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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?

Hashir Omer
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  • 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: http://math.stackexchange.com/questions/820686/obvious-theorems-that-are-actually-false . – anomaly Apr 03 '15 at 18:11
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    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!!! – Frank Apr 03 '15 at 18:18
  • 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.... –  Apr 03 '15 at 18:19
  • @Frank nice example – Hashir Omer Apr 03 '15 at 18:25
  • 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? – Pedro Apr 03 '15 at 18:53
  • What would it mean to say that little (or much) rigor is needed in the application of mathematical results to the real world? The word "rigor" is usually applied to doing mathematics rather than to applying it, I think. One could argue that rigor is needed in doing mathematics, even applied mathematics, in order to end up with something that applies in all situations rather than just the few particular situations that inspired the research. Otherwise one would have to worry that the non-rigorous reasoning that was good enough for one application might not be good enough for the next. – Trevor Wilson Apr 03 '15 at 22:24

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