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Over the past few years there have been some high-profile cases in experimental sciences in which prominent researchers have been caught manipulating or falsifying data in important or highly-cited papers.

I was thinking about the difference between experimental science and pure mathematics and it seemed like it would be hard to do something like this in pure math - if you write up a proof, the reasoning is fully on display to everyone and errors are often (though not always) caught.

Then again, perhaps this would be possible. A mathematician could take a result they knew was definitely false, then attempt to obfuscate the error in the reasoning in a way that would be hard to detect or easy to miss.

Have there been any examples in pure mathematics where a researcher

  • who was studying pure (e.g. not applied or experimental) mathematics,
  • had a result they knew was false or a proof they knew was flawed, but
  • attempted to pass it off as genuine through underhanded or deceptive means?

These criteria exclude the kinds of honest mistakes that lead to incorrect proofs of theorems being published, or circumstances where someone explicitly shares a known flawed proof that they think may be of interest to the community, or instances where empirical data from applied experiment were manipulated. (That last one is more along the lines of the research misconduct that could take place in the sciences.)

templatetypedef
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  • I have no example in mind, but a case where someone claimed having a proof when it was probably not the case is the famous Fermat quote "I have a proof which is too long to fit here..." Although the case is quite different from what you look for I assume, since no mathematician took his word for it (and the result was indeed correct). – Rondoudou Oct 09 '24 at 05:55
  • While it might satisfy the OP's criteria, I doubt the OP means to include pranks/April fool's jokes that the perpetrator intended to be understood as fake reasonably quickly. That being said, there's a collection of such incidents on MathOverflow. – Greg Martin Oct 09 '24 at 06:28
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    Would work for you Technical analysis? – Joako Oct 09 '24 at 06:59
  • "had a result they knew was false or a proof they knew was flawed, but" how could you ever proof that? (unless the researcher would admit to it, but for obvious reasons this is unlikely) – jd27 Oct 09 '24 at 07:30
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    On retractionWatch.com there are 7 pages of retracted papers in mathematics, https://retractionwatch.com/category/by-subject/physical-sciences-retractions/math-retractions/ but whether or not they are due to misconduct that you're describing is difficult to tell. – Randy Marsh Oct 09 '24 at 07:35

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