Not tautological, I'd say. It is entirely reasonable to say, about a field, that its deepest mysteries have been elucidated centuries ago. One might be mistaken about that, sure. But it is a sensible and non-tautological statement to make.
(Having said that, the article struck me as fairly vacuous.)
> It is entirely reasonable to say, about a field, that its deepest mysteries have been elucidated centuries ago.
I can imagine this being true of a field that is no longer studied, although I can't think of any good example—the only unsatisfactory one that occurred to me is penmanship, but (a) that's not exactly a scientific discipline and (b) there are probably still people out there making strides in penmanship—but I find it hard to believe of any living discipline. In fact, I would argue that, if it is true of a discipline that its deepest mysteries were discovered in the past, then that discipline is effectively dead.
Re:The Philosophy of Linear Algebra (2021)
by macrolocal on Sunday June 12, 2022 @01:49AM
(#31711815)
The pure side also: spectral sequences, quiver representations, etc.
Spectral sequences (and sheaves) were developed by Leray in the 1940's while he was a prisoner of war captured by the Nazi army. Not exactly new.
Re:The Philosophy of Linear Algebra (2021)
by macrolocal on Sunday June 12, 2022 @06:12PM
(#31718765)
Yep, and they're still an active research topic, eg.
I think this becomes less surprising when phrased as: the deepest knowledge about linear algebra that we have so far is that gained most recently—at which point it sounds almost tautological. There's no reason to think that we've plumbed all the mysteries of linear algebra, no matter how much more we know (especially about the computational side of it) than we used to.