[colin7snyder]

I don't disagree with you zingar. I think Erdős problems are great for testing a system's capability on genuinely hard math, which has value as a benchmark in itself, and maybe as a stepping stone toward more real-world impact. Your sentiment is well put.

To answer your question directly: most Erdős problems don't have practical applications on their own; the value is the techniques and the machine-checked proofs they leave behind. But there's more real world value in solving some of the FrontierMath Open Problems or Millennium Problems. There's a Venn diagram of "hard problems" and "real world impact" for sure.