[zingar]

I feel like I'm seeing a maths+AI change from "let's test the limits of LLMs by seeing if they can do useful math" to "LLMs can do useful math, now let's solve lots of problems!", or put a different way the goal has shifted from "interesting exercise for AI" to "making a big difference in math". Am I correct?

Are there practical applications of any these problems being solved? No judgement implied, I'm well aware that "no" only means "not yet".

[pfdietz]

At some point the effort shifts from proof of concept to exploration of impact. Of course doing proving at large scale provides further feedback for improving the AIs. Visual reasoning, for example, may still need work.

The big impact will be with scaling, for example complete autoformalization of existing math, and automatic exploration for new conjectures, with emphasis on how interesting they are. Automatic conjecture generation goes way way back, to the days of Lenat's AM system. Modern AI should do a far better job.

[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.