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Barbara Fantechi dropping some wisdom here:
If you think referees for top level journals require clear exposition (including complete proofs, or at least making them available somewhere, or upon request; crystal clear definitions) than I've got a Leaning Tower to sell you.
That ship sailed LONG ago. 1/
I'm not speaking about such once in a lifetime papers; I assume (hope?) those get checked seriously. rather, I'm talking about your average Inventiones-level paper, by your average "clever" author(s), who are allowed, if they so please, incredible levels of carelessness. /2
We* all know examples. And Inventiones is just one case, there's plenty everywhere. I'm all for rigorous refereeing, but let's please apply it all around, not just in this one case. /end
*Seniors.
What particular blunders in Inventiones is she referring to here? I don't know if I'm aware of the background story here
I think this is a bit more pessimistic than necessary. Just because the ship sailed long ago doesn't stop us from continually demanding better. Or better than demanding, thinking carefully about the system of incentives in publishing and trying to adjust it
Morgan Rogers said:
What particular blunders in Inventiones is she referring to here? I don't know if I'm aware of the background story here
I had a vague memory that there was something, but I couldn't find anything while searching. This Nautilus article claimed that Wiles submitted his proof the first time round to Inventiones, but that was successfully resolved.
Perhaps she brought up Inventiones as a journal of relatively high quality, but not quite Annals or Crelle's, c.f. "your average Inventiones-level paper".
Also, gotta love alluding to things without citation, though the 140 char limit on Twitter is probably a problem.
Jules Hedges said:
I think this is a bit more pessimistic than necessary.
Realism is often mistaken for pessimism when the situation is far from optimal. This opinion is a realistic one, given the current situation.
Just because the ship sailed long ago doesn't stop us from continually demanding better.
Yes, we should demand better. However, as she's said:
I'm all for rigorous refereeing, but let's please apply it all around, not just in this one case.
The issue here is with the moral hazard of the uneven application of standards.
Or better than demanding, thinking carefully about the system of incentives in publishing and trying to adjust it.
Which we should, but this goes into a lot of systemic issues.
Morgan Rogers said:
What particular blunders in Inventiones is she referring to here? I don't know if I'm aware of the background story here
one of the more notorious would be the strange case of Daniel Biss: https://en.wikipedia.org/wiki/Daniel_Biss#Mathematics_career
Huh.
Gershom said:
one of the more notorious would be the strange case of Daniel Biss: https://en.wikipedia.org/wiki/Daniel_Biss#Mathematics_career
Interesting. Annals of Mathematics, Advances in Mathematics, Inventiones Mathematicae and Topology and its Applications: that's quite a list.
Fantechi's comments were in response to discussions about demanding that Mochizuki should rewrite his paper to be more readable (this was the minimum desideratum for one person who turned down the chance to referee the IUT papers). She was essentially saying that it was like 'the pot calling the kettle black', since there are many people who get stuff published in top journals that just write really badly and unclearly and skip explanations of things and they get away with it. I don't think it was so much about errors in papers that get published.
But if things are written unclearly and skip explanations then that makes them harder to check, and makes it more likely that there are errors. Which is part of the discussion over IUT as well -- if the papers were more clear, then it would simplify the debate over correctness.
David Michael Roberts said:
She was essentially saying that it was like 'the pot calling the kettle black', since there are many people who get stuff published in top journals that just write really badly and unclearly and skip explanations of things and they get away with it. I don't think it was so much about errors in papers that get published.
They're different aspects of the same issue, as Gershom's pointed out. As I've said to Jules here, Fantechi is talking about the moral hazard of uneven standards, i.e. "the pot calling the kettle black".
Gershom said:
Which is part of the discussion over IUT as well -- if the papers were more clear, then it would simplify the debate over correctness.
Or if we could simply "run" proofs on our computers, and Mochizuki's work keeps producing the same compiler errors, and these compiler errors were written for humans.