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I know a lot of people, some of them mathematicians, who have trouble telling right from left. This can lead to problems when you are composing functions, for example.

When did this seemingly innocuous confusion lead to wrong results being published? Here is an example from arithmetic geometry.

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    $\begingroup$ This makes me wonder more generally about when conflicting conventions have lead to incorrect results. $\endgroup$
    – Wojowu
    Commented May 14, 2019 at 7:56
  • $\begingroup$ it's a constant issue in group theory, how to evaluate compositions, from left or from right... $\endgroup$
    – Dima Pasechnik
    Commented May 14, 2019 at 9:35
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    $\begingroup$ Per @Wojowu's musing: signs! See, for example, Lawson - A note on sign conventions in homological algebra. (At least, that's the advertised title on Lawson's web page; the title on the linked page better describes the experience of those who have to deal with this sort of thing.) $\endgroup$
    – LSpice
    Commented May 14, 2019 at 11:16
  • $\begingroup$ actually, if we are talking about conventions, here is one amusing article about Hamiltonian vector fields: symplecticfieldtheorist.wordpress.com/2015/08/23/… $\endgroup$
    – user138661
    Commented May 14, 2019 at 12:57

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I don’t know about wrong results, but compare Godement’s Algèbre (1966, and still 1980):

on dit que l’ensemble $x\mathrm H$ est une classe à droite modulo $\mathrm H$

(translation: “we say that the set $x \mathrm{H}$ is a right class modulo $\mathrm{H}$”)

with everyone else, e.g. his associate Bourbaki (1970):

les ensembles $x\mathrm H$, qu'on appelle classes à gauche suivant $\,\mathrm H$ (ou modulo $\,\mathrm H$)

(translation: “the sets $x \mathrm{H}$, which are called left classes following $\mathrm{H}$ (or modulo $\mathrm{H}$)”)

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    $\begingroup$ maybe you should include a translation (as a sidenote, it kind of annoys me when people use French excerpts in articles written in English expecting everyone to understand). My French tells me "droite" is "left" and "gauche" is "right" (or I am making the exact mistake we are talking about?). $\endgroup$
    – user138661
    Commented May 14, 2019 at 8:51
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    $\begingroup$ but then the answer is not fully self-contained, it requires you to visit another website to comprehend it. $\endgroup$
    – user138661
    Commented May 14, 2019 at 9:00
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    $\begingroup$ In English, "adroit" is skilful, adept, and "gauche" is unsophisticated and clumsy, so you can kind of guess which is which :-) $\endgroup$
    – J.J. Green
    Commented May 14, 2019 at 9:10
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    $\begingroup$ @schematic_boi Um, sorry to point it out, but you have just demonstrated one example of how mix-ups happen. Yes, droit also means a right (in law), so there are hints. $\endgroup$
    – GregT
    Commented May 14, 2019 at 10:45
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    $\begingroup$ @GregT ah OK. I am not even a native speaker of the English language, so I guess it is OK for me not to know what droit means. My belief is that while the person giving an MO answer is not obliged to provide a translation, it kind of makes sense for them to do that, because it is easy for them, and how many other people will not understand what is written there and will have to use Google Translate? Probably more than one. $\endgroup$
    – user138661
    Commented May 14, 2019 at 10:53

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