My school, the United World College in Mostar, is a very beautiful place to study in. It is such a pleasure to be here that my most used verb is “amazing”: pronounced, of course, in a thick Venezuelan accent.
Something that is baffling about our campus is that it does not exist as an unit. Rather than being shut in a single physical location, our residences and buildings are all over Mostar: in fact, it takes 25 minutes to get from the easternmost residence, Mejdan, to the westernmost, Novi Sušac.
This means that we are contributing to unite a little bit more the still-fractionated city of Mostar: however, we do not really see this change in our everyday lives. The most obvious consequence of this is that we walk a lot.
A week in UWC Mostar is enough to make your ankles bleed and your step counter explode. A good portion of those steps are curiously used to cross bridges.
Mostar is full of bridges. Its name was taken from “mostari”, which means “guardiants of the bridge”, and every single road leads to the ever-present Stari Most, “the Old Bridge”. Even the coat of arms of the city makes reference to the Old Bridge, and its rebuilding in 2003 is a landmark of the healing of the city after the tragic war that struck it in the 90s.
And bridges, of course, are very important. Engineers build them to connect people, economies and cultures: the rest of us also struggle with bridges. The simple act of reading a book, for example, is building a bridge from the unknown to the known.
Almost every thing we do can be related to bridges in some sense. When we meet a new person, we build a bridge between their world and ours. When we think before doing any action, we build a bridge between civilization and primitiveness.
Every single second we spend alive, we are building bridges.
Leonhard Euler was a very brilliant man that liked to take a look at things. Whether they were comparatively obscure curiosities about infinitesimal calculus or simply the development of the mathematical notation that we use today, Euler was a very curious man.
Of course, such a burning curiosity ended up leading him to make an observation about an element present in our everyday lives: bridges. While looking at the streets of Königsberg (now Kaliningrad), he noticed that the city was located in both sides of the Pregel river and in two islands located there, Kneiphof and Lomse.
This layout of the 18th century Königsberg was all put together by seven bridges: could it be possible to take a walk around the whole city by passing through each bridge a single time?
The short answer is no. By trying to solve this problem, often referred to as the Seven Bridges of Königsberg, he ended up setting the ground for two brand-new fields of mathematics to be developed: graph theory and topology.
Euler realized all of this by asking questions about his environment and trying to answer them rigorously. Quite literally, he built a bridge to a new area of knowledge by looking at bridges.
However, was Euler trying to develop a branch of mathematics every single time he crossed a bridge? We cannot know for sure if this was the case, but I would argue for the opposite.
Anyways, Euler was not an average person: his works are so many and so complex that we haven’t studied them all yet. But, as far as we know, he developed the grounds of graph theory by just looking at bridges.
How many people had passed those seven bridges before him? Certainly, a lot: at the moment Euler developed his theories, the population was of around 30.000 persons.
Thirty thousand people who needed to cross those bridges back and forth frequently. Thirty thousand people that did not realize that something might be hiding underneath those structures: thirty thousand people that certainly did not envision the reason why are we still talking about those bridges three centuries after.
And Euler just asked questions about his surroundings. Here, at the United World College in Mostar, we have the need to walk through many streets everyday to make it to school. In fact, almost every single resident of a city has to streetwalk a little to keep up with their urban lifes.
How many strange problems with great solutions might be hidden in the streets that separate Mejdan from Novi Sušac? How many knowledge treasures are patiently waiting to be unearthed from those walks?
No one can tell for sure, but I can assure you that we can learn something from walks, whether they be to our residences, our jobs, or our own houses. We just need to be curious and inquisitive just for the sake of it.
After all, neither Euler nor Königsberg knew that the Seven Bridges were going to be the birthplace of new maths. Maybe every other bridge in the world is hiding similar secrets.
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