Undergrad Is Diagrammatic Tensor Notation Widely Used in Mathematics?

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Penrose's diagrammatic tensor notation, introduced in "The Road to Reality," is not widely adopted in mathematics due to its complexity and challenges in typesetting and quality assurance. While some physicists, like Cvitanović with his "bird tracks," have developed similar representations, mathematicians generally prefer to avoid coordinate systems. The discussion highlights a divide between mathematicians and physicists regarding the use of coordinates, with mathematicians often favoring abstract tensor notation that does not rely on specific coordinates. Despite its cleverness, Penrose's notation is considered impractical for mathematicians, who typically opt for more conventional representations. Overall, the diagrammatic approach remains largely underutilized in mathematical contexts.
  • #31
fresh_42 said:
How about Euclid?
I dont know. Can you show me a paper by him so that we can see?
 
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  • #32
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.
 
  • #33
Orodruin said:
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.
 

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