nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpq9g86fe4my0hhfks50t2049zlmstlfrwyd6kahh3fhg5xwc8lt3cqls5k3r (nprofile…5k3r) nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqc9m22hkc5h6zgrwkz48crhcpw6vch2rf6j97746ugl3neys86jeqcr59k6 (nprofile…59k6)
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 /
npub1kp…gr9jw
2025-04-14 16:42:22
in reply to nevent1q…mc50
Author Public Key
npub1kpf5nh0jvj3ygrlz3zw2s2qvy2dpdp5zdlwnl2nqujugfugumkfqngr9jwPublished at
2025-04-14 16:42:22Event JSON
{
"id": "cc12ea8aadfc90715eaada3a935a8aaee33efe0ba9f14cd0145f03bd37b7a7de",
"pubkey": "b05349ddf264a2440fe2889ca8280c229a1686826fdd3faa60e4b884f11cdd92",
"created_at": 1744648942,
"kind": 1,
"tags": [
[
"p",
"2a0fa4e6bb23ef74da147ad4fa945fdc17f48dc46eaddbde29ba286760ff5c70",
"wss://relay.mostr.pub"
],
[
"p",
"c176a55ed8a5f4240dd6154f81df0176998ba869d48bef575c47e33c9207d4b2",
"wss://relay.mostr.pub"
],
[
"p",
"3422fcbc32f333fb2d3481b2e981258af8a0b571869cbfe93c42962410e232ef",
"wss://relay.mostr.pub"
],
[
"p",
"a46835d2c6ad0499d0fd2450ead839544ebb297a471d6ce8e7efeffb33610497",
"wss://relay.mostr.pub"
],
[
"e",
"ae109a9be8282c3cce4f09f3a1d40d9d94819bf61e6fcf1eb67ceff47f86f6ce",
"wss://relay.mostr.pub",
"reply"
],
[
"proxy",
"https://mathstodon.xyz/users/TobyBartels/statuses/114337313114931042",
"activitypub"
],
[
"client",
"Mostr",
"31990:6be38f8c63df7dbf84db7ec4a6e6fbbd8d19dca3b980efad18585c46f04b26f9:mostr",
"wss://relay.mostr.pub"
]
],
"content": "nostr:nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpq9g86fe4my0hhfks50t2049zlmstlfrwyd6kahh3fhg5xwc8lt3cqls5k3r nostr:nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqc9m22hkc5h6zgrwkz48crhcpw6vch2rf6j97746ugl3neys86jeqcr59k6\n\nThat's who I thought of, but I don't know.\n\nIt 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.\n\nThis could be in Michael Spivak's Comprehensive Introduction to Differential Geometry, which has a lot of historical material.",
"sig": "74421c0b242c08bd092509780bc3e774150a21a7b203e25c3bad86853ee3887d21ff8b08f7a328667e22d8bde892f12d69b81cf49f85f15853816ade8c6b1719"
}