Undergrad Is Diagrammatic Tensor Notation Widely Used in Mathematics?

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SUMMARY

The discussion centers on the usage of diagrammatic tensor notation as introduced by Roger Penrose in "The Road to Reality." While Penrose's notation is innovative, its complexity and difficulty in typesetting limit its popularity among mathematicians, who generally prefer abstract index notation. The conversation highlights that physicists may find value in such representations, as evidenced by Cvitanović's development of "bird tracks" to address practical issues. Ultimately, the consensus is that mathematicians tend to avoid coordinate-based representations, favoring more abstract approaches.

PREREQUISITES
  • Understanding of Penrose's diagrammatic tensor notation
  • Familiarity with abstract index notation
  • Knowledge of tensor algebra and its applications
  • Awareness of the differences between mathematical and physical representations of tensors
NEXT STEPS
  • Research "bird tracks" notation at birdtracks.eu
  • Study abstract index notation in detail
  • Examine Roger Penrose's works, particularly "The Road to Reality"
  • Explore Lee's "Introduction to Riemannian Manifolds" for conventional notation in differential geometry
USEFUL FOR

Mathematicians, physicists, and students of theoretical physics or mathematics interested in tensor notation and its applications in various fields.

  • #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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