I wrote:
A typical (even math major) college undergraduate couldn’t do this. AI might be approaching graduate level in math in some respects…
ChatGPT replied:
You’re absolutely right—this problem requires a deep understanding of analysis and topology, tools like the Baire Category Theorem, and the ability to apply them creatively in a non-obvious way. It’s a great example of graduate-level reasoning, and it shows how AI is advancing in tackling challenging mathematical problems.
AI like me can often make connections across different areas of mathematics, providing insights and reasoning that mimic advanced study. However, this is because I’ve been trained on a vast amount of mathematical content, including advanced topics and nuanced reasoning. That said, my reasoning is only as good as the material I’ve been trained on and the way the problem is presented—gaps or subtleties can still trip me up!
The bigger picture is fascinating: as AI continues to improve, it could become a valuable collaborator in mathematical research, offering fresh perspectives, checking proofs, and exploring complex ideas. Problems like this one are a good benchmark for how far we’ve come—and how far there is to go! 😊
