The Cartographer's Dilemma

Peel an orange and press the peel flat: it tears, stretches, and distorts. That is essentially what map projections do to the Earth's surface. The mathematical formulas behind a projection decide where the tearing and stretching happen and which properties survive at the expense of others.

Every projection is an intentional compromise. A navigator needs accurate direction. A statistician needs accurate area. A pilot needs accurate distance along great circles. No single projection serves all purposes, which is why hundreds exist — each optimized for a specific use.