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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

Dattier
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    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. – Francesco Polizzi Nov 15 '21 at 08:44
  • One minor point: in English it's usually translated Renaissance. And one maybe less minor point: did they stop? There's certainly still a culture of offering prizes for proof or disproof of conjectures; maybe it's just that the nature of the challenges has changed. – Peter Taylor Nov 15 '21 at 08:47
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    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. – Francesco Polizzi Nov 15 '21 at 08:47
  • "When will the last challenge take place?" I guess this is very difficult to answer. It is like asking "When did the last duel take place?" – Francesco Polizzi Nov 15 '21 at 08:49
  • Related question: https://mathoverflow.net/questions/242178/mathematics-contests-before-1800?rq=1 – Francesco Polizzi Nov 15 '21 at 08:51
  • There is a user here at MO who knew the answers to the questions he posted https://meta.mathoverflow.net/q/5116/82588 . Thus one can consider this as posing challenges to other mathematicians. So the practice has not stopped, contrary to your claim. – Martin Nicholson Nov 15 '21 at 09:05
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    This seems a question for [hsm.se], not for this site. – Federico Poloni Nov 15 '21 at 09:08
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    Maybe we should clarify whether history questions are suitable for MO. If not, we should remove the tag ho.history-overview. – Francesco Polizzi Nov 15 '21 at 09:09
  • @FrancescoPolizzi This has been asked on meta in the past, and discussed again more recently. – Federico Poloni Nov 15 '21 at 09:12
  • Historically, there were famous mathematical "duels in effect", they just had happened. – Wlod AA Nov 15 '21 at 09:27
  • The question is asked as "when did we stop" but it seems not to be your point, since you're asking in comments "will the last challenge take place?", "do you think it would be a good thing to relaunch the tradition?", and even posted an answer to propose a new tag. So it looks like it's launching a discussion and not a real question. And it seems anyway mostly off-topic and opinion-based. – YCor Nov 15 '21 at 12:58
  • It is also possible that the sad epilogue of the Tartaglia-Cardano-Ferrari dispute had a role in putting an end to the practice of the "disfida" (as a result of the defeat, Tartaglia lost his position in Brescia; Ferrari, as winner, got a good career improvement, but at the price of the shadow of having betrayed and ruined a talented mathematician; eventually both Cardano and his student Ferrari had an unfortunate life. A nasty business after all). – Pietro Majer Nov 15 '21 at 13:28
  • A more productive version of this question would be to ask what other significant occasions there were when mathematics was conducted in this fashion. The Tartaglia--Fiore contest was by far the most prominent; there's an account of it in "The equation that couldn't be solved" by Mario Levio. – Paul Taylor Nov 15 '21 at 13:32
  • @PietroMajer: I think you have the episodes of this story mixed up. – Paul Taylor Nov 15 '21 at 13:33
  • @PaulTaylor where exactly? thank you :) – Pietro Majer Nov 15 '21 at 13:36
  • (Tartaglia accusations were against Cardano, but Ferrari was Cardano's student) – Pietro Majer Nov 15 '21 at 13:41
  • @PietroMajer:the public contest was between Fiore and Tartaglia; Cardano extracted the solution from Tartaglia by other means that probably included a quantity of wine. See Levio's book, which also recounts the misfortunes but unfortunatly not the mathematics of Abel and Galois. – Paul Taylor Nov 15 '21 at 13:43
  • Tartaglia-Fior was a preceding dispute, I was referring to Tartaglia-Ferrari – Pietro Majer Nov 15 '21 at 13:58
  • Yes, Wikipedia says that there was a second contest. I didn't know about that. – Paul Taylor Nov 15 '21 at 14:00
  • @PaulTaylor The whole story is far from clear to me, but the feeling is that it's not a nice story. If this feeling, rational or not, was the same in 1550-1600, no wonder the "disfida" lost some appeal :) – Pietro Majer Nov 15 '21 at 14:15
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    @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. – Paul Taylor Nov 15 '21 at 19:20

2 Answers2

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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.

coudy
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    Would the Arnold-Serre debate fit the bill? https://mathoverflow.net/questions/153604/the-arnold-serre-debate – coudy Nov 15 '21 at 09:56
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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.

Pietro Majer
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    Gutenberg's Bible dates back to 1450. Tartaglia and Cardano were active a century later. – Francesco Polizzi Nov 15 '21 at 09:13
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    I know, of course; I said "in connection with". It took time. – Pietro Majer Nov 15 '21 at 09:30
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    But are there documented challenges taking place before Gutenberg? – Francesco Polizzi Nov 15 '21 at 09:32
  • Isit relevant? I'm saying that in an environment where knowledge is more easily shared, the practice of the disfida loses interest, both for the public and for competitors (and harder for them: you can just hope to win hundreds of competitions just with the same secret trick). As a matter of fact, Tartaglia notoriety was diminished by Cardano publication of Tartaglia's formulas. When mathematical treatises like Bombelli's Algebra (1571) started being printed and spread in European libraries, publishing a book became by far much more safe and durable way of gaining celebrity. – Pietro Majer Nov 15 '21 at 10:03
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    "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). – Francesco Polizzi Nov 15 '21 at 10:08
  • By the way, J. Bernoulli still challenged mathematicians on the brachistocrone curve in 1696, almost 250 years after Gutenberg's.

    https://en.wikipedia.org/wiki/Brachistochrone_curve

     – Francesco Polizzi Nov 15 '21 at 10:23
  • Well, yes, and even today we have Olympiads of Maths – Pietro Majer Nov 15 '21 at 10:43
  • I agree. But Bernoulli's challenge was very much in the same spirit as Tartaglia's (challenging peers on open problems), whereas IMO is a competition for students. – Francesco Polizzi Nov 15 '21 at 10:49
  • Certainly, but note that the disfide were not just a sport game; they were also a form of public concours for academic positions, and were also a mean (even if not so efficient) to share the mathematical skills. Yes, the increasing importance of mathematics in science and in economy at a certain moment required more efficient ways to publicize and propagate the mathematical knowledge, and a good tool to this aim was the press. May I say we mostly agree? – Pietro Majer Nov 15 '21 at 11:16
  • (As to Bernoulli's challenge: good point, but the objection would also apply to what you said before, since in 1696 mathematics was already fundamental in all human economy, industry, war, world navigation, etc ;) ) – Pietro Majer Nov 15 '21 at 11:18
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    "May I say we mostly agree?" Yes, I think so :) – Francesco Polizzi Nov 15 '21 at 11:40