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This can be generalized to more broader question as to how mathematicians go about forming their theorems, as far as starting a new theory with completely new axioms are concerned, or even extending the previous work. Is it gradual or is it something where mathematicians form different statements, and guesses and with more careful observation convince themselves of the truth of the statement, and thereafter work deductively to prove the statement/conjecture to convince others and themselves of its truth, thereby forming a theorem/proposition from a mere statement?