The wonderful world of mathematics

At the Wolves LUG meeting last night, we got into a discussion of mathematics (see, I told you these meetings were exciting). Jono took the Luddite position that maths was extremely boring and of no relevance to the real world, a position that I imagine he’s not the only person to hold. So I tried convincing him that maths was interesting and had a point, but didn’t get very far. The attempt to demonstrate its interestingness was by relating a couple of maths anecdotes. Firstly, Euler’s formula, e^iπ^ + 1 = 0, which relates the five most fundamental constants in mathematics and is the clearest evidence I know of of some kind of underlying order in the universe, since e and π are both transcendental and i is imaginary and yet they combine to make 1. Jono liked that one. Secondly, I talked about Hilbert’s Hotel, since I think stuff to do with infinities is fascinating and the idea of a full hotel being able to accommodate one new guest, an infinite number of new guests, and an infinite number of coaches each with an infinite number of guests on board is just mind-blowing. That one didn’t go down too well, so I abandoned my third attempt, which was to talk about the difference between aleph-null and the continuum (which is handy since I can’t remember how to prove there is such a difference without Cantor’s diagonal proof and you need pen and paper to demonstrate that). So, I throw the question open. Since I’ve had snarky maths comments every year when I play guess-the-age on my birthday (2003 2004 2005), I assume there are some mathematically capable people reading this. Tell me some examples of how mathematics is beautiful and simple and elegant that can be used to convince a non-maths person what you see in the tumbling world of numbers. Note that the last part is important; if you think that Andrew Wiles’ proof of Fermat’s last theorem is elegant and beautiful then I don’t want to hear about it. I spoke a little about axioms, with the intention of then going on to Russell’s Principia Mathematica and then knocking it all down with Gödel, but we never got that far. The second thing to demonstrate is that maths is really relevant to the real world and has a point. I talked a little about how pure maths came up with i as a pointless theoretical concept and it then turned out to be useful in electrical engineering, but we never got very far into that. So, again, the question’s open. Demonstrate to a non-maths person why maths is important to the real world. Answers involving the phrases “joy of discovery” or “sacred guild of scholars” or similar are not wanted here. These also have to be semi-constructive demonstrations: when Dan presented the argument that “maths describes quantum physics and that’s where computers come from”, there was no clear recognition by our Luddite audience that that actually meant anything. How does maths make quantum physics work? Speak on, maths readers.

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