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> Interestingly enough, linear algebra only exposed its deepest secrets to us in the 20th century, despite having existed for many centuries. I think this beco

by JadeNB 4y ago

> Interestingly enough, linear algebra only exposed its deepest secrets to us in the 20th century, despite having existed for many centuries. 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.

FabHK 4y ago
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.)
- JadeNB 4y ago
  > 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.
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macrolocal 4y ago
The pure side also: spectral sequences, quiver representations, etc.
- WoahNoun 4y ago
  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.
  - macrolocal 4y ago
    Yep, and they're still an active research topic, eg. https://arxiv.org/abs/2107.02130 https://arxiv.org/abs/2107.02130

by JadeNB 4y ago

FabHK 4y ago

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.)

JadeNB 4y ago
> 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.

deleted 4y ago

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macrolocal 4y ago

The pure side also: spectral sequences, quiver representations, etc.

WoahNoun 4y ago
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.
- macrolocal 4y ago
  Yep, and they're still an active research topic, eg. https://arxiv.org/abs/2107.02130 https://arxiv.org/abs/2107.02130