Is a proof still valid if only the writer understands it? Say that there is some conjecture that someone has just proved. 
Let's assume that this proof is correct--that it is based on deductive reasoning and reaches the desired conclusion.
However, if he/she is the only person (in the world) that understands the proof, say, because it is so complicated, conceptually, and long, does this affect the validity of the proof? Is it still considered a proof?
Essentially, what I'm asking is: does the validity of a proof depend on the articulation of the author, and whether anyone else understands it?
The reason I ask is that the idea behind a proof is to convince others that the statement is true, but what if no-one understands the proof, yet it's a perfectly legitimate proof?

There only appears to be a problem because we are using the same word for closely-related but distinct concepts (not an uncommon situation in philosophy), namely


*

*"proof" as in formal proof, which Wikipedia defines as

a finite sequence of sentences each of which is an axiom or follows from the preceding sentences in the sequence by a rule of inference


*"proof" as in "any argument that the listener finds sufficiently convincing"
The situation you describe contains a proof according to the first meaning, but not the second. Conundrum resolved.
