I Is Diagrammatic Tensor Notation Widely Used in Mathematics?

[martinbn]

How about Euclid?

I dont know. Can you show me a paper by him so that we can see?

 

[fresh_42]

I guess I could find one. But this isn't necessary. Euclid lived before Descartes and before analytical geometry was developed. Moreover, he undoubtedly was a Greek Geometer and as such had a completely different understanding than ours today. He didn't feel the necessity to determine a specific point from where he measured everything. (I would start to search for it in van der Waerden's oeuvre.)

Euclid is an example and one that doesn't use a circular argument.

Has anybody here ever wondered why nobody writes $f_\alpha \in C(X)$? This is because index notation refers to finitely many components.

 

[jbergman]

Are you claiming mathematicians never multiply temsors together? Never have the need to take a trace or similar?

No, but they don't need abstract index notation to do it. Look at a mathematical differential geometry book and their use of this notation is infrequent.

 

[jbergman]

I suggest people look at Lee's book to get a feel for how differential geometers typically notate things. https://books.google.com/books/about/Introduction_to_Riemannian_Manifolds.html