When we think about a map, we don't really consider how much mathematics there is behind it, and I mean both to make a map, but also to read a map. That's how we get fooled by maps. We don't understand maps fully without understanding the mathematics behind it. My main argument is that we should understand math to understand maps, and from many different angles. So many different areas of math.

If you go to a city, on a subway, and you trust the subway map to understand how far the two stations are, you might be very wrong. The subway map does not care about distances, and it's actually a big part of mathematics that works similarly, topology, and this is a topological map. Sometimes we don't care about distances, or the exact directions, we just care about the connections, right? There's a reason these maps are constructed this way, because otherwise they would be useless. It would be just too much going on.

But if you were to walk in New York City or London using this kind of a map, it might be tricky. It's a simple mathematical concept, but actually many people still get fooled by these maps.

When you look at a map, you have to understand who made it, and why, and what were they thinking. They had to make some choices. There's no perfect map. To make a perfect map, you just have to take the globe, and still there will be some simplifications. So, you need to understand what is correct in this map, what is perfect in some way, but there are also some distortions. And actually, mathematically, we know that when we make a map, we have to have distortions. It's impossible to make a perfect map.

With the subway map example, we have to understand that what the author kept are connections, and also the order of stations. But everything else, basically, is gone. The distances are gone, the directions are gone, the angles are gone. But we need to know it. Maybe this example is kind of natural, although I still think I was fooled by the subway map in London once, or twice. But there are many trickier examples where you can show the same problem.

There are many examples in my book about the Cold War. I show Russia and United States on very different maps, and sometimes it seems that they are very far away from each other. Sometimes it seems they're right next to each other, and you can tell different stories, and sell different narratives, using these two different maps. Again, they're both useful, it's just that if you don't know how they work, you might misunderstand, or understand just one part of the story.

Many people are aware that if you look at a graph, maybe you should consider what's in this graph. Well, maps, I think, we take for granted. When we use the word ‘manipulate,’ people often think it's some bad person trying to manipulate what we think, which absolutely happens with maps. But there's also the point that we cannot show everything. So even if you want to show a particular thing, you have to make some simplifications.

When you develop a map, you only want to show the information that's necessary and useful. In statistics, for example, the worst plots I've seen are the ones that are trying to show everything. You have colors, shapes, different sizes lines, and in the end, I'm like, well, what am I looking at? Maybe the person wanted to show as much as possible, but in the end, you are not telling the story. It's the same for maps. When you get on a subway, you are not driving the subway. You just need to know that you get on this line, you have to get out at the other station, and that's all you need to know. You need to know what's connected, what's not, and in which order. If you were to drive above the ground, that's a different story. Then you might also consider the distance, right? So then you need a different map.

That's why you can have two people making a map of the same thing with the same purpose, but they will look different.

I'm a mathematician by training. I have a PhD in math. And, I've always really loved maps. I loved geography as a kid. I spent a lot of time with maps, and honestly, at some point in 2020, I was thinking about how we transfer the globe onto a flat map. I knew how more or less they work, but I just wanted to read more. I couldn't find a good book about it. Then I started thinking about what other math comes into maps, because I just mentioned two very different examples, like projecting the world onto a flat piece of paper, and subway maps–very different ideas. I started thinking about all these concepts that come into play when it comes to maps. There was no book about it. That’s why I decided to write one.

The book has 10 chapters, and each considers different mathematical concept and I'm sure I didn't include many things that I'm not even aware of. I want to bring awareness to the fact that there's something we have to consider when it comes to maps, but also it's another of these sneaky ways of showing that math matters, and that math is important, but also is interesting. When you look at the map, we all use maps every day, pretty much. And when you open Google Maps on your phone, you don't think about math. But maybe it's worth thinking about. It's worth thinking about what happens when we zoom in and out, how this map is made. My point was, you don't need to know the equations, you don't need to know the exact theorem, you don't need to be a mathematician, but just being aware that there is something behind it. That’s what I want people to know.