Mathematician requests two retractions for “subtle inaccuracies” 

Janusz Czelakowski

A mathematician has requested the retraction of two recently published articles “claiming proofs of big results in number theory,” as one observer put it

After publication, the author said he “found some subtle inaccuracies” in the work. 

The editor-in-chief of the mathematics journal Studia Logica, where the papers were published, posted a notice to the publication’s website weeks ago stating that it had retracted the two articles. 

But the online versions of the papers still show no signs of having been retracted, as the editors wait on their publisher, Springer Nature, to process the retractions. 

The papers, “The Twin Primes Conjecture is True in the Standard Model of Peano Arithmetic: Applications of Rasiowa–Sikorski Lemma in Arithmetic (I)” and “There are Infinitely Many Mersenne Prime Numbers. Applications of Rasiowa–Sikorski Lemma in Arithmetic (II),” were both published on October 25 by Janusz Czelakowski, a professor of mathematics and the chair of algebra and logic at the Institute of Mathematics at Opole University in Poland.  

The next day, users on Math Overflow, an online forum for mathematicians, started discussing an error in the logic of the first paper. In an October 28th comment, James Hanson, a postdoctoral researcher at the University of Maryland, exhaustively explained his mathematical reasoning for identifying this error in Czelakowski’s work. He wrote: 

The proof of Theorem 7.2 is immediately suspicious because of how vague it is in places and because of how lofty the expository text before and after it is.

On October 30th, Jacek Malinowski, the editor-in-chief of Studia Logica, sent an email to mathematician and Math Overflow user David Roberts, which he posted to the site, saying that the two articles had been retracted from the journal’s website. The email stated:

Recently two articles on the applications of Rasiowa-Sikorski Lemma to arithmetic were published online in Studia Logica without proper examination and beyond reasonable standards of scholarly rigor. As it turned out, they contained an irreparable mistake and, consequently, have been retracted from the journal’s website. The papers will not appear in print.

I want to thank all our readers who alerted us to this unfortunate incident. I feel responsible for the reputation damage caused by these publications, and I want to offer my sincere apologies to the scientific community and the author.

Studia Logica editors have examined the journal’s review procedure to ensure that a similar situation will not happen again.

Roberts also runs the blog and corresponding twitter account theHigherGeometer, which posted the retraction message on October 30, tagging Retraction Watch. On November 1, the account added that it was now posted on the journal’s website as well. The online statement adds:

The managing editors of Studia Logica testify that the review process at Studia Logica meets the highest scholarly standards of rigour, and that the two papers mentioned above were the only exceptions to the rule that papers are accepted solely on the basis of careful and strict anonymous reviewing.

Retraction Watch reached out to Malinowski to ask when the online versions of the articles might be updated to detail their retraction, as well as when retraction notices might be published. He replied:

As an Editor-in-Chief of Studia Logica I asked Springer – our publisher – to retract two papers you mention. Also an author – Janusz Czelakowski asked me to retract them. I pass my decision to Ute Motz – Studia Logica assistant at Springer. It was all I could do in this matter. The rest is on Springer. I believe they will finalize retraction soon.

When we reached out to Motz, she responded in November that the retractions were in the process of being finalized:

We are aware of the situation and we are in the process to arrange for the retraction of the two articles from our platform.

However, it takes some time at our end to go through all the necessary steps and to get the approval from all internal parties involved. But I do hope that we will be able to retract the articles with a proper retraction note within the next two weeks.

The online version of both articles still have no published retraction notice or other indication of having been retracted. Motz did not respond to our follow up about when the retractions might appear online.

Czelakowski, who is on the journal’s editorial board, told us:

I decided to retract these papers from Studia Logica, because after submitting and accepting them, I found some subtle inaccuracies there. I am afraid that one of them could not be detected, even by a very demanding reviewer. These errors have been corrected. I posted new, improved versions of the paper on twin primes and on Godbach’s Conjecture on Research Gate. I also explain there in the introduction, where the erroneous argument in the earlier version was localized. I hope that the proofs are now correct.

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4 thoughts on “Mathematician requests two retractions for “subtle inaccuracies” ”

  1. Hmm. The paper was “Presented by Jacek Malinowski”.
    Czelakowski is an associate editor at the journal.

    It’s certainly embarrassing. One needs a good process, but one also needs editors who follow the process.

    1. No edit button, so I’ll just add (with apologies): clearly they need to remove Czelakowski from that editorial board. Ethical issues aside, he shouldn’t be involved in overseeing a process requiring intellectual rigor.
      The conduct of Malinowski looks quite dubious from what is posted so far, and from what he has to say about the matter, but that may just be the usual impulse toward damage control.

    2. Sorry…why are you suggesting punishing people for what seems like an honest mistake that was corrected pretty promptly?
      Get a grip.

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