That's who I thought of, but I don't know.
It probably passed through the idea of differential operator. In local coordinates, a vector field (X¹,…,Xⁿ) defines a differential operator ΣᵢXⁱ∂ᵢ (where ∂ᵢ = ∂/∂xⁱ), which will get attention because it can be used in differential equations, and it doesn't take much to notice that the vector field can recovered from the operator (and even from its action only on infinitely differential functions if it occurs to anyone to consider that); but it could have been a while until someone worked out a coordinate-free description of which operators come from vector fields in this way.
This could be in Michael Spivak's Comprehensive Introduction to Differential Geometry, which has a lot of historical material.
TobyBartels
npub1x4…z6lp6
2025-04-14 16:42:22 UTC
in reply to nevent1q…5dce
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2025-04-14 16:42:22 UTCEvent JSON
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