It’s just so beautiful

16 04 2010

“Mathematics possesses not only truth, but also supreme beauty”

-Bertrand Russell (English Logician and Philosopher 1872-1970)

Bertrand Russell

What did he mean by this? Do you believe him? Have you ever seen anything in maths that you think is beautiful?

When considering what to put in this post, I had to sift through literally dozens of beautiful and mysterious things that I’ve seen in maths including:

  • The idea that all natural numbers (except one) can be made by just multiplying together prime numbers. What is a prime number?
  • That insects called cicadas spend most of their lives underground as grubs but then pupate and come out of their burrows after 13 or 17 years (prime numbers) after which they live for only a few weeks. Why is this interesting? It is thought that they do this because it would make it hard for predators to have evolved that could specialise in eating only the cicadas. If instead they appeared in intervals which were not prime numbers, say every 15 years, predators appearing every 1, 3 and 5 years would definitely meet (and eat) them. Amazing!
  • Pythagoras’ Theorem about how you can work out the length of sides in right angled triangles. The history of this one is amazing, seeing how he proved it with only geometry rather than with algebra.
  • The idea of irrational numbers. Those are the ones that have an infinite number of non repeating numbers after the decimal point. I find this fascinating because infinity is such a hard idea to get your head around.

All these things are interesting, but, for me there has always been one thing that totally amazed me and it’s to do with a really simple bit of maths that seems to appear in all sorts of different places in nature: Fibonacci Numbers. Read the rest of this entry »