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In The Equation that Couldn't be Solved, Mario Livio writes of academia in 16th century Bologna. Apparently, mathematicians would take part in public debates, sometimes involving solving problems. They were extremely well-known, and could result in great discoveries.

What was the format of a mathematical debate? Do any accounts exist of one?

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    $\begingroup$ A good example is the dispute about the method for the solution of the cubic equations, involving Niccolò Tartaglia, Gerolamo Cardano and Scipione del Ferro. See Cardano's method. $\endgroup$ – Mauro ALLEGRANZA Jul 29 '15 at 11:37
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    $\begingroup$ You can find the details in many book on history of math, or see : the Foreword to : Girolamo Cardano, Ars Magna or The Rules of Algebra (1545 - Dover reprint 1993). $\endgroup$ – Mauro ALLEGRANZA Jul 29 '15 at 11:42
  • $\begingroup$ @MauroALLEGRANZA Thanks for that. By the way, the cubic dispute inspired this question. $\endgroup$ – HDE 226868 Jul 29 '15 at 13:34
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    $\begingroup$ For a XVII Century case, see : Galileo Galilei & Christoph Scheiner, On Sunspot (translated and introduced by Eileen Reeves & Albert Van Helden - 2010) $\endgroup$ – Mauro ALLEGRANZA Jul 29 '15 at 15:28
  • $\begingroup$ Perhaps the most striking difference from modern debate formats was the occasional settling of disputes through armed combat. :) $\endgroup$ – David H Aug 17 '15 at 12:29

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