As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality. - Albert Einstein
The Collatz conjecture, also known as the 3n+1 conjecture or the Syracuse conjecture, is an unsolved mathematical problem that has puzzled mathematicians for decades. The conjecture is named after German mathematician Lothar Collatz, who first proposed it in 1937.
The conjecture is defined as follows: Take any positive integer n. If n is even, divide it by 2 to obtain n/2. If n is odd, multiply it by 3 and add 1 to obtain 3n+1. Repeat the process indefinitely for the resulting values, and the conjecture states that no matter what value of n you start with, eventually you will reach the value 1.
This project is a research on manipulating and analysing the Collatz Conjecture to make it useful for Computers and real life applications. Collatz Conjecture is an unsolved problem and has been worked upon for years now and still there is no proof of the Conjecture to be true or false (atleast while writing this). Mathematicians are working on it and I hope they solve it but till then, we can manipulate it's behaviour to develop an algorithm that can have a real application, benificial to the community.
Despite of the simplicity of its formulation, many mathematicians simply think that mathematics is not ready for solving it. Paul Erdös said
“Mathematics is not yet ripe for such question”
and Richard Guy puts it in his list
“Don't try to solve these problems”.
Mathematics and Algorithms are something that can be worked upon with multiple minds to make a progress with an exponential rate. If you have any recommendation or ideas to work upon this project, I would be more than happy have you as a contributer. Feel free to reach out me!