History of World Maps — 2-part series

• Part 1: Mapping the World’s Contours
• Part 2: The Lies of Flat Maps (this article)

History of World Maps, Part 2: The Lies of Flat Maps

Think back to the world map that hung on your classroom wall. How large was Greenland? Compared to Africa, it probably looked roughly similar in size — maybe just a bit smaller. Now consider the actual numbers. Africa covers about 30.37 million km²; Greenland, about 2.16 million km².^[1] Africa is fourteen times larger. That classroom map showed almost none of that difference.

This is not because the map was wrong, or because the cartographer was careless. The moment you project a spherical earth onto a flat surface, distortion somewhere is mathematically unavoidable. And the choice of which distortion to accept has turned out to be surprisingly political.

Peeling an Orange onto a Table

To understand why projecting a sphere onto a plane is fundamentally impossible, think of an orange peel. If you cut a section of orange peel and try to flatten it completely on a table, it will always tear or wrinkle somewhere. A surface that curves like a sphere is structurally different from a flat plane.

The mathematician Carl Friedrich Gauss proved this rigorously in 1827. His Theorema Egregium (“Remarkable Theorem”) demonstrates that the curvature of a sphere and the curvature of a plane are fundamentally different, making it impossible to map one onto the other without tearing or stretching.^[2] Applied to cartography, this means every flat world map must sacrifice something — area, angles, distances, or shape — and no map can preserve all of them at once.

The techniques for dealing with this problem are known as map projections: methods for “projecting” the surface of a globe onto a flat plane in a chosen way. A projection that preserves angles exactly is called a conformal projection; one that preserves area exactly is called an equal-area projection. A projection that achieves both is mathematically impossible. Every map must choose what to keep and what to give up.

The Mercator Projection: A Map Built for Sailors

In 1569, Gerardus Mercator, a cartographer from Flanders (present-day Belgium), published an enormous world map — 202 cm wide and 124 cm tall — printed across eighteen sheets.^[3] The map had a clear purpose: to let sailors plot a course using only a compass.

The Mercator projection’s defining property is conformality. At any point on the map, directions are preserved exactly. If a sailor draws a straight line between his departure port and his destination, the angle that line makes with any meridian remains constant throughout the voyage. This is called a rhumb line.^[3] For a navigator in the open ocean with nothing but a compass, that property was literally a matter of survival.

The cost was area distortion. The Mercator projection stretches the spacing of its grid lines progressively as you move from the equator toward the poles, causing high-latitude regions to balloon in apparent size. The result is that Greenland looks comparable to Africa. Russia appears vastly larger than it is; Canada and Alaska are similarly inflated. Meanwhile, equatorial regions — Africa, Brazil, Southeast Asia — appear smaller than reality.^[3]

There are good reasons the Mercator projection endured as a standard for so long. During the Age of Exploration from the fifteenth to eighteenth centuries, the practical demands of navigation were paramount, and Mercator’s map met them precisely. It was subsequently adopted as an official map during the era of European colonial expansion. As it spread to school textbooks and the walls of government offices, it became synonymous with “the world map” itself. In the early twenty-first century, Google Maps initially used the Mercator projection without modification.^[4]

The Political Controversy: The Gall-Peters Projection

The challenge to the Mercator projection arrived in 1973 from Arno Peters, a German historian. He announced that he had invented a new world map, and he attacked the Mercator projection head-on. His charge: “The Mercator projection exaggerates Europe and the Northern Hemisphere, reinforcing the Eurocentric worldview of the colonial era.”^[5]

Peters’s map was an equal-area projection, preserving the relative area of every region at its true proportion. On his map, Africa appears far larger than on Mercator’s, and Europe and North America shrink accordingly. Peters argued that his map restored the true size and presence of non-European regions — particularly Africa and Latin America — to their rightful place in the world’s view.^[5] When the United Nations Development Programme (UNDP) and several aid organizations adopted it, the map gained international attention.

Cartographers were not impressed. First, the equal-area projection that Peters claimed to have invented was mathematically identical to one already published in 1855 by a Scottish clergyman named James Gall. The academic community accordingly calls it the Gall-Peters projection.^[5] Second, the Gall-Peters projection preserves area only by severely distorting shape. Africa appears stretched vertically; European countries look squashed flat. In 1989, seven professional cartographic organizations in North America — led by the American Cartographic Association — issued a joint resolution urging that no rectangular map projection be used as a standard world map.^[6]

The criticism that the Mercator projection carries a political bias has merit. High-latitude regions — Europe, North America, Russia — do appear substantially larger than they are. But Peters’s alternative introduced distortions of its own, and some of his claims were overstated. The controversy exposed something important: choosing a map projection is both a technical question and a question of values. A map must decide what to represent accurately, and that decision is never neutral.

Attempts at Compromise

The Gall-Peters controversy prompted cartographers to search for projections that were balanced overall rather than optimized for any single property.

The Robinson projection, developed in 1963 by American cartographer Arthur H. Robinson, was created in an unusual way: rather than starting from a mathematical formula, Robinson first drew a map that looked right to his eye, then worked backward to derive the equations.^[7] The result preserves neither area nor angles perfectly, but reduces both distortions enough to produce a map that feels natural and readable. The National Geographic Society adopted it in 1988, replacing the Van der Grinten projection it had used previously.^[7]

In 1998, however, National Geographic switched again — this time to the Winkel Tripel projection. Devised by German cartographer Oswald Winkel in 1921, the Winkel Tripel aims to simultaneously minimize three types of error: area, shape, and distance. Tripel is German for “triple.”^[8] It remains one of the most widely recommended projections for general world maps today.

Other experiments took entirely different directions. In 1943, Buckminster Fuller published the Dymaxion map, derived by unfolding an icosahedron (a 20-sided solid).^[9] Slicing the globe into triangular faces and laying them flat produces a map with no single center, no continent given special size or prominence, and a visual impression of the world as one continuous landmass — a planet whose people share a single surface.

In 1999, Japanese architect Hajime Narukawa developed the AuthaGraph projection, which won Japan’s Good Design Grand Award in 2016.^[10] The method divides the globe into 96 triangles, maps them onto a tetrahedron, and then unfolds that into a rectangle, greatly reducing area distortion. Though not yet widely adopted as a standard, it draws interest for representing both area and shape more accurately than most conventional projections.

Why Is North at the Top?

There is one more convention worth questioning. We accept north-up maps as a given, but this is not a law of nature.

As noted in Part 1, medieval European T-O maps placed east at the top — the Garden of Eden was to the east — and the English word “orientation” comes from the Latin oriens, meaning east.^[11] Islamic cartographic tradition placed south at the top. Ancient Egyptian maps tended to do the same.

The north-up convention owes much to Ptolemy’s Geography, which already used north-up maps when it was rediscovered and printed in fifteenth-century Europe.^[11] The spread of the compass in twelfth- and thirteenth-century Europe reinforced the habit: since compass needles point north, orienting maps to the north became a practical standard for navigation and exploration.^[11] The great mapmakers of the Age of Exploration — Mercator, Martin Waldseemüller, Henricus Martellus Germanus — were devoted followers of Ptolemy, and as their maps became the global standard, the north-up convention became global too.^[11]

The most famous challenge to this convention appeared in Australia in 1979. Stuart McArthur, then twenty-one years old, published “McArthur’s Universal Corrective Map of the World” — with south at the top and Australia at the center.^[12] He had first drawn the idea at age twelve, only to be told by his teacher to redo it properly. At fifteen, while on a student exchange in Japan, American classmates mocked him as someone from “the bottom of the world.” He resolved then to publish the map. It has sold more than 350,000 copies. Few examples illustrate more plainly that “up” and “down” on a world map are cultural choices, not mathematical facts.

The Choices Inside Every Map

There is an old saying in cartography: there is no such thing as a perfect flat world map. What Gauss proved mathematically means that every map is ultimately a compromise. Choose area accuracy and you lose shape; preserve angles and sizes grow distorted.

Who decides the terms of that compromise, and by what standard, is not a purely technical question. Which continent appears largest, what sits at the center, which direction points up — all of these choices carry the values and needs of the era in which the map was made. When Mercator chose angles over area for the sake of navigation, that choice occupied classroom walls around the world for centuries. When Peters came forward with area accuracy, cartography became a political argument.

A world map is a window onto the world, but it is not a transparent one. Someone decided the frame, the angle, and what to draw large and what to draw small. When we look through it at the world, we are simultaneously looking at the choices made by the age that built the frame.

Gauss proved a mathematical limit. But the choices cartographers have made within that limit are a story that mathematics alone cannot tell. Which map hangs on a classroom wall is also a question of which worldview gets handed to the next generation. In that sense, the flat world map has never been a simple measurement. It has always been an object that carries the perspective of the people who made it and chose it.

The Gall-Peters controversy has had tangible consequences in English-speaking countries. In 2017, the Boston Public Schools made international headlines when it became one of the first US school districts to formally replace Mercator-based classroom maps with the Gall-Peters projection — a decision driven explicitly by the argument that showing Africa and South America at their true relative sizes would help students challenge inherited assumptions about which parts of the world “matter.”^[13] The move drew both applause and criticism: supporters called it a long-overdue correction; detractors pointed out that replacing one distorted map with a differently distorted one does not resolve the underlying mathematical problem. The episode illustrated, as vividly as any classroom exercise could, that a decision about which map to hang on a wall is never merely a technical one.

Previous: Part 1: Mapping the World’s Contours