The Collatz conjecture is one of the most famous unsolved problems in Mathematics. It states that whatever number you start with you will always reach 1 after following a certain set of calculations. The calculations are as such:
Take any number. If it is even: half it. If it is odd: triple it, add one, and then half it. Repeat until you get to 1. The conjecture is very easy to state but to this day no one has found a number that doesn’t reach 1 nor proved why this is so. The Collatz conjecture is more widely known by an image which was first created by a famous Mathematician, Edmund who expressed all numbers below 10,000 in such a way that from 2 if the next number up is even, the branch bends clockwise, and if the next number is odd the branch moves anticlockwise. Once all the numbers have been removed the image would look something similar to a mesh of seaweed. This image is among several famous images that beautifully illustrates how such a basic piece of Arithmetic leads to such beautiful complexity.
Here at MathsOne, one of the Best Tuition Centres in Kerala we educate our students in the beauty of Mathematics as well as its unique complexities.