IF the earth really were flat, then a flat map would be very easy and would have been worked up long ago. IF the earth were really flat, then maps of the earth would all look the same, except be printed in different sizes. And they wouldn't require higher mathematics, just a simple ratio.
But the earth is round, not flat, a making a map of the earth requires higher mathematics to project a sphere onto a flat map. There are hundreds of different projections for earth maps, each different and each with its own distortions ("interrupted" maps have the fewest distortions). Distances on flat maps of the earth are difficult to approximate.