I thought Marcel Grossmann was usually credited with helping Einstein with the tensor approach to General Relativity. All of this was more salient at the time, which the article points out: Hilbert carried a grudge against Einstein for a period of time. Lorentz was bitter about Einstein getting credit for special relativity to the end of his days, and Einstein denied ever having read Lorentz's or Poincare's papers even long after he had moved to the Institute for Advanced Studies. The bitterness and personal politics involved have faded. It is now interesting just from an academic (historical) standpoint.

A lot of quantum field theorist refer to "Einstein summation convention" which is a special case of Ricci calculus and is a notation that was developed together with Levi-Civita by Ricci in their contributions to the field of relativity. At least most quantum field theorist know about Levi-Civita through the Levi-Civita tensor. Given the controversy described in this article one wonders why they are called the Einstein equations and the Hilbert-Einstein action when Einstein indusputably had nothing to do with the derivation of the action principle but Hilbert disputably is responsible for the derivation of the field equations. At the very least people talk about the Lorentz transformation and the Poincare group.

Since general relativity was essentially a unification of the spacetime defined by Maxwell's equations (special relativity) and gravitation, the quest to fully unify the theories that began with Lorentz and Poincare pointing out the strange transformation properties of electric matter continued. A lot of people are aware of Einstein's continued search for a Grand Unified Theory. But in general people are less aware of what theories he introduced (teleparallel gravity for example) or that other people were all trying (Kaluza and Klein for example) and continue to try to this day. In the case of things like dark matter, there might be some hope of measuring the Kaluza-Klein scalar fields or maybe we genuinely need a completely different theory. The history is more interesting because of the missteps, mistakes and politics along the way. It helps us understand the missteps, mistakes and politics of science that are still happening today.

Stigler's law of eponomy says that no scientific law is named after its discoverer [0]. What you're describing is far more common than you might think!

[0] https://en.wikipedia.org/wiki/Stigler%27s_law_of_eponymy

Great, new member in the elite club of rules that make their own exception

I don't think it's the case here: "Stigler himself named the sociologist Robert K. Merton as the discoverer of "Stigler's law" to show that it follows its own decree, though the phenomenon had previously been noted by others.", from the wikipedia article.

I was thinking of this indeed, but felt I was already becoming a bit long winded. ;)

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

"Who got it first?" has always been a salient question.

See: https://en.m.wikipedia.org/wiki/Leibniz%E2%80%93Newton_calcu...