I have doubts about the construction of mathematical elements. There are proofs, that are proven using other theorems (corollaries) and/or axioms or definitions, such as Fermat's Last Theorem, the "weak" Goldbach theorem and thousands more.
I recently read proof of the "weak" Goldbach theorem, and it really is amazing the amount of resources, theorems, definitions and general aspects of mathematics that were used to prove that. My question is, why can not this proof become a law?. In fact, I've never heard the word "law" in mathematics, except for definitions like "closure law" or similar. I assume that the axioms act as "laws", or something like that.
Someone once told me that:
mathematics is a house of cards: if the bases are broken, the whole structure will fall.
I can not understand how such a large and complex structure could be compared with that example, but I assume that just because the proofs are not absolute laws.
In conclusion, my specific questions are:
- What is the difference between laws and theorems?
- can ever become law a theorem?
Sorry about my ignorance, and thanks!