Mathematicians (just like builders, carpenters, cabinet makers, metal workers, designers, architects, nurses, doctors, engineers, etc.) know how easy it is to make computational errors or to make misunderstandings. So, to overcome that, they check their thinking.
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We will add some more information soon. It's important to know that mistakes happen to everyone (if you're paying attention) and whilst it feels good to be 'right', being 'wrong' is a powerful source of new learning.
A note about 'mistakes'...
Read more at http://ww2.kqed.org/mindshift/2015/11/23/why-understanding-these-four-types-of-mistakes-can-help-us-learn/