This is just the rationalist-empiricist[0] tension, from philosophy. Most empiricists (usually people who are _not_ from continental European cultures), take a position that knowledge and creativity come from observation and imitation, while rationalists believe that knowledge and creativity can be endogenous to the mind.
One could say that, stereotypically and cartoonishly, empiricists believe that invention is a false concept, and a synonym for discovery, while rationalists would oppose this view.
That catch is, if you look at the etymology of words "invention" and "discovery", you will find that they both share the _same_ root: _Ars Inveniendi_.
A natural question arises: does this mean that people from a millennium ago did not have a dyad equivalent to our invention-discovery dyad? And the answer, surprisingly, is _no_. Even a millennium ago, the empiricists and rationalists were going at it. If _Ars Inveniendi_ is art of discovery/invention, then its counterpart is _Ars Demonstrandi_ (the art of demonstration/proof).
So, how do these differ? Is one just observing/creating and the other just math and language-games?
In general, Ars Demonstrandi is about writing down axioms, and then expanding those axioms recursively (similar to rewrite rules in any formal system), until you get to some end-state, or, if there is none, a novel or surprising state. I, personally, call this source-to-sink thinking.
Ars Inveniendi is about taking conclusions (often using observations from the physical world) and trying to figure out what axioms can lead to those conclusions. I, (again) personally, call this sink-to-source thinking.
Put differently, Ars Inveniendi can help one discover starting points for Ars Demonstrandi.
If you read the dialectics (e.g. Plato and friends), you'll find that most of them are just a mutual recursion between Ars Inveniendi and Ars Demonstrandi.
I believe (again, I am not a philosopher, and this is just my intuition), that the thing that we call "creativity" and "invention" _emerges_ from the recursive loop[1]. A favorite example: Esperanto (the conlang). It is a language, which is remarkably elegant and consistent and (in my opinion) beautiful, because it _is_ derived from first principles, which were themselves derived from the various languages spoken in Europe (not all of which are Indo-European -- the agglutinative features have more in common with Finno-Ugric and Turkic languages). There is something about it, that makes it _qualitatively_ different (and thus holistically novel) from all other languages (and I speak, fluently, _two_ national languages, that are very different from each other, so I can attest to the difference personally).
My guess, is that people will not accept that AI/LLMs are creative or inventive, until they can produce an original[2] (non-plagiarized) artifact that feels the way Esperanto feels.
[0]: By Rationalist, I do not mean the "Bay Area Rationalists", who are, in fact, empiricists.
[1]: I am unsure if the loop requires only one human, at least two humans, or if it can be fully automated.
[2]: Note that Centos are poems made completely out of line-numbers (e.g. fragments from the Iliad, or the bible, etc). Every line is borrowed, yet some of them are considered beautiful and original works of art. Similarly, Labatut and Burroughs and Perec, write using a technique called _the cut-up method_, where they take books, magazines, and newspapers, and superimpose page-fragments, and use that as an inspiration -- they are all considered artists, and good ones. It is unclear to me why LLMs (which seem to be built on the cut-up method, and have cut-ups of all of human knowledge) cannot match these artists. What's missing?