How to be a mathematician

In close to two years that I have been at Warwick I have learned lots of (questionably important) mathematics and one very important fact about mathematicians: They are the most prepared people in the world.

Prepared for what? Prepared for everything!

They solve problems of past, they solve problems of presence, they even solve problems of future. Just in case. We may not have quantum computers yet, but hey, we already have all these amazing algorithms the computer could run !

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Seriously now, what do mathematicians do all day long?

We solve problems and when we do, we shoot for robust solutions. For example – in order to go from Warwick to London, as a mathematician you would first spend a few years drawing the map of Europe and then(!) make the journey.

And what if I don't want to wait so long?

You see, that is exactly the point – you draw the map well before you go. It may seem completely useless for a century or two, but then it suddenly proves invaluable.

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This is the philosophy in a nutshell – and in practice the education works similarly. We have abstract modules, where we look at already created maps, so that we know they exist, when the opportunity comes. In more applied modules we then learn how to use a "map" to travel faster.

My favourite module in the former category is called Metric Spaces. Here we study worlds, where we can say what the distance between two things is. Since we do not specify what exactly the world looks like, in the future we will be able to use the "map" for every world with distance defined on it.

Now if you have a world, you can divide it into say countries. An important property that a country may or may not have, would be the following: if you are anywhere in the country, then you can make a short step in any direction and you still stay in the country(1).
You might then want to know, whether this property is preserved say under joining two countries into a bigger one and so on.

A thorough understanding of "maps" turns out to be useful when you travel. You might be interested in the shortest path between Warwick and London, knowing how to avoid traffic or what the optimal distribution of postcards and souvenirs among your relatives is.

In fact, these patterns reappear in the real world in more serious settings (for example matching doctors and hospitals) and we study algorithms that have been developed so that a computer (not necessarily a quantum one) can solve the problem when the number of options is too large for humans.

Emphasis is given on understanding the ideas behind the algorithm, so that we could tailor it if necessary - and it is a lot of fun when you get it right (and apparently you can make money too).

This is about it for the mathematical part, there are other aspects of being a mathematician, but I think I had better save that for next time.

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(1) This actually does not necessarily mean the country is infinitely large.