How hard is it to prove that problems are hard to solve? Meta-complexity theorists have been grappling with this question for decades. The central open question in theoretical computer science, the P versus NP problem, asks whether difficult computational problems can actually be solved easily or if they truly are hard. Researchers in the subfield of meta-complexity have discovered that the difficulty of proving computational hardness is closely tied to fundamental questions about hidden patterns in data and the frequency of truly hard problems. Despite efforts, a resolution to the P versus NP question has remained elusive, and researchers continue to navigate the uncharted landscape of computational complexity.

https://www.quantamagazine.org/complexity-theorys-50-year-journey-to-the-limits-of-knowledge-20230817/