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^*i*π^ + 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.