only with literal and real meanings. K. Schwarzschild soon died after the publication of his (1916) paper and the later mathematicians interpreted his paper within the inherent limitation of mathematics itself. The so just “assumed” “point mass” eventually became a real and literal “singularity” for mathematics.

Related post: How idea of The Big Bang Initial Singularity Emerged?

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