In general relativity, it is common to use the comma notation for partial derivatives

$$\frac{\partial g_{\mu\nu}}{\partial x_\rho} = g_{\mu\nu_,\rho}$$

Where did this notation first appear? Was it known in general mathematics before Einstein?

I don't know much about mathematics books, but I traced it back to Synge's book on General Relativity(1960). Could it have arisen earlier?

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    $\begingroup$ I'm surprised Cajori A History of Mathematical Notations vol. 2 §§593-619 {covering "Euler, Karsten, Fontaine, Monge, Condorcet, Legendre, Lagrange (1788), Lacroix, Da Cunha, L’Huilier, Lagrange (1797), Arbogast, Lagrange (1801), Crelle, Barlow, Cauchy, M. Ohm, W. R. Hamilton, W. Bolyai, Cauchy and Moigno, C. G. J. Jacobi, Hesse, B. Peirce, Strauch, Duhamel, Carr, Méray, Muir, Mansion"} doesn't appear to have an answer to your question. Perhaps it is a later development. $\endgroup$ – Geremia Jul 7 '20 at 22:37
  • $\begingroup$ Isn't comma notation a subset of tensor notation? The phrase appears here which is from 1931. $\endgroup$ – Ross Presser Jul 14 '20 at 19:11

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