If the number is odd, we multiply by three and add one. The Collatz conjecture is that this process will eventually reach the number 1, regardless of which positive integer is chosen to start with. Now form a sequence by performing this operation repeatedly, beginning with any positive integer, and taking the result at each step as the input at the next. If the number is odd, triple it and add one. The conjecture is that these sequences always reach 1, no matter which positive integer is chosen to start the sequence.Ĭonsider the following operation on an arbitrary positive integer: If the previous number is odd, the next number is 3 times the previous number plus 1. It uses sequences of integers in which each number (or term) is obtained from the previous number as follows: if the previous number is even, the next number is one half of the previous number. This conjecture asks whether repeating two simple arithmetic operations will at some point transform every positive integer into 1. The Collatz conjecture is the most famous unsolved problem in all of mathematics. This math problem is both famous and infamous as no respectable mathematician is still trying to find a solution for it. It’s a simple conjecture that not even the world’s best mathematicians have been able to solve. This is the most dangerous problem in mathematics, one that young mathematicians are warned not to waste their time on. It’s also known as the Ulam conjecture, Kakutani’s problem, Thwaites conjecture, Hasse’s algorithm, the Syracuse problem, and simply 3N+1. This problem has many origin stories and many names. It’s was named after Lothar Collatz in 1973. Even though it’s easy for almost anyone to understand it’s also at the same time impossible to solve. Jeffrey Lagarias said in 2010 that this math problem: “Is an extraordinarily difficult problem, completely out of reach of present day mathematics.” Richard Guy has this on his list of “Don’t try to solve these problems.” What is the simplest equation no one can solve?ģx+1 popularly called the Collatz conjecture is the simplest math problem no one can solve. Concerning the above math problem, Paul Erdös said that “Mathematics is not yet ripe for such questions.” He also offered $500 USD for its solution.
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