Mankiw mentions two schools of thought:
The Real Business Cycle View - eveything is determined by supply “you may passionately believe that the business cycle is driven by exogenous shocks to technology,” which he strongly rejects.
The New-Keynesian, “synthesis,” view - “aggregate demand” matters for the short-run (where the economy is Keynesian), but neoclassical forces dominate in the long run. He argues in favor of teaching that.
On my side, I lean towards a third school of thought, which argues that aggregate demand might actually matter even for the long run (it is the mirror image view, compared to that which argues that everything is determined by supply).
I have worked on this very intensely since I started my ph.D. in 2010 and defended my dissertation in July 2013 entitled “Bubbles and Asset Supply.” The first chapter argued that there was an excess of savings over investment in the world.