# How do mathematicians know that they're right? [closed]

How do mathematicians know that they're right? How do they know that there's no flaw in a proof, or know when something has been proved?

Is this a welldefined concept, is it is some kind of intuition that must be developed?

• Please ask one question at a time. Sep 20, 2017 at 14:16
• but others can Control the proofs Sep 20, 2017 at 14:16
• People certainly make mistakes and errors, so peer review is very important to make sure all the mistakes are corrected in a proof (if there are any).
– Dave
Sep 20, 2017 at 14:21
• math.stackexchange.com/questions/139503/… Sep 20, 2017 at 14:22
• In order to philosophise constructively about this, it's important to understand that all mathematical theorems are of the form "If $A$ then $B$". We never say that some fact is categorically true, only that if you start out with some given set of assumptions $A$, then necessarily you get the consequence $B$. Sep 20, 2017 at 14:27