Some of the oldest projections are equal-area (the sinusoidal projection is also known as the "Mercator equal-area projection"), and hundreds have been described, refuting any implication that Peters's map is special in that regard. In any case, Mercator was not the pervasive projection Peters made it out to be: a wide variety of projections has always been used in world maps.[26] Peters's chosen projection suffers extreme distortion in the polar regions, as any cylindrical projection must, and its distortion along the equator is considerable. Several scholars have remarked on the irony of the projection's undistorted presentation of the mid latitudes, including Peters's native Germany, at the expense of the low latitudes, which host more of the technologically underdeveloped nations.[27][28] The claim of distance fidelity is particularly problematic: Peters's map lacks distance fidelity everywhere except along the 45th parallels north and south, and then only in the direction of those parallels. No world projection is good at preserving distances everywhere; Peters's and all other cylindric projections are especially bad in that regard because east-west distances inevitably balloon toward the poles.[25][29] The cartographic community met Peters's 1973 press conference with amusement and mild exasperation

Gall-Peters is an improvement over the standard Mercator in terms of equal area - because that's not what it's for. If anyone was actually suggesting the Mercator was good for it Gall-Peters might be useful. They're not, it isn't.

The Waterman Butterfly makes me quite happy; you take a physical globe made up of spheres and unfold it onto a 2d surface. It's like the Goode Homolosine but less ugly. The Goode Homolosine looks like a snake drawn by a child. Actually thinking of that makes it quite charming.