I'm not quite sure if anybody is an expert in the history of mathematics, but I would be interested to learn the history of some of the symbols used, particularly, the "curly d" symbol used to represent partial derivatives, but if you know any others, please do share. Where did these symbols come from and when were they first used?
You're in luck, Cajori's History of Mathematical Notations is available online:
https://archive.org/details/historyofmathema031756mbp
The partial derivative symbol was used here and there before 1841 when it was popularized by Jacobi (of Jacobian, or matrix of partials, fame).
The curly ∂ used for partial derivatives (as distinct from Leibniz’ use of d for regular derivatives) was introduced by the Marquis de Condorcet in 1770.