Mathematical proof is a social compact
By late-undergrad, it was intuitive to me that &quot;proof&quot; means &quot;all mathematicians who reads this agrees with it&quot;. Mathematics is unique in that, mostly, the field can achieve consensus on results, which we then call &quot;proofs&quot;.<p>But similarly, it makes sense that, even if a result is is &quot;true&quot; in a universal, objective sense, if the mathematician cannot communicate this in a convincing fashion to the rest of the mathematics world, I don&#x27;t think we can call that result &quot;proved&quot;.