in the center, since the air gap is almost zero, there is no path difference between two reflected beams, but there is a 180 deg. phase shift of the beam reflecting from the bottom surface (air-glass interface) (Light waves change phase by 180° when they reflect from the surface of a medium with higher refractive index than that of the medium in which they are travelling. A light wave travelling in air that is reflected by a glass barrier will undergo a 180° phase change, while light travelling in glass will not undergo a phase change if it is reflected by a boundary with air.(https://en.wikipedia.org/wiki/Reflection_phase_change)) so the interference is destructive.
this article describes the math comprehensively -http://physical-optics.blogspot.com/2011/06/newtons-rings.html