Try Harder
The essence of Dirac's problem was simply that: \(\sqrt{p^2c^2 + m_0^2c^4} \neq pc + m_0c^2\) and, in general: \(\sqrt{a^2 + b^2} \neq a + b\) (for non-zero \(a\) and \(b\)), as everyone learns (or should learn) at school.
At which point mere mortals give up. Geniuses try harder.
(Norman McCubbin, "Beauty in physics: the legacy of Paul Dirac" , in Contemporary Physics, Volume 45, Number 4, July-August 2004, pp. 319–333)