Training the model is going to be amortized over other uses.
Say that it turned out that the total cost of the proof of the Erdős unit-distance conjecture was $50 million.
Then the question really becomes: yes, these models are capable of proving important mathematical results, but at a very high cost. Is it worth it?
If a mathematician applied for a research grant of $50M USD for proving the same thing, they would have been laughed out of the bank.
What's more is that when you have a research grant, you train PhDs and postdocs, you hire new staff, and you disseminate. That is, you get much more value for the money spent.
I'm just curious what the cost is.
Hours needed for prompt + Hours needed to check result + API costs.
You don't say "well let's add together the total yearly compensation of all the engineers and mathematicians at OpenAI that were involved" and throw that into the total cost. That's simply nonsense accounting.
The actual comparison you are making is some university researcher weighing between getting a grad student (several tens of thousands of dollars) vs typing up a prompt and sending a request to OpenAI for inference (as mentioned in the article, around $2000 in API and maybe a few hours for the prompt and harness).