One of the most persistent popular and urban legend-associated physics questions is whether glass is a liquid or a solid. The first-order answer is that it's a solid, and does not flow, even over centuries. The notion that glass is a liquid comes from two sources: that old church windows are thicker at the bottom than the top, and an erroneous reading of an old physics book by German physicist Gustav Tammann (1861-1938), which referred to it as a "frozen supercooled liquid." The myth omits the "frozen" part.
Somewhat more subtly, glass is an unconventional solid, known as an amorphous solid. For most liquid substances, cooling results in crystallization and a first-order transition to a solid state. For amorphous solids, instead of crystallizing and undergoing a first-order transition, the viscosity continues to increase and no crystallization occurs. That is part of why it is transparent — materials with irregular atomic arrangements transmit light better. Though there is a second-order transition in which the material properties of a glass change when it solidifies, this is not as substantial as the first-order transition found among most other compounds.
Glass can have a range of different material properties depending on how quickly it is cooled and the presence or absence of trace impurities, which can provide nuclei around which crystallization occurs. This is different than classical solids, which have the same basic material properties no matter what. Glass is sometimes defined as a system not at an equilibrium point — technically, it could crystallize at any time, and this sometimes does occur in material with impurities. Only a crystalline solid is considered to be at equilibrium.
Basically, what the argument boils down to is that "solid" and "liquid" are merely idealistic labels that people apply to various physical substances, even though there is a continuum of possible atomic arrangements with properties that mix between the two. For instance, a non-Newtonian fluid seems like a liquid, but under the sudden application of pressure, becomes like a solid. Fundamentally, to truly understand the world, peoples need to become familiar with the numerous possible states of matter beyond the simplistic first-order approximation of "solid," "liquid," and "gas."
