AI Assistant Helps Mathematician Quickly Solve Complex Problem with Markov Chains and Code Optimization

This morning, I provided an answer to a MathOverflow question using traditional pen-and-paper methods. My solution, however, was not in a closed form, so I decided to simulate it to get a rough numerical approximation. I turned to o3-mini-high, an AI assistant, for some coding help. Interestingly, the AI initially claimed that the quantity I was trying to compute was infinite, which was incorrect. Despite this oversight, it still provided numerical code that gave a decent approximation to one decimal place. Realizing that a more precise answer could be obtained using the theory of Markov chains, I asked o3-mini-high for both a theoretical formula and the corresponding code. The AI was notably helpful, as it not only provided the code but also corrected a basic error in my prompt. I had mistakenly written "max" instead of "min" when specifying a truncation, but the AI caught the mistake and gave me accurate, usable code. With this assistance, I was able to adapt the code to produce a more numerically precise answer to the MathOverflow question. Overall, the interaction with o3-mini-high was quite beneficial. Although the AI made an initial error that I had to correct, it also identified and fixed a mistake I had made. The process, which would have taken me about an hour to complete on my own, was significantly accelerated with the AI's help. From generating the code to testing, modifying, and reporting the results, the entire task was completed in roughly ten minutes. This experience highlights the potential of AI tools to enhance productivity and accuracy in mathematical problem-solving, even when both human and machine errors are involved.