“Homological stability for Hurwitz spaces… II” temporarily withdrawn

Akshay Venkatesh, Craig Westerland and I have temporarily withdrawn our preprint “Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields, II,” because there is a gap in the paper which we do not, at present, see how to remove.  There is no reason to think any of the theorems stated in the paper aren’t true, but because some of them are not proved at this time, we’ve pulled back the whole paper until we finish preparing a revised version consisting just of the material that does in fact follow from the arguments in their current form, together with some patches we’ve come up with.   We are extremely grateful to Oscar Randall-Williams for alerting us to the problem in the paper.

I’ll explain where the gap is below the fold, and which parts of the paper are still OK, but first a few thoughts about the issue of mistakes in mathematics.  Of course we owe a lot of people apologies.  All three of us have given talks in which we told people we had a proof of (a certain version of) the Cohen-Lenstra conjecture over F_q(t).  But we do not.  I know several people who had work in progress using this theorem, and so of course this development disrupts what they were doing, and I’ve kept those people up-to-date with the situation of the paper.  If there are others planning immediately to use the result, I hope this post will help draw their attention to the fact that they need to go back to treating this assertion as a conjecture.

One thing I found, when I talked to colleagues about this situation, is that it’s more common than I thought.  Lots of people have screwed up and said things in public or written things in papers they later realized were wrong.  One senior colleague told me an amazing story — he was in the shower one day when he suddenly realized that a paper he’d published in the Annals four years previously, a result he hadn’t even thought about in months, was wrong; there was an induction argument starting from a false base case!  Fortunately, after some work, he was able to construct a repaired argument getting to the same results, which he published as a separate paper.

Naturally nobody likes to talk about their mistakes, and so it’s easy to get the impression that this kind of error is very rare.  But I’ve learned that it’s not so rare.  And I’m going to try to talk about my own error more than I would in my heart prefer to, because I think we have to face the fact that mathematicians are human, and it’s not safe to be certain something is true because we found it on the arXiv, or even in the Annals.

In a way, what happened with our paper is exactly what people predicted would happen once we lost our inhibitions about treating unrefereed preprints as papers.  We wrote the paper, we made it public, and people cited it before it was refereed, and it was wrong.

But what would have happened in a pre-arXiv world?  The mistake was pretty subtle, resting crucially on the relation between this paper and our previous one.  Would the referee have caught it, when we didn’t?  I’m not so sure.  And if the paper hadn’t been openly shared before publication, Oscar wouldn’t have seen it.  It might well have been published in its incorrect form.  On balance, I’d guess wide distribution on arXiv makes errors less likely to propagate through mathematics, not more.

Sociology of mathematics ends here; those who want to know more about the mistake, keep reading past the fold.

Two views on peer review

• The mysterious number theorist Persiflage on “Why is my paper taking so long to review?”
• Mike Eisen says peer review is a  joke.

Elsevier boycott in the Notices

Douglas Arnold and Henry Cohn have posted “Mathematicians Take a Stand,” their sober, carefully argued, and thoroughly researched case for the Elsevier boycott on the arXiv.  It will soon appear in the Notices of the AMS.

I don’t know what shape the mathematical publishing of the future will take but it seems almost impossible that it will look much like it does now.

Update:  Mathematics is important as a kind of avant-garde but the money is in biology, as we all know.  That Wellcome is considering launching an open-access competitor to Nature and Science, and requiring grantees to publish only in open-access journals, is a big deal.

Would the death of the journal system be good for women in math?

I am not one of the most radical signatories to the “Cost of Knowledge” statement:  there are certainly some among us who look forward to a world without commercial journals, or even a world without journals at all.  I don’t yet see a clear path to that world.

Nonetheless, I want to add one possible item to the case against journals.

There is lots of inequity in the way mathematicians are assigned status — we all have researchers we think are underappreciated (and some people are quite willing to talk about who they think is overappreciated.)

One very simple source of inequity — but I’ll bet a pretty large one — is that authors decide what journal to submit to.  Some people “aim high” — their method is to ask “what’s the best journal where this paper would fit?”  Others “aim low,” asking something more like “what’s the median journal where papers like this appear?”  You can’t get in the Annals unless you submit to the Annals, and you won’t submit to the Annals very often if you aim low.

Women in the workplace are socialized not to ask for things.  I wouldn’t be surprised to learn that there are disproportionately many men in the “aim high, why shouldn’t my paper be in the Annals?” group.  (And of course, for those who get het up whenever I talk about women in math, this applies just as well to any group of mathematicians disinclined to push for their own work.)

Would things be different if papers in the Annals were selected from all papers, not just those whose authors decided to nominate themselves?  Then publication in a top journal would be a little more like being invited to speak at a prestigious conference.  Would that be an improvement?

 

Statement on the Elsevier boycott

A group of mathematicians, myself included, have prepared and signed a statement which attempts to summarize the reasons so many mathematicians and other scientists (nearly 5000 at this count) have signed on to boycott Elsevier publications.

This is an important moment for mathematical publishing, a rare time when the attention of the community is really fixed on an issue that’s been torturing our librarians for many years.  What’s the next step?  A good place to follow people’s thinking will be Gowers’s blog.  Tim, of course, has been a driving force behind the current movement to stop complaining about rent-seeking academic publishers and start doing something about it.

 

Is the time right for bundling?

I asked “why don’t books come with e-books?”  Publishers Weekly answers.

Math linkdump Nov 11

• Tim Gowers destroys and rebuilds mathematical publishing.
• Mosteller and Youtz randomize Mozart.
• The Open Graph Archive is trying to generate a community-built, openly accessible library of graphs.
• Eugenia Cheng on what mathematicians are talking about when they use the word “morally.”
• Philipp Habegger just proved that the field F obtained by adjoining to Q all torsion points of an elliptic curve E/Q  has the Bogomolov property; the logarithmic height of a non-torsion element of F^* is bounded away from 0.  About a year ago I was going around asking a lot of people whether this was true, and no one knew; at some point I’ll write a longer blog entry explaining why I wanted to know.

Two wise men I know

Allen Kornblum, founder and publisher of Coffee House Press, interviewed on the future of the book industry. Eric Walstein, mentor to a generation of little kids in Maryland who liked math, tells the Washington Post we’re using calculators wrong.

Reader survey: which journals are fast?

I’m often asked by students and junior colleagues where I think they should submit a paper they’ve just finished. It’s not so hard to figure out whether a given journal is a good mathematical fit for the paper. What’s harder is when the author has a job application coming up, and really wants the paper not to sit in referee hell for a year and a half.

My go-to journals for a fast response are Mathematical Research Letters and International Math Research Notices. But it would be great to have some others. So: which journals, in your experience, are reliably fast? Bonus points if they’re cheap, or even free.