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Fields of dreams

There is a buzz of expectancy waiting for the announcement of this year’s Fields Medal for mathematics, always assuming that they award one this year. All the smart money, indeed all the money full stop, is on Grigory ‘Grisha’ Perelman for outlining a proof of the Poincare conjecture. There is plenty of chatter about Perelman’s supposed eccentricities, whether he will accept the million dollar prize from the Clay Mathematics Institute if his proof is correct and generally why the Poincare conjecture is important in the first place, but I want to highlight the way that Perelman chose to share his discovery.

In 2002 Perelman posted a paper on arXiv, “The Entropy Formula for the Ricci Flow and its Geometric Applications“, claiming to give “a sketch of an eclectic proof of this conjecture“. Two more papers followed in 2003: “Ricci Flow with Surgery on Three-Manifolds” and “Finite Extinction Time for the Solumtions to the Ricci Flow on Certain Three-Manifolds“. Since then other mathematicians have taken up the challenge of explicitly proving that Perelman’s approach provides a proof for Poincare, and indeed surpasses it by proving a more general conjecture of which Poincare’s is a special case.

This is a superb example of how peer review in the open works. Perelman put his work out in the public domain and the mathematical community has collaborated to bring out its full impact. Indeed it is highly debateable whether Perelman’s paper could have been published in a ‘conventional’ journal with a ‘conventional’ impact factor.

This isn’t unusual with papers published on arXiv, it is just a particularly high profile example. If Grisha Perelman is awarded the Fields on Tuesday it perhaps it should be viewed not just as the acknowledging a specific Russian genius but also as a victory for collaborative approaches to science.

  1. Chris: There’s another peculiarity in Perelman’s way of sharing his results. As you note, he’s posted his three papers to arXiv and benefited from its form of open review. But to date he’s refused to publish the same papers in peer-reviewed journals. The problem is not that a conventional journal would refuse them, at least now that consensus is building that his proof is sound. Steven Krantz, editor of The Journal of Geometric Analysis, has offered to publish Perelman’s three papers or any new ones that he would like to submit, but Perelman has not accepted the offer. (See my blog postings on this here and here.)

    Perelman is not just saying, by his actions, that open review suffices. If that were all, he could still accept conventional publication for whatever increment of authority it would bring e.g. for mathematicians who are waiting for the imprimatur of a peer-reviewed journal. He’s apparently saying that there is no such increment of authority and that he doesn’t care to persuade mathematicians who think there is.

    PLoS ONE uses two forms of review –one closed, internal, and prospective and the other open, external, and retroactive. I believe that Perelman would only support half this model.

  2. Peter,

    I thought that was Perelman’s stance but when I was writing the entry this morning I couldn’t find a confirmatory reference. Why I didn’t check Open Access News is beyond me. Thank you for pointing this out.

    You are absolutely right that Perelman would most likely find PLoS ONE too ‘conventional’. However, unlike him, the vast majority of scientific disciplines aren’t embracing arXiv and its philosophy. PLoS ONE is aimed more at these disciplines, trying to provide them with the benefits of open, retroactive review but in a way that they will find more attractive.

  3. hey, I think this model for publishing approaches perfection:
    1) cost of publication is not a barrier for authors
    2) open access, of course
    3) papers are judged on TECHNICAL merit, not subjective opinions about relevance. This point might have been objectionable to our mathematician friends above, but it seems a good idea to me- just to keep the databases from getting clogged with non-reproduceable data. I feel this has been a growing problem.

    I have two other suggestions that would render this project perfect to me.

    1) double blinded review to eliminate unconscious bias.
    2) VERY IMPORTANT TO ME: Quantitative ratings of reproduceability and support of claims which could be incorporated into array analysis pathways software for building relational outputs. These ratings will be happening informally in a non-quantitative fashion with the blogs around papers-lets make it quantitative and based solely on readers input. we just need an infrastructure to do so incorporated into the feedback/blog area of papers.

  4. While there are reasons for blinded (or double-blinded) peer review, there is also something to be said for “identifiable” peer review, especially in an open forum like PLoS ONE. If reviewers are identifiable, then concern for their own reputations will motivate them to keep their comments as constructive (or at least, valid) as possible. A glance at almost any internet forum will show how poor an online discussion can get when some participants feel they have nothing to lose.

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