- #1
Manny46
- 28
- 5
What I basically want to ask here is, about the process of forming mathematical truth/theorem. This seems like a bit broad question, but I have this specific query. We all know that Euclid started with his basic postulates or what we may call axioms, and common notions. Now did he form those propositions in a gradual manner, something like a follow up step which naturally proceed the previous proposition or postulate with the support of common notions? Or were those propositions intuitive in nature, which he reached through intelligent speculation, believed in its truth, and then deductively, with the help of other propositions/postulates proved its truth, forming a proposition finally?
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?
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?