Fiddling while Rome burns
To occupy oneself with unimportant matters and neglect priorities during a crisis.
The source of this phrase is the story that Nero played the fiddle (violin) while Rome burned, during the great fire in AD 64.
There are two major flaws with the story. Firstly, there was no such instrument as the fiddle (violin) in first century Rome. There's no definitive date for the invention of the violin, or of its synonym as fiddle, but it certainly wasn't until at least the 16th century. If Nero played anything during the Rome fire, it was probably the lyre.
Secondly, the story may be completely false and Nero may very well not have neglected his duty at all. Nero died four years later, and we should remember that history is written by the victors. The historian Suetonius records the Nero was responsible for the fire and that he watched it from a tower while playing an instrument and singing about the destruction of Troy. Others record this story merely as a rumour.
By modern-day standards Nero certainly appears a bizarre character, but that doesn't make this story true. Roman scholars differ over interpretations of events surrounding the fire. The rivalries and conflicting accounts, even those in contemporary reports, make the 'fiddling' story uncertain.