We already wrote about mathematical statements that are true but impossible to prove. So this time let’s consider one interesting example: the ‘simplest’ problem which no one has solved yet.
Still image from YouTube video.
We are talking about the Collatz Conjecture, or so-called 3x +1 problem. The written expression of this sequence and its function is quite simple and easy to get a grasp of for anyone with some basic knowledge of algebra. But as a renowned Hungarian mathematician Paul Erdős once said, “mathematics may not be ready for such problems”. And indeed, the Collatz Conjecture has been calculated numerically for all initial values up to 268 ≈ 2.95×1020, but all the generated series of numbers eventually end up with number 1.
Scientists say this particular numerical verification is not enough to prove that the Collatz Conjecture principle is true for absolutely all numbers. However, this statement has not been proven yet. The following video tells more about this simplest but unsolvable math problem:
