The General Assembly did something on Friday afternoon that I have wanted somebody to do since I was a kid staring at a pull-down map in a Texas classroom, wondering why Greenland was so enormous and why nobody seemed to think that was strange. One hundred and sixty-four countries voted to stop drawing Africa small.
And then almost every account of it described the vote as swapping the Mercator projection for a more accurate one. That sentence went into the note I clipped on Friday night in quotation marks, because it was the thing I wanted to argue with — it is the single claim the mathematics forbids. The strange, hopeful part of this story is that the resolution itself never makes it. The document is more careful than nearly everything written about it.
A fair map does not change the geography of the world, it changes how we see the world.Robert Dussey, Togo’s foreign affairs minister, introducing the resolution — UN News
What 164 states actually voted for
The text is A/80/L.104, “Correct the map”: rebalancing global cartographic representation and promoting equitable representation of the world’s regions, particularly Africa. It was sponsored by fifty-five African states and the Bahamas, and introduced by Togo on behalf of the African Union. It carried 164 in favour, 1 against, 6 abstentions. The one against was the United States. The six abstentions were Estonia, Georgia, Lithuania, Moldova, Serbia and Ukraine; Ukraine’s objection was to how a world map renders occupied territory, which is a real argument about a different property of maps entirely.
It is non-binding, and its verbs say so plainly: it affirms, recognizes, declares, encourages, invites and urges. Nothing in it bans a projection or mandates one. The operative paragraph that carries the headline, number five, encourages states and organisations to use Equal Earth and other equal-area methods — and then adds four words that most reports dropped: “where their sizes are critical.”
That qualifier is not a hedge. It is the whole design.
The one vote against
The United States publishes its own explanations of vote, so this one can be read whole rather than in fragments. It was delivered before the ballot by Yaryna Ferencevych, Deputy U.S. Representative to the UN Economic and Social Council. Its two substantive paragraphs:
“This resolution mocks the work and purpose of this institution. While this initiative is presented as an anodyne effort to update cartographic proportions, the United States clearly sees it cannot be separated from the much larger and more radical ideological project it belongs to – as its most vocal and committed proponents plainly and openly state.
Instead of focusing on genuine problems of international peace, prosperity, or good relations, this body is debating map projects from the 16th century, and their role in promoting reparations and ‘cognitive justice.’ Resolutions like this and the ideological agenda they promote, are barnacles on our work here, and the reason this institution is losing its credibility.”
Two things are worth saying about that, and only one of them is mine to settle.
The first is checkable. Cognitive justice is in scare quotes there, and it is the resolution’s own phrase — its preamble states that correcting these distortions “constitutes an act of cognitive justice and memorial reparation”, and it cites the African Union’s 2026–2035 reparations decade by decision number. So the objection lands on language the document really does use, in a paragraph anybody can look up. Where the statement is wrong is its setup: the resolution is not “presented as an anodyne effort” with something larger concealed behind it. It says what it is on its own face, in its preamble, several paragraphs before it asks anyone to do anything.
The second is not mine to settle. Whether that reasoning is right is a political argument, it is a real one, and it is going to be had loudly — a five-page cartography text is already being made into a proxy for something much larger. What I will say is where the argument now sits: a recorded vote, a published explanation with a name on it, and a document with numbered paragraphs. That is a better place to have it than a classroom wall with no legend on it. A projection that nobody argues about is not a projection everyone agreed to. It is one whose choice went unread.
The qualifier that keeps falling off
Here is the claim as it travelled. The Guardian reported that the Assembly “officially retired the 16th-century Mercator projection in favour of one based on the more accurate 2018 Equal Earth design”, and that the resolution called to phase out the old map. Al Jazeera, CNN, NPR and the rest ran the same shape of sentence.
The resolution retires nothing. Read its preamble:
“Recognizing that a variety of map projections have been developed over time, using different methods and preserving different cartographic properties, that no single projection can perfectly represent the curved surface of the Earth on a plane, and that each projection is therefore suited to particular purposes… and is without prejudice to the established practice with regard to the use of cartographic material for navigational purposes”
That is the Theorema Egregium in the voice of a UN resolution. Gauss proved in 1827 that a sphere’s curvature is intrinsic, so no amount of bending flattens it without stretching — which means every flat map must sacrifice area, angle, distance or direction, and no cartographer will ever be careful enough to escape it. Not a limit of technique. A theorem.
There is no undistorted map waiting to be drawn by someone more careful. There is only the question of which distortion, chosen by someone, for something.
So Equal Earth is not more accurate. Equal Earth is equal-area: it reproduces the relative sizes of things exactly, and it pays for that in shape, continuously and everywhere. Mercator kept angle and paid in area. Equal Earth keeps area and pays in angle. Neither is the true map, because there isn’t one, and operative paragraph 3 knows it — it says Equal Earth “offers a more accurate representation of the sizes of continental landmasses” and is, in its own careful words, “a relevant option”.
None of which weakens the case. Africa really is about fourteen times Greenland, a classroom Mercator really does say otherwise, and five centuries of that really did settle into how the world pictures itself. The campaign is right. It is just not right because Equal Earth is accurate. It is right because area is the property that matters for the job that map is doing, and Mercator was optimised for a different job by people crossing oceans in 1569.
Three maps that are all exactly right, and all disagree
Here is the part I did not expect when I started checking. Equal Earth is not the only equal-area world map. It is not even the only one in this news story. So I computed three of them from their own published equations — Gall–Peters, Eckert IV and Equal Earth — and measured what they do.
Every one of them encloses exactly 4π square units on the unit sphere. Every one has a local area scale of 1.000000 at every point I sampled. They are equal-area in the strict sense, with no rounding and no argument. And they look nothing like each other.
Look at Gall–Peters, the map Arno Peters made famous in 1973 and the one most people mean when they say “the fair map”. Its shape error is 2:1 at the equator — countries pulled to twice their height. Equal Earth’s is 1.35. And the equator is precisely where the continent this resolution is about happens to sit.
On Gall–Peters the indicatrix stands upright at the equator and lies flat at 60°, because the stretch swaps axes as you go north. Both are 2:1. The map is not uniformly bad in one way; it is badly wrong in opposite ways in different places, which is exactly the sort of thing a single “accuracy” score cannot tell you and a picture can.
Why the fair map was not the one they chose
Which raises the obvious question: if Peters got there in 1973, why does a 2026 resolution name a projection from 2018?
Because in March 2017 Boston Public Schools switched its classroom maps to Peters, it made news around the world, and three cartographers went looking for something better to offer and could not find one they liked. So they built it. In their own words:
The creation of this projection was motivated by a wave of news stories about Boston Public Schools switching to maps using the Peters projection.Šavrič, Jenny & Patterson, Advances in Cartography and GIScience of the ICA, 2019
Equal Earth was published in August 2018 — Bojan Šavrič, Tom Patterson and Bernhard Jenny, in the International Journal of Geographical Information Science. It is deliberately modelled on the familiar look of the Robinson projection, which is a compromise map that preserves nothing exactly, and it makes that look equal-area. The abstract is blunt about the goal: “Continental outlines are shown in a visually pleasing and balanced way.”
So the sequence runs: a theorem forecloses a perfect map; a political argument in 1973 forces a choice into the open; a school district acts on it in 2017; cartographers respond in 2018 by making the honest choice easier to live with; the African Union endorses the campaign in August 2025; and the General Assembly votes in September 2026. Nobody at any step became more accurate. They got better at choosing, and better at saying so.
By Friday evening there were already two answers
The best evidence that this is a choice rather than a correction arrived within hours of the vote, from one of the resolution’s supporters.
Speaking at the Sorbonne before the vote, France’s foreign minister Jean-Noël Barrot announced that France would abandon Mercator — and then named a different map from the one the resolution recommends. France is adopting Eckert IV, a pseudocylindrical equal-area projection from 1906. Not Equal Earth. Barrot’s phrasing for what France was moving to is the most quietly precise sentence anyone said all day: “map representations tailored to specific uses.”
Two governments, one vote, the same afternoon, two different equal-area projections. That is not a crack in the consensus. It is the consensus working correctly, because the resolution never claimed there was one right map — it claimed area is the property that ought to be preserved when size is what is at stake, and left the rest open. Eckert IV and Equal Earth are both honest answers to that. They differ by about five percent in shape error and by rather more in taste.
The paragraph nobody quoted
I read every article I could find about this vote. Not one of them quoted operative paragraph 10, which is the best thing in the document and, I think, the actual news.
“Urges Member States, international institutions and civil society organizations to explain to users the methods of cartographic projections, including their characteristics, limitations and appropriate applications, and, acknowledging that each projection serves specific cartographic purposes, to undertake awareness-raising initiatives…”
And paragraph 11(a): to “integrate the critical teaching of cartography into school curricula”.
That is not a request to hang a better map on the wall. It is a request to teach the choice — to hand children a map that says what it kept, what it dropped, and who it was drawn for.
In 1859 Nicolas Auguste Tissot worked out that you cannot remove a projection’s distortion, so you should draw it instead: a grid of ellipses across the map, each one a circle on the globe, each one showing exactly what this map did to this place. The map carries its own error bars on its face. It concedes that it is distorted everywhere and refuses to let the distortion be invisible.
Paragraph 10 is Tissot’s move, made policy, for eight billion people. Publish the indicatrix.
| As it travelled | A/80/L.104 |
|---|---|
| The UN “retired” and will “phase out” Mercator | Bans nothing. Without prejudice to navigational use; Mercator is named in a paragraph that recognizes its area distortion, not one that prohibits it |
| Equal Earth is “the more accurate” map | “a more accurate representation of the sizes” and “a relevant option”; adoption urged “where their sizes are critical” |
| A new world standard | Non-binding throughout. Encourages, invites, urges. France picked a different projection the same day |
| — not reported anywhere I could find | ¶10: explain projections’ “characteristics, limitations and appropriate applications”. ¶11(a): “critical teaching of cartography” in schools |
Being at the edge was never information about you
A globe has no edges. Every point on a sphere has exactly as much sphere around it as every other, and peripheral is a property of flat things with borders. The margin arrives with the projection — the edge of a world map is not a feature of the world, it is where somebody decided to cut.
Five centuries of one cut taught a great many people that they lived at the rim. On Friday, one hundred and sixty-four countries said out loud that the rim was a decision. They did not fix the map, because the map cannot be fixed. They did something better: they moved the argument into the open, and then asked that it be taught there.
That is what a correction looks like when the thing being corrected is a silence rather than an error.
- Not a more accurate map. No such object exists, and reaching for one concedes the argument. Equal Earth is equal-area; it pays in shape everywhere, by about 1.35× at the equator and 1.69× at 60°.
- Not Mercator’s fault. Gerardus Mercator solved a navigation problem in 1569 and solved it beautifully. The scandal was never the distortion — it was hanging his answer in a classroom without the question attached.
- Not settled by science. The mathematics says no projection is perfect; it does not say which sacrifice to make. Choosing area over shape is a judgement about what matters, and it is a good one, and it is still a judgement. The resolution is more careful about this than its own coverage.
- Not the end of the argument. Ukraine abstained over how a world map renders occupied territory. Two supporters adopted two different projections in one afternoon. Arguing in the open is the win condition, not a sign of failure.
- Not because of. Gauss proved something about surfaces. Everything here about margins and belonging is a rhyme, not a proof — down to is not because of, and nobody’s standing rests on a theorem about paper.
Go and look
The resolution is five pages and it is free to read. It takes ten minutes and it is better than every article written about it, including this one. Read the preamble especially — the paragraph beginning “Recognizing that a variety of map projections…” is a General Assembly quietly agreeing with a theorem from 1827.
The resolution. United Nations General Assembly, eightieth session, agenda item 13, A/80/L.104, “Correct the map”: rebalancing global cartographic representation and promoting equitable representation of the world’s regions, particularly Africa, dated 4 August 2026, adopted 4 September 2026. Sponsored by 55 African Member States and the Bahamas. Full text (PDF). Read in full. Every quotation from the resolution on this page is taken from that document, not from coverage of it, and the paragraph numbers are its own.
The vote. 164 in favour, 1 against (United States), 6 abstentions (Estonia, Georgia, Lithuania, Republic of Moldova, Serbia, Ukraine) — UN Meetings Coverage, GA/12779 and UN News. Dussey’s remarks, France’s adoption of Eckert IV and Barrot’s Sorbonne speech, the #CorrectTheMap petition figure and the planned Lomé implementation meeting are from The Guardian, 4 September 2026, read in full. Open: Ukraine’s stated reason for abstaining is given from summaries of the meeting record rather than from the verbatim record, which we have not read; it is characterised here, never quoted.
The United States’ explanation of vote is quoted from the primary — Yaryna Ferencevych, Deputy U.S. Representative to the UN Economic and Social Council, “Explanation of Vote Before the Vote for UNGA 80 Adoption on the Resolution to ‘Correct the Map’”, 4 September 2026, published by the United States Mission to the United Nations. The two paragraphs quoted are verbatim and consecutive; the statement’s remaining sentences are its opening attribution and its closing two lines (“We urge countries to instill common sense to this body, and fully reject this text. The United States will vote ‘no’ on this resolution.”), omitted for length rather than for content. One characterisation declined: The Guardian reports the US representative as calling the resolution “superfluous”. That word appears nowhere in the published statement, so it is not used here — and it would have understated the objection, which is substantive rather than procedural. This page reached the statement only because a reader flagged the fuller quotation; thehill.com and the Mission’s own page both refuse automated requests, and the Mission’s page was retrieved directly.
Equal Earth. Bojan Šavrič, Tom Patterson & Bernhard Jenny, “The Equal Earth map projection”, International Journal of Geographical Information Science 33(3), 454–465, published online 7 August 2018, in issue 4 March 2019, doi:10.1080/13658816.2018.1504949. The paper is paywalled and we have not read it. The description quoted — equal-area, inspired by Robinson, “continental outlines are shown in a visually pleasing and balanced way” — is from the published abstract. The Boston Public Schools motivation is quoted from the authors’ own open-access conference abstract: Šavrič, Jenny & Patterson, “The Equal Earth Projection: Distortion Characteristics, Adoption, and (Social) Media Impact”, Advances in Cartography and GIScience of the ICA 1:321 (2019), doi:10.5194/ica-abs-1-321-2019. The projection’s forward equations, used for Figure 1, are the published ones and are widely reproduced (PROJ, ArcGIS, D3).
Figure 1 is computed, and here is how, so it can be checked. Each projection’s forward equations were evaluated directly: Equal Earth with its published coefficients A₁ = 1.340264, A₂ = −0.081106, A₃ = 0.000893, A₄ = 0.003796; Eckert IV by Newton iteration on its defining equation; Gall–Peters as cylindrical equal-area with standard parallel 45°. Enclosed area was integrated numerically and comes to 12.5663–12.5664 for all three, against 4π = 12.56637. Tissot indicatrices are the singular values of the numeric Jacobian in a local east–north frame; the determinant is 1.000000 at all 35 sampled points on all three projections, which is the definition of equal-area and is the check that the drawing is right. Shape error is the ratio of the larger axis to the smaller. Panel outlines are simplified to 0.35 px, which is below the stroke width.
The theorem. Carl Friedrich Gauss, Disquisitiones generales circa superficies curvas (1827). Given from the standard mathematical statement, not read in the original Latin. Tissot’s indicatrix: Nicolas Auguste Tissot, 1859, popularised in his Mémoire (1881). The Greenland/Africa ratio near fourteen uses approximate areas of about 2.2 and 30.4 million km² and is stated as approximate.
Prior art on this site. You Cannot Flatten a Sphere (No. 44) is the argument this news walked into — the theorem, the 1569 choice, the Gall–Peters fight, Tissot’s answer, and the turn to what a single number about a person has to delete. It was published on 13 August 2026, three weeks before the vote, and nothing in it needed changing afterwards. The Lines We Drew (No. 9) holds the constructed border and who holds the pen. Not a Line (No. 21) holds the spectrum.
A rhyme, not a proof.