It’s strange, it’s insoluble, but it always works. 3X+1 is in infamous Collatz conjecture. And it works like this. Take any positive integer(whole number). If it’s odd, multiply by three and add one. If even, divide by two. And just keep going. And going. And going. Sooner or later your operations will end in a loop of just three integers:4, 2 and 1. No one has formally proved it yet, but every number tried always ends up the same.

This is the fascination of mathematics. It’s one of those curious small ideas which suddenly produce a vast ecology of learning. Like fractals, imaginary numbers, fibbonacci sequences and so on. Mathematicians spend careers studying them, ending up with mountains of data and vast computer algorithms. Sometimes they get a formal proof, sometimes they don’t. But for us, it’s not quite the point, maybe because we are not mathematicians.

What we are is scientists, much of the time. Or at least Natural Philosophers. And what interests us is the way these mathematical conjectures describe deep patterns in nature. Take fractals-they are more than a mathematical game, they describe patterns of growth in all sorts of living things. The Collatz conjecture seems to accurately describe the way corals grow. Imaginary numbers were entirely made up-but you can’t understand the equations for all sorts of electromagnetic phemonena without them. Are all these formulae hinting at deeper structures in reality which we do not yet understand, or have hardly glimpsed?

We have a nice video by some enthusiastic Americans which explans Collatz incredibly well. You’ll be amazed by the amount of data they have squeezed out, and the pictures. And remember, any learning, if honestly done, will probably be useful some day.