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How common is it to mention that a discovery was made by accident and if it is acceptable to say that in a paper?

We often hear historical accounts on how discoveries were made by accident, however, I never saw it mentioned in a paper. I wonder if here would be a good place to ask for examples.

I am asking that because I recently made a discovery and the specific conditions I used were simply by mistake. These conditions were not used before and it was not my intent to use them, I just used the buffer of a different experiment.

Usually, there is an explanation of why a specific condition was chosen, but if there is no reason beforehand, is it better to come up with an explanation or to state it was by trial?

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    Why would it matter? A paper should be informative. In my field, this means that it should explain its contribution, and explain why the contribution is important and new. A paper is not the story of how one ended up with the contribution. – lighthouse keeper Oct 29 '20 at 9:19
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    If the "discovery" is the result of playing around with statistical data, it is important to mention that your approach has been explorative rather than rigorous hypothesis testing. Otherwise you will commit the sin of HARKing. (Not an answer, because you are doing experimental research.) – henning -- reinstate Monica Oct 29 '20 at 9:26
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    You can highlight the serendipitous nature of the discovery as a backstory if you are giving a research talk to make it more interesting and personal. – Sourav Oct 29 '20 at 15:41
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    My recollection is that Koichi Tanaka won the 2002 Nobel Prize in Chemistry for something that started off as an experimental mistake. As Asimov would have said, "That's funny..." – Mark Morgan Lloyd Oct 29 '20 at 16:49
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    @lighthousekeeper doesn't mean it has to... I find the papers that explain the path to be the most useful and interesting. – Džuris Oct 29 '20 at 17:41
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The paper is not the place to give a step by step account of everything that happened. You should have a research log, or lab log, or some other form of documentation that does that, but that is separate from the paper. The paper is there to present your finding in a clear and concise way. Based on the paper you should be able to replicate the results, but, depending on the kind of research you do, is not necessarily the same as a complete list of every step taken. I think of the paper as the summary for the research log and code.

I can imagine accidents where it is worthwhile to mention that in the paper, others where it can be entertaining and other accidents where it is not appropriate in the sense that it wastes the readers time. It depends on the accident and the style of paper you are writing, where the latter in a large part depends on the journal you intend to sent it to.

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    Agreed: The history of a discovery is a topic of science history, not science. Unless there is something in the incident which will tell us something about how the science works, it has no real role in the paper. If it motivates the research, though, it might be worthwhile mentioning. – Captain Emacs Oct 29 '20 at 9:23
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    Perhaps this varies by field. In my field (pure maths/theoretical CS), light-hearted asides are not uncommon; they can be very welcome for leavening the tone of otherwise dense papers, making them more readable. Of course, the scientific content is the priority, and they mustn’t get in its way or distract from it; but used sparingly, they’re generally accepted as appropriate and good style. – PLL Oct 29 '20 at 19:07
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If there was no rational motivation for the discovery, I would write "We serendipitously discovered..."

Some people might just give no reason. Most people (except maybe clickbait writers) will not care if the discovery was an accident.

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    I think that quite a lot of insight into deep issues arises through serendipity. +1. – Buffy Oct 29 '20 at 9:54
  • I'd go a step further and agree with Isaac Asimov (or so the quote is attributed): "The most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka' but 'That’s funny...'" – Dan Nov 2 '20 at 10:18
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I think you should briefly describe the fortunate accident that led to the discovery. Those few words will add to the human dimension of science at no cost to the reader and perhaps some benefit: they won't waste time wondering "how in the world did they think to try that?!"

I wonder if Fleming's paper on his discovery of penicillin discussed the accidentally exposed petri dish. A haven't found the paper on the web (after not too long a search).

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    It's here: ncbi.nlm.nih.gov/pmc/articles/PMC2048009/pdf/… He notes only that "While working with staphylococcus variants a number of culture-plates were set aside on the laboratory bench and examined from time to time. In the examinations these plates were necessarily exposed to the air and they became contaminated with various micro-organisms." – Xerxes Oct 29 '20 at 20:31
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There is absolutely nothing remarkable about being able to have some random lab mishap. The actual accomplishment lies in following up, namely noticing the unexpected nature of the results and tracing their causes instead of just dumping the failed experiment and starting over.

So the main point of relating the details of the mishap would be if there were some expectation that variation along related lines could lead to similarly relevant discoveries, basically indicating a class of phenomena that your discovery could possibly be part of.

For example, if you have a paper about the microbial properties of a substance, it would make sense to specify just where in nature you encountered this or a functionally similar substance that may have evolved as an organic defense. That opens up a lot more "hot" research venues rather than if you present the substance in isolation, without giving out the details of the origin of your research.

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