  The moving sofa problem, posed by L. Moser in 1966, asks for the planar shape
of maximal area that can move around a right-angled corner in a hallway of unit
width. It is known that a maximal area shape exists, and that its area is at
least 2.2195... - the area of an explicit construction found by Gerver in 1992
- and at most $2\sqrt{2}=2.82...$, with the lower bound being conjectured as
the true value. We prove a new and improved upper bound of 2.37. The method
involves a computer-assisted proof scheme that can be used to rigorously derive
further improved upper bounds that converge to the correct value.
