http://math.stackexchange.com/questions/261685/paul-erdoss-two-line-functional-analysis-proof .

does anyone know about what the problem was and what was his solution.

[Edit by quid:] please follow the link before trying to answer, there is already quite a bit of relevant information behind the link. [End edit]

notbe closed, because we still don't know what the problem was, much less P.E.'s solution! The information given at mathstackexchange was curiously and frustratingly incomplete. – Todd Trimble♦ Mar 2 '13 at 2:11