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## Main Question or Discussion Point

I was reading a document from the time of Einstein where the metric is refered to as "the fundamental tensor". That made me wonder if it's possible to derive all concepts of tensor field, scalar product, connectivity etc. starting from the requirement that the metric is invariant under change of coordinate patches?

Also, did the mathematics of the time of Einstein and other physicists/mathematicians differ from the current mathematics for Relativity that we encounter currently in Textbooks/etc?

Also, did the mathematics of the time of Einstein and other physicists/mathematicians differ from the current mathematics for Relativity that we encounter currently in Textbooks/etc?