I had a discussion with a friend about the need of mathematical rigour in the real world. He argues that little rigour is needed for the "application of mathematical results.Mathemticiians complicate 'obvious facts'. I don't agree with the idea that being obvious makes something true. For instance BanachTarski paradox, 0.999...=1,etc but all of such examples come from purely mathematical point of view and have no real world applications. This makes me wonder if there is a need of mathematical rigour in the real worl situations?

  • $\begingroup$ Well, most of mathematics isn't concerned with the "real world," in the sense of applications that companies will pay you for. Ditto even for physics, if you restrict the "real world" to classical Newtonian mechanics. What sorts of applications do you have in mind? As for ostensibly obvious things that are actually false, here's a related question: math.stackexchange.com/questions/820686/… . $\endgroup$ – anomaly Apr 3 '15 at 18:11
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    $\begingroup$ I had a tutor at university once who often expressed genuine fear that the nearby nuclear power station would blow up because a mathematician employed there would find a solution to an differential equation and not ask if it was the.... only one!!! $\endgroup$ – Frank Apr 3 '15 at 18:18
  • $\begingroup$ A level of rigour is definitely required for applying statistical results to the real world. You could get an idea of this at the cross validated site.... $\endgroup$ – user2055 Apr 3 '15 at 18:19
  • $\begingroup$ @Frank nice example $\endgroup$ – Hashir Omer Apr 3 '15 at 18:25
  • $\begingroup$ Did he give an example in which "little rigour is needed"? Could you tell us some situation that your friend don't agree that rigour is needed? $\endgroup$ – Pedro Apr 3 '15 at 18:53

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