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Can it be (are there real examples/anecdotes of) that, say during international séminaires or conferences in mathematics, people of different linguistical origins could understand each other with the help of pure -or almost- mathematical formalization and notation ?

Is it possible ?

Thanks.

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    $\begingroup$ Harvard and other top universities require one foreign language exam (French, German, Russian) to translate a piece of mathematical work for a PhD in mathematics. You can find students claiming on the web that they translated without knowing the language. Can't recall the link but I was searching for translation issues in chemistry for my own paper last year. $\endgroup$ – M. Farooq Feb 6 at 17:59
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    $\begingroup$ Why conferences? English speaking mathematicians, who do not read French or German, can usually make out what mathematical papers written in French and German are about by looking at the formulas and similarly spelled words around. This is another reason why French and German mathematical papers are rarely translated into English. $\endgroup$ – Conifold Feb 6 at 20:53
  • $\begingroup$ Most scientists in the field chemistry, physics, and mathematics had to have a reading knowledge of these European languages to read the extensive literature in other languages. This tradition continued until the 1990s. Harvard or Stanford now give Chinese as one of the choices. $\endgroup$ – M. Farooq Feb 7 at 5:01
  • $\begingroup$ @Seb it's a good question, don't worry about the comments and down votes too much. Each Stack Exchange site is a little different, some more encouraging/helpful to new contributors than others. This might be a difficult question to answer in Stack Exchange unless there are good documented sources recounting such an event that can be cited in an answer. $\endgroup$ – uhoh Feb 7 at 23:51
  • $\begingroup$ @M.Farooq I don't believe Stanford's math PhD program has a language requirement anymore. Where did you see anything about Chinese? Harvard's requirement on their website is F, G, or R, or Italian if you work in algebraic geometry. This does not explicitly include Chinese, but they allow anyone with a degree from a non-English-speaking country to request not to take the exam. (FWIW, Princeton and Harvard each used to require passing a language exam in two of F, G, or R, not just one. Now they both require one. I wonder when that changed.) $\endgroup$ – KCd Feb 9 at 9:09
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I am not completely sure about the kind of information you're looking for.

I think that common experience of many scholars coming from non English speaking countries is that their first experience of international congress is something of this kind: you rely 80% on formulas that you see at the blackboard (whiteborad/slides) and 20% ore less form the few words that you're able to understand from the speaker. Many of us passed throught this moment (and, somewhat, survived). Percentages here are to be understood as a half-joke, each case is of course different.

Whether this is of help to answer your question I do not know. True is the fact that among scientists mathematicians were always much interested in developing a lingua franca that allowed to communicate more easily. Leibniz was the first to think that developing a language for logic and at the same time for universal communication was one of the principal concern for science. At the 1900 International Congress of Math there was a session discussing the problem of communication between mathematicians that adressed the problem on whether one should choose a natural language to communicate between different mathematicians or develop an artificial one. It is not by chance that the Italian logician Peano both tried to write an encyclopedi treatise of math relying on set theory (Formulario Mathematico) and developed an artificial international language based on Latin (Latino sine flexione).

You can find some interesting information of the sort in this paper: https://jcom.sissa.it/archive/01/01/A010103/jcom0101(2002)A03_it.pdf

Ironically enough, it is in Italian so you'll need help to understand it :D

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I’ve read that certain linguists actually wonder, given the complexity of language and thought, as to how people actually communicate given that they most manifestly do.

I don’t really know the research literature on this but my tuppence is that it matters a great deal as to whether people are on the same wavelength, so to speak.

After all, if one is going to a conference then one might suspect that there is already much in common that one already has with the other participants in terms of the major questions at hand. Also, it’s important to recognise that scientific language despite its wide vocabulary - mainly due to its many specialisms - actually uses quite simple language on the whole. This makes it relatively straight-forward to learn scientific English as it only uses a small fragment of the language and its resources. The main problem, is understanding the concepts.

As for anecdotes I can’t recall any offhand that is about what you are asking for. I do recall Richard Feynman writing about his teenage years how he by inventing his own symbols for already existing terms wasn’t helping him to communicate and that having a common language to communicate in was important.

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