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?