How are you defining “new information”? If I ask Claude "what is 235 x 567 + 57,899? " There is a high likelihood that that question was not in its training data, but it still gets it right and generates new information. It will be using existing methods from its training data to “reason” to get the answer, and it hasn’t shown the ability to devise new methods. But 99.99% of the problems in the world can be solved by using existing methods.

Open AI isn’t going to go bust because it can’t make novel math techniques, almost all of the knowledge work requiring math doesn’t require new methods. If it’s able to master every existing technique used by knowledge workers without creating new methods, ie. your finish line, then they’ll have automated a huge chunk of labor and probably become a hugely profitable company.

Recursive self improvement may not be panning out currently so we won’t see any singularity style exponential take off, but we’re still seeing steady linear improvement in tasks such as math and reasoning through other techniques, like the opaque recurrence that astra is using.