The problem of the “flat earth” has been around for centuries. It is believed that as early as the year 354, pre-medieval scholars asserted that the earth was in fact spherical (University of Waterloo). The problem for map-makers, then, is to find a way to depict a spherical object on a 2D surface, and this is turns out to be an impossible task. Take a look at the animation below for what’s called a “Myriahedral projection” developed by Jack Van Wijk from the Netherlands.
In trying to depict a spherical surface onto a 2D plane, one can try to preserve distances, shape, areas, or shortest distances between points by straight lines. It is impossible to have all these desirable properties in one map. For instance, the Mercator projection map is the one that we are probably all most familiar with as it preserves angular distances, making it easy for navigation, but it drastically skews areas the further away the land masses are from the equator. See this true size (thetruesize.com) comparison below, showing how large the continent of Africa actually is compared to the US, China and India:
Here’s another great video explaining “Why all world maps are wrong” that was recommended to me by Mr. Schwartz, a geography teacher and the humanities Department Head at my school.