Math is fascinating to me, though I struggled with math in high school and only took the minimum I needed. (Age changes things, man.) I’m reading a book on Wiles’ proof for Fermat’s Last Theorem and got curious about proofs.
At what point does something move from an assumption with examples (well yeah. Look at this) to a full proof?
Simple example that came to mind:
For any number n, where n is a prime >2, the sum of the factors of n cannot be odd.
In: Mathematics
You generally start out with something that is assumed to be true and then use stuff like equivalencies to prove that it must also mean that thing you are wanting to prove is true.
There are many different approaches to prove something like showing it its true for every single case or that is is true for a single case but also true for every case subsequent to one that is true or by showing that if it wasn’t true that would mean something that can’t possibly be the case or any number of things.
Proofs you learn in school and in college tend to be simple affairs but some of the newer more out there stuff can’t really be proven just by writing for a few pages with pencil on paper and may even require computers to get it all sorted out.
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