This morning I gave an answer to a MathOverflow question using traditional pen-and-paper analysis: https://mathoverflow.net/a/489533/766 . The answer was not in closed form, so I wanted to simulate it approximately. At this point I asked o3-mini-high for some code for this. Interestingly, it first declared that the quantity I was trying to compute was infinite (it wasn't), but nevertheless provided numerical code which did give a rough approximation to the quantity I wanted (to one decimal place): https://chatgpt.com/share/67d71204-3510-800e-8bca-11bfbf53fc3d . At that point I figured out that one should use the theory of Markov chains to get a more precise answer and asked o3-mini-high first for a theoretical formula, and then code to compute the result. Interestingly, it was able to correct a basic error in the prompt (I had written max instead of min when writing a truncation), and gave me perfectly good code, which I was able to adapt to then give a more numerically precise answer to the MO question.

So all in all a pretty good assist from o3; it made a mistake that I corrected, but I also made a mistake that it corrected, and code that would have taken perhaps an hour of my time on my own was generated, tested, modified, and reported in maybe ten minutes.