"§ 91.181 Course to be flown.
Unless otherwise authorized by ATC, no person may operate an aircraft within controlled airspace under IFR except as follows:
(a) On an ATS route, along the centerline of that airway.
(b) On any other route, along the direct course between the navigational aids or fixes defining that route. However, this section does not prohibit maneuvering the aircraft to pass well clear of other air traffic or the maneuvering of the aircraft in VFR conditions to clear the intended flight path both before and during climb or descent."
An article written more than 50 years ago that appears in Wikipedia is entitled "The Paradox of Navigation," The author concludes that the "more accurately we navigate, the more likely mid air collisions will occur."
Also see a previous post on this Blog entitled "Randomness is Good!"