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In this video(*) of Veritasium, you can see a challenge(**) between two mathematicians : Tartaglia and Fior, during the Renaissance in Italia.

When did we stop the challenges(**) between two mathematicians?

(*) : https://m.youtube.com/watch?v=cUzklzVXJwo

(**) : disfida

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    $\begingroup$ Do you expect that there is a unique answer? I guess that the perception of Mathematics changed over time. At a certain point, it became a serious subject, lying at the very roots of the other branches of science, and leading to reputable careers. So people started to act professionally and publish their results in journals, instead of playing challenges with their peers. $\endgroup$
    – Francesco Polizzi
    Commented Nov 15, 2021 at 8:44
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    $\begingroup$ An echo of those challenges remains in the section "Problems" of some journals like the former Newsletter of the EMS. And, maybe, in the culture of mathematical competitions like IMO. $\endgroup$
    – Francesco Polizzi
    Commented Nov 15, 2021 at 8:47
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    $\begingroup$ This seems a question for History of Science and Mathematics, not for this site. $\endgroup$
    – Federico Poloni
    Commented Nov 15, 2021 at 9:08
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    $\begingroup$ Maybe we should clarify whether history questions are suitable for MO. If not, we should remove the tag ho.history-overview. $\endgroup$
    – Francesco Polizzi
    Commented Nov 15, 2021 at 9:09
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    $\begingroup$ @PietroMajer: "The past is like a foreign country- they do things differently there" but in our own age at other times there are plenty of other ways of having nasty academic disputes. $\endgroup$
    – Paul Taylor
    Commented Nov 15, 2021 at 19:20

2 Answers 2

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I don't think we have ever stopped. You can submit your own work here if you want to compete for the Fields medal. Most countries have some sort of scientific academia or national foundation that distributes money in the form of prizes or grants. Mathematicians compete for that money. Some of these prizes target specific problems or areas of mathematics. These competitions happens at all levels of research or education. The international mathematical olympiad is a famous competition at the level of secondary education.

Arguably, today the disputatio are not done by climbing on a ladder and shouting at opponents, but instead by submitting some work to a committy.

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Trying an educated guess: the practice stopped in connection with Johannes Gutenberg's invention of the printing press. After that, it became harder and harder, and not so worthwhile, keeping one's own secret tricks in order to win maths competitions. On the other hand, authorship of printed signed books allowed to gain reputation in a wider and more safe way.

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    $\begingroup$ Gutenberg's Bible dates back to 1450. Tartaglia and Cardano were active a century later. $\endgroup$
    – Francesco Polizzi
    Commented Nov 15, 2021 at 9:13
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    $\begingroup$ I know, of course; I said "in connection with". It took time. $\endgroup$
    – Pietro Majer
    Commented Nov 15, 2021 at 9:30
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    $\begingroup$ But are there documented challenges taking place before Gutenberg? $\endgroup$
    – Francesco Polizzi
    Commented Nov 15, 2021 at 9:32
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    $\begingroup$ "Isit relevant?" Well, perhaps so. If the practice of challenges started after the printing press, maybe the printing press was not the main reason for the stopping. My impression is that the spreading of knowledge was surely involved in the disappearing process, but the main reason was the changing role of mathematics in science and society: not a game anymore, but something extremely serious (and that moved a lot of money). $\endgroup$
    – Francesco Polizzi
    Commented Nov 15, 2021 at 10:08
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    $\begingroup$ "May I say we mostly agree?" Yes, I think so :) $\endgroup$
    – Francesco Polizzi
    Commented Nov 15, 2021 at 11:40

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