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The question referred to is here

The OP asked for:

  • Were there other related definitions defined around this time?

  • How has today's definition of a tensor changed compared to its beginnings?

My focus was on the latter.

The question was deleted by a moderator, who at the same time, explained why I was wrong - he commented:

"Here you are describing only a certain type of contravariant 2-tensor, known as a 2-vector (these lie in ⋀2(TM)⊂⨂2TM, not an arbitrary contravariant 2-tensor."

This is quite wrong and he betrayed his own knowledge of the subject by stating that I was describing an contravariant antisymmetric 2-tensor field when in fact I was discussing - as the OP requested - the modern notion of a tensor.

Whilst the moderator acknowledges that I mention some history in the subject - I mention that Einsten & Infeld explore the subject of a vector; I think its safe to say that they didn't feel the notion of a tensor field could be easily explained to a lay public; I've read enough around the subject to know that there is No book on the subject - it is yet to be written.

Given all this, I'm asking the moderating team to reinstate my post.

edit

I rewrote my post to include an explanation as to add more detail to my discussion of what a tensor is (and which shows, despite @danu's accusation, I wasn't discussing a differential form, but the modern notion of a tensor defined by universal properties). This was deleted by a second moderator (@HDE226868)...his reason - those given by the first moderator (@Danu)...

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In your original post, the only historical content was contained in the following paragraph:

Einstein in his book with Infeld, The Evolution of Physics, pays careful attention to the notion of a vector. They both regard it as an important concept. Unfortunately, they do not pay the same attention to the notion of a tensor. Unfortunate, simply because its key to understanding General Relativity, the theory that Einstein is remembered for.

I think that it is fair to say that this does not address either of the two questions you list in this meta-post. It does not discuss competing definitions, nor does it go into the historical development of the concept of a tensor. The answer was flagged by another user, and after reviewing it I found that they were right that your answer did not address the question, and so I deleted it.

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  • $\begingroup$ As you've noted, I discussed some of the history; moreover, the post was deleted without actually understanding what I was sketching out as the modern definition of a tensor; given that it was a sketch, and you are a moderator - don't you think it fair to first suggest adding a little more detail where you didn't understand what I was saying? $\endgroup$
    – Mozibur Ullah
    Mar 10, 2020 at 10:04
  • $\begingroup$ I mean, that you deleted the post, saying I had described a tensor field suggests that you hadn't either a) understood what I wrote; or, b) hadn't properly read it; after all, I said right off that one of the many confusions around the subject is that whereas vectors are of interest in their own right; I mean as distinct from vector fields; likewise the same is true of tensors; and in fact the modern treatment of tensor shows exactly that. $\endgroup$
    – Mozibur Ullah
    Mar 10, 2020 at 10:19
  • $\begingroup$ There is no point in us discussing your point of view on the modern notion of a tensor or tensor field. What's essential here is that all of that is not historical. The remaining, small, part of your post which does mention some history is not sufficient to justify posting as an answer to the question. That is why the post was deleted. $\endgroup$
    – Danu Mod
    Mar 11, 2020 at 12:17
  • $\begingroup$ I think that this is an essential and important point given that the OP asked 'How has today's definition of a tensor changed compared to its beginnings?'; my answer mentioned some history and discussed the modern definition - thus it answered both parts. $\endgroup$
    – Mozibur Ullah
    Mar 14, 2020 at 22:15

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