It feels odd to me that they wouldn't prefer applied problems. Seems like an easy way to profitability. Probably based on what attributes they're looking for in a problem when picking them.
At first this was my take as well. That plus, well, maybe they are just on a serious PR kick with maths. But I am starting wonder if they have determined, or strongly suspect, that the road to exponential model improvement must first be paved with extraordinary improvements in math. Like in some sense this seems like a test case for where their true intensions might go: vast improvements in the efficiency / size / speed of models and their training. Hard to imagine trusting the models in all those spaces without first trusting them / training them to address new or unsolved math.
This is a really interesting observation, especially given their current valuation and circumstances. Probably the verifiability of mathematics is enabling this progress, and making progress on science and engineering is not so straightforward. You can be sure that this is a top priority for them, especially now that there is concrete evidence that LLMs can achieve super-human performance at math. A model that achieves similarly super-human performance at things like material or drug design would be incredibly valuable. In fact, maybe this is why Anthropic hasn't been making such enormous strides in mathematics - they have been prioritizing biology instead.
You can't really profit from proving theorems of applied problems (that are widely regarded to be true). Those who need to apply those theorems on real problems would have already done so (and if they don't work in some cases, well, congratulations... you found the counter example!)