About the Mollweide Projection
Karl Brandan Mollweide devised this projection in 1805, in response to a similar projection devised by Georg Gottleib Schmidt in 1803. Both projections are elliptical pseudo-cylindrical projections, but Schmidt's projection lacks the equal area property present in the Mollweide projection.
The Mollweide projection is a pseudo-cylindrical projection. Ie. a mathematical projection with straight line parallels (like a cylindrical projection) but with curved meridians (unlike a cylindrical projection). With the exception of the central meridian, all of the meridians in the Mollweide projection are elliptical arcs. This results in a projection which that has a smooth, continuous outline at the poles, and is more aesthetically pleasing than the Sinusoidal projection.
The Mollweide projection remained in relative obscurity until 1857 when Jacques Babinet reintroduced it as the "Homalographic" projection. As such, it saw some use in late 19th century atlases for thematic world maps. It has since become more popular, and is the only 19th century pseudocylindrical projection to have seen practical applications other than those of novelty (eg. Collignon projection) or purely academic interest.
Author's Note: Of the projections presented here at Equal-Area-Maps.com, the Mollweide projection is probably the most suitable for producing global thematic and geospatial distribution maps. It is one of the most practical for online mapping use with support from ESRI, Proj4, and Proj4JS; shape distortion is amongst the best of the available projections; and it is one of the more aesthetically pleasing projections. Similar support is available for the Sinusoidal and Behrmann projections, but the Sinusoidal projection is less aesthetically pleasing, and the Behrmann (Cylindrical Equal Area) projection has a greater level of shape distortion.