Mapmatics: How We Navigate the World Through Numbers

by Paulina Rowińska

How does a delivery driver distribute hundreds of packages in a single working day? Why does remote Alaska have such a large airport? Where should we look for elusive serial killers? The answers lie in the crucial connection between maps and maths.

In Mapmatics, Dr Paulina Rowińska embarks on a fascinating journey to discover the mathematical foundations of cartography and cartographical influences on mathematics. From a sixteenth-century map that remains an indispensable navigation tool despite emphasizing the North-South divide, and maps of voting districts that can empower or silence whole communities, to public transport maps that both guide and mislead passengers, she reveals how maps and maths shape not only our sense of space and time but also our worldview.

Through entertaining stories, surprising real-world examples and a cast of unforgettable characters, Mapmatics helps us to appreciate the mathematical methods and ideas behind maps. And, by illuminating how our world works, leaves us better equipped to understand and look after it.

Genres: Nonfiction, Science, Mathematics, Geography, History, Nature, Maps

385 pages, Kindle Edition

Published June 6, 2024

About the author

Hi! I’m Paulina Rowińska, a writer, mathematician, and science communicator based in Cambridge, MA. I’m the author of the popular science book 'Mapmatics: How We Navigate the World Through Numbers'.

During my PhD in mathematics and statistics at Imperial College London, I realized I preferred communicating science to conducting research. I’ve shared the beauty and relevance of mathematics with diverse audiences through newspaper articles, radio shows, and TV programs. I also created interactive math and data science content for Brilliant, an educational company.

In September 2024, I joined the Graduate Program in Science Writing at MIT. I aim to continue exploring the role of mathematics in our daily lives while also covering topics like mental health and environmental issues.

When I’m not writing, you’ll probably find me devouring a book from my ever-growing to-be-read pile, learning a new language, or enjoying a cheesy musical.

Reviews

[Marc · Rating 3 out of 5]

It was a decent science history book, but I grew tired of the constant woke comments. Lots of snarky racist, sexist, exploitive and orientation related comments. Unrelated to the topic at hand other than to bring in "enlightened" woke ideology to the subject. At one point she added a section on a female scientist that "might" have helped a male scientist make a discovery and didn't get credited for helping. I thought it was odd for a historian to include that without any evidence just because she hoped it was true.

First half of the book was better than the second half.

[Mehtap exotiquetv · Rating 3 out of 5]

"**Mapmatics**" von Paulina Rowinska bietet einen interessanten Einblick in die Welt der Kartografie und der mathematischen Modelle, die dahinterstehen. Rowinska schafft es, komplexe Konzepte auf eine zugängliche Weise zu vermitteln, und ich fand es spannend, mehr über die theoretischen Grundlagen zu erfahren, die Karten zu präzisen und nützlichen Werkzeugen machen.

Allerdings hätte ich mir mehr technische Tiefe gewünscht. Die Erklärungen bleiben oft an der Oberfläche, und gerade bei einem so spezialisierten Thema hätte ich mir detailliertere Erklärungen und komplexere Beispiele erhofft. Die Autorin hätte die Chance nutzen können, tiefer in die mathematischen und algorithmischen Aspekte einzutauchen, um den Lesern ein umfassenderes Verständnis zu vermitteln.

Insgesamt ist "Mapmatics" ein gutes Buch für Leser, die einen Einstieg in das Thema suchen, aber für diejenigen, die eine tiefere Auseinandersetzung mit der Materie erwarten, könnte es etwas enttäuschend sein. Daher gebe ich 3 Sterne.

[jlreadstoperpetuity · Rating 5 out of 5]

I didn't realize I'd love reading maps and math together. Reiterating, MATH. Numbers and I didn't jive in Uni nor at work 🙃 but the author really did simplify the approach and the theories described were so easy to understand. I didn't even realize I browsed through the book from start to finish in a day!

[Buchdoktor · Rating 5 out of 5]

Der Begriff Karte weckt auch heute noch Erinnerungen an die Landkarte, die in der Schule in unserem Klassenzimmer hing, aber auch an Stadtpläne oder Karten von U-Bahn-Netzen auf Papier. Paulina Rowińska schlägt einen weiten Bogen von mathematischen Grundlagen, die die Abbildung unseres dreidimensionalen Planeten auf der Ebene einer Papierbahn erfordert, bis zu ihrer Anwendung in Google-Kartierung und Autonomem Fahren in der Gegenwart. Kartografie dient heute der Erforschung von Seuchen, der Erstellung tagesaktueller Routen (Paketzusteller, Rettungsdienst), Planung von Schaltanlagen, der Suche nach Schiffswracks und nicht zuletzt der Verfolgung von Serientätern und damit der Prävention von Straftaten. Das Gerrymandering in den USA (willkürliche Einteilung von Wahlbezirken zur Manipulation von Wahlen), und die Planung von Schulbezirken (mit ihren Auswirkungen auf die Qualität von Bildung) zeigen uns den immens politischen Einfluss, den die Kooperation von Mathematik und Kartografie erzielen kann. Kartografie findet sich im Verhalten von Ameisen ebenso wie durch kognitive Karten im menschlichen Gehirn. Paulina Rowińska legt übrigens Wert darauf, dass geschlechtsspezifische Gehirntätigkeit nicht angeboren ist, sondern anerzogen.

Von der Mercator-Projektion mit ihrem eurozentrischen Weltbild haben Interessierte sicher gehört, nicht weniger interessant fand ich allerdings James I. Craigs Modell, die Welt einmal um Mekka als Zentrum herum zu kartieren. Breiten Raum nimmt das Thema Linien ein. Weder muss der kürzeste Weg zwischen zwei Punkten der schnellste sein, noch geben U-Bahn-Pläne reale Entfernungen zwischen zwei Haltestellen an. Einige Großstädte haben auf diese banale Erkenntnis inzwischen mit eigenen Plänen für Fußgänger reagiert.

Die Autorin nennt Expert:innen, die durch interdisziplinäres Denken brillierten, wie den kanadischen Kriminologen Kim Rossmo, den Arzt John Snow und seine Choleraforschung auf dem Londoner Stadtplan, die Seismologin Inge Lehmann, die noch im Alter von 99 Jahren publizierte, und die Geologin und Mathematikerin Marie Tharp, die sich um die Meeresbodenkartierung verdient machte.

Positiv ist mir die sprachliche Präzision aufgefallen, mit der Rowińska unterscheidet zwischen Ideengebern, Förderern (ohne eine streng auf Gleichberechtigung bedachte Lehrerin wäre die 1888 geborene Inge Lehmann vermutlich kaum über die 6. Volksschulklasse hinaus gelangt) und denen, die am Ende Ruhm und Karriere beanspruchen konnten. Beispiele für ihre differenzierende Sicht sind die Idee der gleichwertigen Weltkarte, an der mehrere Personen beteiligt waren, aber auch der durchaus umstrittene John Snow, der als begnadeter Storyteller eine Theorie vermarktete, die zuvor Vertiefung erfordert hätte.

Da am Anfang von Fantasy-Romanen im Kopf der Autor:innen häufig „die Karte stand“ (Verrückt nach Karten: Geniale Geschichten von fantastischen Ländern), habe ich mich als Romanleserin von Rowińskas interdisziplinärem Blick auf Kartografie und Mathematik sofort fesseln lassen. Bis auf das spezifisch amerikanische Gerrymandering ein hochinteressantes, vielfältiges Buch, das die Anwendung von Wissenschaft zeigt – und keinen Mathe-LK voraussetzt.

[Peeter Talvistu · Rating 4 out of 5]

I think it is more of a 4.5 but doesn't reach quite the level of marking it as a 5.

So the book cover maps and mathematics, focusing on their intersection. Sometimes one wins out, sometimes the other. The really mathematical parts were certainly quite complicated and I'm not sure I understood all of them completely. The really mappy (cartographical) parts were, however, sometimes too light on the maths. I think the overall selection of themes was somewhat haphazard and I would probably have preferred a longer time spent on the earlier history. The chapter on gerrymandering was definitely eye-opening. I would definitely recommend this book both to geography/math nerds as well as complete ignoramuses on these matters. The fact, that the author comes from Poland, makes it especially close to heart!

[Lara · Rating 5 out of 5]

Loved it! This was a spontaneous pick in the English section of my local bookstore as the title immediately resonated with me. The author's fascination with the subject shines through, very digestible, well written and filled with interesting anecdotes while still being precise (or at least makes the impression as I don't have the in-depth background on the subject) when it comes to the mathematical aspects.

[Anne Ulrich · Rating 5 out of 5]

This is one of the best books I've read in a long time. The prose is very engaging and the author tells good stories and a lot of them. I really connected with her discussion of gerrymandering in particular--a super important topic that's heavily mathematical on analysis. Would strongly recommend!

[Laurie · Rating 4 out of 5]

maps are so cool ?!

[Javi Hernández Castro · Rating 4 out of 5]

Very interesting book that discovers obvious and not so obvious connections between maps and mathematics.

[Jerry Oconnor · Rating 3 out of 5]

Interesting narrative but math details and overall technical/mathematical specifics are way too heavy.

[sbs transit · Rating 5 out of 5]

#nsreads 70

After a lot of heavier works lately really appreciated this innocent wide-eyed dive into cartography as a comfort read. Apart from being the first popular science book I actually learnt something from in a long time, I appreciated the editorial team doing their homework to offer up refreshing human interest updates to commonly held myths regarding famous figures in math.

[Jim Gise · Rating 5 out of 5]

Straighten your pocket protector and firmly affix your propeller hat for this delightfully nerdy romp through cosines, Mercator projections, four color theorems, Gaussian curvatures and gerrymandering cracking and packing.

[Jeff Lochhead · Rating 4 out of 5]

My annual summer math book read combined two things I really enjoy…maps and mathematics. It didn’t disappoint.

[Nikolas Mavreas]

The boom in popular science books has been going strong for decades now. The mathematics of maps is the latest topic to be mined from dusty textbooks for our entertainment. Mapmatics: A Mathematician’s Guide To Navigating The World is the last in the long line of the publishing world’s attempts to make everyone’s dreaded subject approachable. The mathematician of the subtitle is Paulina Rowinska, an aspiring science communicator with a PhD in mathematics and statistics from Imperial College London, whose “2017 Tedx talk ‘Let’s Have A Math Party!’ explained that math is all around us.” This is her first book.

Read the rest of my review on Open Letters:
https://openlettersreview.com/posts/m...

[Brian Clegg · Rating 3 out of 5]

Popular mathematics can be hard to make engaging. Though some topics (such as infinity or zero) can be made interesting in isolation, usually it's best if it can be tied to something more concrete, and what Paulina Rowińska does here is to bring us the story of maps and the the maths behind them. Although Rowińska starts with Mercator and other early projections, it's not really a history of mapping - for example, there is no mention of Roger Bacon's description of using coordinates for mapping - instead the focus is the twin mathematical bases of mapping, geometry and trigonometry before moving onto other maths connections from fractals and operational research to Bayes' theorem.

We start with the nature of a curved world and the compromises that need to be made to translate a 3D surface onto a sheet of paper - compromises that are rarely stated and make a huge difference to the look of the map. This is mostly very engaging, except when it spends too long on geometry and trigonometry. Then there's a dive into fractals, based on Richardson's observations that country border lengths often vary as seen from either side of the border and Mandelbrot's formative 'How long is the coast of Britain?', straying into fractal dimensions. We then move onto the way maps need not be spatial representation - the classic example being the London tube map. Things get even more abstract as we move from maps to graphs (the node and connector type, not charts) and some well known mapping problems like travelling salesman and the four colour theorem. US gerrymandering gets its own chapter, as does Snow's cholera map and other such lifesaving mapping, before finally looking at what can just about be called mapping in terms of identifying the internal structure of the planet.

There are some great stories in here, but for me, unfortunately, once you've got over the genuinely interesting stuff about the difficulties of representing 3D geometry on a 2D map, a lot of the early mathematical basis is, frankly, a bit dull. It's no surprise that geometry and trigonometry figure large (the words do, after all, mean 'earth measuring' and 'triangle measuring'), but I always found them the most tedious aspect of maths. Mostly Rowińska avoids using too many mathematical formulations, but they do creep in quite regularly here. Later on we do get to more interesting mathematical areas such as topology and graph theory, but in these case the reverse happens: the maths isn't given enough depth to really get a grip of it - we might have been better with fewer topics and more detail once past the basics of projection.

In the first section, there's quite a lot about how the Mercator projection makes southern countries look smaller than they are in area, and northern states bigger, which some observers apparently take as a sort of colonial put down. This seems bizarre, as the point of the maps was initially navigation, but also it seems perfectly reasonable that early map makers would have seen things from their own country as a starting point. I presume map makers in the same period from southern countries would have seen things from their own viewpoint too, but this isn't explored.

It was particularly disappointed by the relative lack of illustrations, which I would have thought were essential for a book about maps. There are some, but, for example, when talking about the genuine limitations of Mercator and how other projections allow different types of information to be taken from the map, there are far too few illustrations to show us what those different projections would look like.

I liked what this book is trying to do, but I'm afraid I didn't particularly enjoy reading it.

[Mauricio · Rating 3 out of 5]

Chapter 1 was quite a quite entertaining read focusing on how the shape of the earth not only came to be as round but also in the dilemma of between the French and British on which way the planet was deformed from perfect sphere either like an egg or like a mandarin orange.

Chapter 2 was also quite good on how the mercator map was established, the rhumb line rule and the reasons why it gained prominence in those times. The puzzle of finding places on the planet where you can go 1 mile south, then 1 mile east then 1 mile north (grid cardinal directions) and be back where you started. The book only mentions 1 such spot, the north pole, however there is an infinity of such places. You can consider all the places near the south pole that are 1 mile north of the closed curve created by a plane parallel to the equator cutting the surface of the earth and having a length of 1/k miles. Where k is a positive integer. All those points also count. . Until here the book was fantastic.

Then came Chapter 3 and how the coastlines are really difficult to measure because of the minute details that have to be measured. The book insists that due to this the coastlines are impossible to measure since the coastlines behave like fractals. This is just NOT true. Sure, it tells a more interesting story for the author to shape the book, but the coastlines are NOT infinite. You could have mentioned how the measure of a coastline would converge and although theoretically possible to measure the coastlines, it is not feasible for humans. Then you could introduce the idea that this convergence is not guaranteed. Seeing something that is not only badly explained but wrong makes me wonder what other sections the author sacrifices accuracy for the purpose of telling a nicer story.

Chapter 4 went back to being interesting and informational. Chapter 5 is your obligatory Königsberg bridges insert for a math book, but at least it serves its purpose for quite a nice overview of the 4-color theorem and how mathematicians dealt with disliking computer-based proofs.

Chapters 6, 7 and 8 barely have any mathematical topics involved in them. Chapter 6 had this but to a lesser degree, however I was quite familiar with the topic and just when it seemed like it was about to talk about math, it just changed the subject.

I would recommend this book however it is just not for me, and I review books for myself.

[Richard Thompson · Rating 4 out of 5]

I have loved maps since I was old enough to know what a map was. As a child, I was stamp collector and the first thing that I would always do when I got a stamp from a country that I did not know was to find it on a map. In my days, the British Commonwealth was the best for this because its territories were all over the world and had English language legends on the stamps. In the era before videogames, I had a solo game that I would play with Play Doh. I would mix two colors together, preferably green and brown, but any two colors would do, and then I would smash the ball down on a big coffee table book and mold it into mountains, valleys, canyons, plains and bays. Once my blob began to look like an island, I would get a pin and draw borders, which I would then redraw as I imagined my countries evolving over time. And the mathematics of maps has always interested me. There is even a video of me discussing how the Seven Bridges of Koenigsberg problem relates to a sewing project that I was doing with my wife. https://www.instagram.com/p/C5wS5Y3yBLl/

So this book looked like it was going to be great for me, and it didn't disappoint. It went over a lot of familiar ground, but there was plenty of material that was new for me. Not too hard and not too easy. It covers a lot of topics from the Koenigsberg Bridge problem to the travelling salesman problem to the difficulty in measuring irregular borders, to different kinds of projections of the globe onto a flat map that each have their own kind of distortion, and then it goes on to discuss maps used for legislative redistricting and school districts, maps used in epidemiology and mapping of the ocean floor. In each area there is a discussion of how math is used to solve mapping problems, but it's never more complicated than basic trigonometry which you don't even need to understand beyond a basic idea of how triangulation works to measure distance.

[Florian · Rating 3 out of 5]

3.5/5
Very readable for the supposedly dense subject matter at hand. However, also surprisingly uncomplex for what I expected. I thought the book was going to dive deeper in different kinds of maps. Instead, the author chose to talk about a lot of topics, but none of them in depth (which is a valid strategy, just not something that I expected).
A bummer, because I didn't think most of them to be that interesting. The first half of the book gave me what I expected, that was, information on how maps are created, how (mental) maps are used to get from A to B, how they shape our preception of certain countries, etc.. But the latter half fell a little short. Sure, it still had to do with maps and mathematics but it was somehow more disconnected and did not feel as relevant to what I hoped to get out of this book.

Something another reviewer pointed and that I wholeheartedly agree with is the lack of, well, maps in there. Or visual representations in general. Sure, there are a few to visualize the key concepts in each chapter, but I wanted to see a more diverse range of map projections, learn more about the interior of the earth and actually also see it.

Ultimately, it felt a little too targeted at a broad audience for my taste. I would've liked to see more of the nitty-gritty math stuff, which was at times also not explained in a way to make it immediately graspable to me, even if I already knew the concept. But that could be on me and how I understand things. Still, it feels hard to think of a target audience for this. Everyone that could be convinced to read a book about maps would be nerdy enough for this book to not go into depth enough and everyone else cannot be convinced to read a book about maps in the first place.

[Sky · Rating 4 out of 5]

Rarest of science books - educational, entertaining, enlightening. Ms Rowinska manages to find the fine balance between informative, factual and writing with an incredible ease.
The book focuses on the different kinds of maps, their advantages, their limitations and their deceptions. The author always gives a historical and mathematical background, keeping the maths to the necessary minimum ( and if readers are scared even by that sliver of Maths, they do not need to understand the details just the general concept). I was astonished to learn all the ways Maths shapes the science of cartography and the variety of maps and how they are used.
I applaud Ms Rowinska for giving due to scientists (especially women) and folks who have been creating maps long before Europeans, for pointing out how maps shape our world view, extremely consequential elections and for showing that Maths could be super cool.
I wish the publishers have worked with a higher budget and included some maps ( especially the obscure ones) - it would have been a delight to see them in colour as well. Hopefully this edition will be successful enough to guarantee a second one with the mentioned additions.
Cannot wait to see what her next book will be. I certainly wish her success and could recommend the book to anyone who wants to learn more about the world.

[Marius Oberberger · Rating 5 out of 5]

The book combines elements of maps, mathematics and science history, grouped around eight chapters, each with some specific examples. I very much liked the accessible tone of this popular science book always connecting mathematical examples to specific cases of application.
In the end, I learned the basic principles behind various topics, such as the Mercator Projection, measuring, cards of metro networks, epidemic spread and analyzing the earth's core or the submarine ground. The author very often explains also the history of this knowledge, pinpointing at the influence of neglected (mostly female) contributors, which adds a historic and social dimension to the narrative.
I assume that mathematicians will find the book superficial, and you won't delve into the depths of one of the various subjects, but if you're in general interested in understanding various kinds of maps and the basics of the math behind it, the book offers a great read. Sometimes more illustrations would be useful and simplify the understanding (a bit ironic because it's about maps and projections), but this doesn't damage overall.

[Adam Duncan · Rating 5 out of 5]

Such an awesome book! As someone who is equal parts fascinated and also bewilderingly lost by complex mathematical concepts, this book was the perfect read. So many concepts were presented in a way that make perfect sense while reading it, while letting you know there was so much more to know. It led me to many rabbit-hole searches online between chapters (from trawling through different world maps to spending almost a whole day drawing out voronoi diagrams). If all nonfiction writers wrote like Rowińska, we'd be as addicted to learning as this nerdy primary teacher dreams the world could be.

A highly recommended read for anyone with an interest in any of the related subjects covered in this entertaining and informative text. A great quote from the end of the book summarises the purpose of the book perfectly: "Mapping goes beyond filling the gaps in the atlases. It's hard to care for something we don't know, so mapping is an act of love for our planet - and ourselves."

[DW Rowlands · Rating 4 out of 5]

A quite-interesting collection of short discussions of topics related to the history and math of maps. Some of the sections were more mathematical than others, but they were all fairly interesting, and I was particularly interested in learning about the history of map projections and the like. It was also worth reading the discussion of why the story of John Snow and the Broad Street Pump is a bit exaggerated in terms of the actual science and analysis he did...but still important because he was an effective scientific story-teller, and that was important to convincing people to take the idea that cholera and other diseases were water-borne seriously, even if he gets more than his share of the credit for the discoveries.

[Chris Geggis · Rating 4 out of 5]

I really enjoyed this book, but I am going to get persnickety about this one particular sentence...

"As Marie Tharp discovered, volcanoes appear where tectonic plates meet, but this doesn’t explain regions such as Yellowstone, Hawaii, or Iceland, which are nowhere near such a boundary."

Rowińska, Paulina. Mapmatics: A Mathematician's Guide to Navigating the World (p. 223). Harvard University Press. Kindle Edition.

Iceland is most certainly at the boundary of the North American plate and the Eurasian plate. Many sources will confirm that, and I've been to some of the specific areas in Iceland where the country of Iceland advertises that these plates meet.

[Ali · Rating 4 out of 5]

A series of essays dealing with how we map our environment, the wonderfully titled Mapmatics takes a surprisingly broad ranging approach to the topic. Rowińska starts with possibly the best chapter, dealing with the history of projections. From there, she leaps into a range of topics from how we have mapped the ocean floor, to epidemiological mapping, to the technology behind parcel deliveries. There is a light sprinkling of math, but the emphasis here is on storytelling. As a result, everything really sings.

[Will Brown · Rating 2 out of 5]

This book had an opportunity to be great, but it unfortunately failed.

The author constantly felt the need to inject woke, thought-terminating clichés. It really ruined the vibe of the book. I kept thinking I was in 2020 again!

The math covered on various topics was quite simple, but that’s to be expected.

Giving it two stars because there were some interesting chapters, such as the one on seismology and seafloor-mapping.

Overall, it was a book that can be enjoyed if you work very hard to ignore the repetitive, unnecessary “wokeisms.”

[Pritesh · Rating 4 out of 5]

Solid book writing style wise i really enjoyed reading most of the book there were a couple of occasion where I felt the diagrams needed more explaining such as the layered shading one on maps and maybe parts that I felt could be explored more like last mile delivery mention in contrast to gerrymandering chapter I felt was too lengthy. I really enjoyed the anecdote used about misplaced headphones to explain Bayes theorem in such a relatable way succinctly really stands out to me as a reason I’ll certainly keep an eye out for more books by Paulina

[Chris Aylott · Rating 4 out of 5]

Highly readable survey of the mathematics lying under the surface of maps and studies of geography. Rowińska excels at making complex concepts understandable, especially with helpful graphs. The history of science is also strong, and I was surprised to learn that concepts like plate tectonics that I had studied in school were wild theories just a few years earlier. My one quibble is that she doesn't reproduce enough of the maps she's discussing, likely due to budget or rights issues.

[Mick de Waart · Rating 3 out of 5]

This book was well-written and had some great parts but overall I don’t really feel like a learned a lot of new things. It feels to me like depth of content was sacrificed to keep it readable for a wide audience. Although I doubt I would’ve understood everything if Rowińska would have gone in depth, I feel like it would have made the book as a whole more interesting for the extra parts that I would have understood.

Definitely not a bad book, but not a great book either in my opinion.

[Alb85 · Rating 3 out of 5]

“Una volta che lo avremo afferrato, il nesso fra matematica e cartografia sarà impossibile da ignorare e ci aiuterà a comprendere come funziona il mondo.” Paulina Rowinska

Si parla delle proiezioni per creare le mappe, di frattali, delle mappe distorte della metro di Londra, del problema del commesso viaggiatore, del teorema dei quattro colori, della famosa mappa delle morti da colera di Londra e di molto altro.

Libro che parla della matematica applicata alla cartografia. Non ho amato la forma del libro, con troppi aneddoti personali dell’autrice. Sul contenuto ho trovato pochi ambiti che non conoscevo. Alla lunga mi ha un po' annoiato.

[Carter P · Rating 3 out of 5]

Enjoyed this as my friends might suspect. Picked up because I love maps and geography, however I haven't taken a math class since 2018. Lots of the math went over my head but I definitely enjoyed the read. Super academic but the author had great style and even threw in jokes (my fav being the reference to Shrek). Took me a hot sec to finish and I definitely enjoyed some chapters more than others.