solution. They are called ‘Constructivists’ (of varying shades) who say the proof
method fails to provide ‘numerical meaning’. They pour scorn on the classical
mathematician who regards the reductio method as an essential weapon in the
mathematical armoury. On the other hand the more traditional mathematician
would say that outlawing this type of argument means working with one hand
tied behind your back and, furthermore, denying so many results proved by this
indirect method leaves the tapestry of mathematics looking rather threadbare.

the condensed idea

Signed and sealed