What is defetcive in mathematical proof?

Mathematics could lead to many ways of solving a theorem rather there could exist infinitely many ways of which only a couple are discovered. So what essentially is the necessity of a mathematical proof? Why there has to be a theorem that serves the way it is and why does it exist in the first place? It is the exploration of the universe in its form that compels the nature to predict a behaviour that is exhibited in mathematical proofs. But there could be an inherent defect in the proof of a theorem that the result might not show a relation to the axiom. The expediency in solving the theorem is lost in the way the theorem manifests itself.

The basic defect in the cognition of mathematical theorem is that the controlling necessity is not evident. What is the purpose behind the proof as Mathematics presupposes space and a magnitude. So inherently a mathematical figure occupies a space and a value describing the space. Why there is a necessity of mathematics in architecture? To make the space feasible I must denote it with a value and cognition of the mathematical proof sans any further necessity but to enclose the bounding space.

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