First, regarding OpenAI's claim on the disproof of a conjecture in discrete geometry:

Against any rosy framing, this piece of advertorial confirms that AI can be used, as an aide, for exploratory problems, like this one:

1) The groundwork is already done and the stage is set; the statement of the problem was based on this firm basis:

Since Erdős’s original work... the problem is explained in the "2005 book Research Problems in Discrete Geometry" as “possibly the best known (and simplest to explain) problem in combinatorial geometry.”

An internal OpenAI model has disproved this longstanding conjecture, providing an infinite family of examples that yield a polynomial improvement.

2) The proof still required the contribution of group of expert mathematicians (internal and external):

This problem was solved in a completely automated fashion. ... internal human researchers and mathematicians began to examine the solution carefully. After preliminary AI-assisted verification and rewriting, a draft was sent to external mathematicians, including several number theory experts, who confirmed the proof’s correctness (and have already simplified and strengthened the argument). ... They have also written a companion paper explaining the argument and providing further background and context for the significance of the result.

3) The proof connects two mature fields:

The proof came from a new general-purpose reasoning model... [and] brings... ideas from algebraic number theory to bear on an elementary geometric question.

4) Advertorial take-away:

Better mathematical reasoning can make AI a stronger research partner: something that can hold together difficult lines of thought, connect ideas across distant areas of knowledge, surface promising paths experts may not have prioritized, and help researchers make progress on problems that would otherwise be too complex or time-intensive to tackle.

That future still depends on human judgment. Expertise becomes more valuable, not less... .