A Fundamental Mistake in a Published Paper

Caroline McWilliams
Friday 20 January 2023

By Anonymous

A group of researchers, including me, doubted a common theory that used to be taken for granted as being true. We were looking for a clear way of showing where our hesitations came from and how to prove them.

After several months of discussion, we managed to do a calculation that proved our hypothesis. The calculation was rather technical, using some fairly sophisticated mathematical techniques. We wrote it up, advertised it throughout academic conferences, and submitted it for publication. As is fairly common practice, we decided to publish a short paper stating the result and explaining why it was interesting, and then follow it up with a longer paper discussing our calculation and the discovery in depth.

Due to the calculation’s ground-breaking nature, our first paper – the shorter one – was cited by numerous other authors.  However, once the first paper was published and while we were discussing the second one, we realised that our result was in fact mistaken, and that we had incorrectly applied one of the mathematical techniques that we had tried to use.

We decided to dedicate the follow-up paper to explaining why we had made the mistake, and the deeper understanding of the problem that came from learning how to do the calculation properly. The follow-up paper ended up being cited almost as much as the first one, especially among PhD students, because through explaining how we fell into making our mistake we also provided guidelines on how to do the calculations properly.

The failure with the calculation was embarrassing and valuable at the same time. I learned the hard way how careful you have to be with your calculations and how an apparently small mistake can change the entire result.

Later, when I was preparing a paper in a different area, I came across a technically similar calculation, albeit in a different context. This time, I knew what the answer was supposed to be, but it didn’t match the one I was getting. My earlier experience definitely helped me not to become discouraged by the mismatch in the results and to check the calculations again. I discovered a subtle detail that wasn’t included in the calculations, and once it was taken into account, the results came together perfectly.

It is very important to realise that failure is a normal mode of being, and as embarrassing as it was to discover the miscalculation in the already published paper, shying away from it was not a solution.

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