> There is even a relevant announcement from today, where OpenAI announced they solve 100 open math problems, without even bothering to state what they are.

That announcement is about exactly this group: https://openai.com/index/advisory-group-on-mathematics-and-a...

This group has been formed to tell OpenAI whether or not (and if yes how) they should release those 100+ problems.

IMO “AI companies are using math to as a PR tool” is not quite it; they are using math problems as a benchmark to evaluate their AIs, but after the prior blowback from the mathematical community, they are happy to sit on the results until the community (this group) tells them how to publish the results.

And as you say, even if they don't publish the results eventually anyone will be able to do this when this model is released, so it's just a matter of time.