Gall-Peters
Cylindrical equal-area at the 45-degree standard parallel. Area is conserved exactly here too, but the shape cost is harsher than Equal Earth's: about 46 times at 84 north.
Equal-area too, and nothing like it
Gall-Peters and Equal Earth give identical area readings - a constant 1.00x - and nobody would confuse the two maps. Equal-area does not mean undistorted. It fixes one quantity and leaves the rest free, and the rest can be spent badly.
Its standard parallel is 45 degrees: on that circle shape distortion is exactly 1.00, the only place on the map where nothing is stretched. It degrades fast either side - 2.0 at the equator, about 45.8 at 84 north, the harshest shape cost of the five.
Why it is famous
It was promoted as a political argument: if Mercator draws the wealthy high-latitude countries too large, use a map that does not exaggerate area. The argument is right about area. The cost is that it stretches equatorial countries into thin strips. It fixes one column and makes the other worse than it was.