The first intimation I had that maps involved mathematics was when I looked up a map projection and came face to face with the equation that generated it. Math was never my strongest subject, so it’s probably for the best that I never went into cartography. Especially since it turns out that there’s a lot more math hidden behind the maps we use on a daily basis than you might think, a point demonstrated in detail by Paulina Rowińska’s book, Mapmatics, which came out in June from Picador in the U.K. and from Belknap in the U.S. in September.
Cartographic problems are often mathematical problems: Gauss’s Remarkable Theorem demonstrates that a flat projection of a round globe must necessarily add distortion. Surveying by triangulation is simple trigonometry. The coastline paradox, whereby the length of a coastline depends on the scale at which it’s measured, is because the coastline is fractal. Real-world navigational problems can be solved via topology and graph theory, algorithms and heuristics. The takeaway from this book is these things are math, and that math is at the heart of so much of this.
Rowińska is a mathematician and science writer, and she very much approaches her subject from the math side of things. Making the subject accessible to non-mathematicians is no small challenge, especially when moving to subjects that, while absolutely part of the discipline of mathematics, don’t obviously code as such to normies. Graph theory, number theory, probability density function and topology make their appearances. (I confess to being surprised at the omission of GPS, but now that I think about it, GPS is really about timekeeping and physics.) No less a challenge is finding the balance between explaining the mathematical concepts and explaining how they apply to mapping, and doing so in a way that doesn’t completely lose the plot and turn the whole thing into a math textbook with cartographic examples.
On balance I think Rowińska mostly succeeds: there were plenty of points where the math was still esoteric to me, but I still got that, yes, this was math, and here’s what it does in these cases. As the book progresses the math gets a bit more remote from popular understanding, and the map side of things is less about maps than the data being mapped, but even then the examples are absolutely real-world and relatable (gerrymandering, disease mapping), and there are plenty of a-ha moments coming from the math behind familiar puzzles like the travelling salesman problem and the four-colour theorem.
I received an electronic review copy from the publisher.
Related: Map Books of 2024.
Mapmatics
by Paulina Rowińska
Picador, 6 Jun 2024 (UK) | Belknap, 17 Sep 2024 (US)
Amazon (Canada, UK) | Bookshop