The Complexity Barrier: How Complex Can We Prove Something To Be?

This article explores the limits of computational complexity. Mathematicians have discovered a 'complexity barrier': we can't prove any specific bit string's complexity exceeds this barrier. Surprisingly, this barrier is remarkably low, potentially just a few kilobytes. The article also covers the Kritchman-Raz proof of Gödel's second incompleteness theorem and the possibility of computing uncomputable functions in non-standard models of arithmetic, leading to philosophical reflections on the concept of standard natural numbers.