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I have gotten the impression that Einstein learned the math that he needed to, when he needed to learn it, and that he had hoped to avoid learning the sort of math that Hilbert was already somewhat comfortable with.



Absolutely.

Einstein is a bit famous for punching well above his weight compared to his own mathematical background. Most of his great work involves beautiful arguments that requiring only maths that a good-but-not-genius high school student could understand.

The GR paper is a bit disappointing in comparison, because after setting out as much as he can of the physics, he just dives into big equations one after another. That probably roughly follows his own trajectory: first he had some intuition for how space-time curvature could cause some gravity-like effects. But to nail it down he just had to buckle-up and learn the mathematics of non-euclidean geometry.

The nice thing about the paper is that it was one of the first applications of such mathematics to physics, so Einstein takes the time to explain it (which also blows out the equation count).


Can you please post a link to the paper?


See https://einsteinpapers.press.princeton.edu/vol6-trans/

Doc. 21 On the General Theory of Relativity https://einsteinpapers.press.princeton.edu/vol6-trans/110

Doc. 22 On the General Theory of Relativity (Addendum) https://einsteinpapers.press.princeton.edu/vol6-trans/120

Doc. 24 Explanation of the Perihelion Motion of Mercury from the General Theory of Relativity https://einsteinpapers.press.princeton.edu/vol6-trans/124

Doc. 25 The Field Equations of Gravitation https://einsteinpapers.press.princeton.edu/vol6-trans/129




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