Applied maths and pure maths are both exciting in different ways.
Pure maths is exciting because you get a feeling of knowing what’s “really” going on. It feels incredibly satisfying to come up with a more general type of structure than the one you started with, and realizing that when you look at the problem from the new lens you’ve created, it turns into putty in our hands. Another thing I love about pure maths i the sense of certainty. I feel like a truly know the results I have learned. Because so much emphasis is put on n applied a lot of the time you have to lean on approximations, and results which we know work because they work in the lab, but we have no mathematical understanding of why. Pure maths on the other hand, eschews this, as every result follows perfectly logically from that last, tracing all the way back to the axioms of your system, which I think of not as immutable logical statements, but as rules to a game, which are to be adjusted depending on what game you want to play. Applied maths on the other hand has to reference back to the real world.
On the other hand, referencing the real world is exactly what makes applied maths exciting. It has the same satisfying line by line logical process as pure maths, but with the added plus that every term in every equation means something in the real world. This means that you can always take a step back, and think about what the maths you are working about says about the real world. While the goal of applied maths is to use maths to learn about the world, it also works the other way around, whenever you are stumped about a problem you can ask yourself what you would expect would happen if you were to try it with real objects, or by running physical experiments. Either way, the two-way street between the mathematics and the real-life problem is deeply satisfying, and the end result of learning something about the living, breathing physical world is deeply satisfying, whereas with triumphs in pure mathematics, the repercussions are often less clear.
Both sides have real charm, and I can’t wait to explore them more.
Alex Savvinos was a recipient of a 2018/19 AMSI Vacation Research Scholarship.