One of the world’s most prestigious mathematics journals has issued what appears to be its first retraction.

The *Annals of Mathematics *recently withdrew a 2001 paper exploring the properties of certain symmetrical spaces.

What prompted this retraction? And why did it occur 16 years after the paper was published?

The retraction notice for “Invariant differential operators and eigenspace representations on an affine symmetric space” says only that the paper has been “withdrawn.” A spokesperson for the *Annals of Mathematics* explained:

The paper was retracted because the proofs in the paper were found to be incomplete.

The paper’s author, Jing-Song Huang, agreed that there were errors in two proofs, but he told us he is confused about why the paper was withdrawn because he had sent the editors corrections to both, which he thinks should have solved the problem.

Huang, chair in the Department of Mathematics at Hong Kong University of Science and Technology, explained that a few years after the paper was published, some mathematicians found a gap in one proof when they were trying to use the techniques.

Huang told Retraction Watch that he wrote to the editors of the journal in June 2008 about the gap in the proof and sent them a one-page erratum to correct it:

I received feedback from the referees on the first correction and improved the manuscript. It was expanded to two pages with more details for the sake of readers.

But one of the referees found a new issue, an error in an argument called a lemma. Huang said:

I replaced that lemma with a new argument. That was most recent version of four pages that I sent to the Annals in August of 2015.

Huang said the journal responded in August 2015 to acknowledge receiving the erratum.

But Huang heard nothing from the journal for over a year, which Huang noted was not unusual given how technical papers in the journal can be:

[T]he expert circle is very, very small…

When the first issue was identified, it even took Huang

a lot of time to understand what went wrong, since it is very technical issue.

In February 2017, Huang emailed the journal to ask about the status of the erratum. The journal responded, informing Huang that they intended to withdraw the paper.

Huang emailed the journal to say that he was “really shocked” by the decision. He had been waiting for input about his erratum from the journal, which he said he never received, so he did not understand why the paper was being withdrawn, instead of corrected. Huang said:

I asked several times for the referee reports.

He began working on the concepts in 1989, when he was a graduate student at MIT. He published a paper in 1996 in the *American Journal of Mathematics* with two colleagues on a related topic, and expanded on it his 2001 paper in *Annals of Mathematics*. Huang told us:

It took me many years to develop these ideas.

The paper has not yet been cited, according to Clarivate Analytics’ Web of Science. Here’s the retraction notice:

The paper “Invariant differential operators and eigenspace representations on an affine symmetric space,” which was published in Vol. 154, pages 703–707 of the Annals https://doi.org/10.2307/3062145, is hereby withdrawn

Now that the paper has been withdrawn, Huang plans to post his correction in arXiv.

*Hat tip: **Miguel*

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12 years of work to put out a paper that doesn’t get cited once in 16 years. Those ARE some crazy numbers. Mathematics sounds like a tough field to be in !

And right when some people were planning to use it, they got it retracted instead. I imagine no one is happy now.

It is very unusual in itself that a paper in Annals doesn’t get cited in 16 years. Citation counts in mathematics are low compared to many fields of science, but not quite that low.

Seems to me that the journal editors are sending an unambiguous message that the original research is not reliable.

I agree with the approach.

If it takes or will take numerous corrections to get it right then retraction is the only appropriate thing to do.

The retractions says that the original was incorrect and does not preclude the author from publishing a correct manuscript when and if they figure it out.

I’m not a fan of the mega correction either but better than a correction series.

It is evident: when problems in the scholarly literature are found, they must be corrected, one way or another. Otherwise, the primary function of scholarly publishing is compromised.

Did you mean to post that link to the paper “Mosquito Detection with Neural Networks: The Buzz of Deep Learning” (arXiv:1705.05180) on the arXiv? Or was it meant to be a link to the math section?

Fixed — thanks.

The author has now put an errata on arXiv https://arxiv.org/abs/1707.04707

“One of the world’s most prestigious mathematics journals has issued what appears to be its first retraction.”

Perhaps not the first. I would call #2 and 4 below retractions of #1 and 3, respectively. While they do not use the words “retract” or “retraction”, they invalidate the proofs of the main statements (theorems) and thus of the substance of the papers (pure math is not an experimental science). An allusion to #1 is made in a comment in a Retraction Watch article (search for Daniel Biss).

All of these papers are from the same period of time, published in 2001-2004. The last one to be published was available on arXiv.org in 2000 (the original version is still there).

1. D. Biss, “The homotopy type of the matroid grassmannian”, Ann. Math. 158 (2003), 929–952

2. D. Biss, “Erratum to “The homotopy type of the matroid Grassmannian””, Ann. Math. 170 (2009), 493

3. E. Ionel and T. Parker, “The symplectic sum formula for Gromov-Witten invariants”, Ann. Math. 159 (2004), 935–1025

4. Editors’ note on “The symplectic sum formula for Gromov-Witten invariants”, Ann. Math. 184 (2016), 1041