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In the book
Mathews, Walker: Mathematical Methods of Physics, Addison-Wesley(1969),
there is a pictorial notation of the solution found by Fredholm about an integral equation.
p.304, p.305

This circle and cross notation might be the authors' original idea inspired by the Feynman diagrams. But I'm not sure.
In mathematics, such a pictorial notation was popular before Feynman?

edit: I fancied some mathematicians were making pictorial representations of equations in the 19th or 18th century as an appendix to the rigorous proof.

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    $\begingroup$ No. Feynman's notation can be reinterpreted as computing (non-existent) "path integrals" by series expansion, and then applied to ordinary finite dimensional integrals in hindsight, see Etingof's Feynman Calculus. But the interpretation of series terms as "amplitudes" of "virtual interactions", which motivated the shape of the graphs, is lost there, and so they were not used classically. $\endgroup$ – Conifold Oct 29 '20 at 22:49
  • $\begingroup$ @Conifold Thanks for the link. It showed me the mathematical background. It makes me assume there are other applications of graph and knot theory to analysis. (I'm not familiar with those.) $\endgroup$ – user12897 Oct 30 '20 at 4:23
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    $\begingroup$ There's a fine line between "pictorial" and "symbolic" . Consider, e.g., the "nabla" $\nabla$ character used as shorthand for some serious equations, or the Dirac brac - ket notation. $\endgroup$ – Carl Witthoft Oct 30 '20 at 11:02
  • $\begingroup$ Calculation with pictures may be avoided after Cauchy if there was such a calculation. The circle and cross notation of the physics book seems the authors' idea, not a mathematic tradition. $\endgroup$ – user12897 Oct 31 '20 at 4:43
  • $\begingroup$ Young tableau is used in quantum physics. It was created in 1900 according to Wikipedia. But the diagram is not a paraphrase of equations. $\endgroup$ – user12897 Nov 1 '20 at 22:36

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