PostThe jumping wheel

The jumping wheel About ten years ago, my friend told me a story. At MIPT, a professor of theoretical mechanics promised to give a free "excellent" mark for his course to anyone who solved a problem and defended the solution. The problem is seemingly simple. There is a wheel of mass M with a small but heavy point mass m at the top of it. You are to find the ratio m/M at which the wheel jumps for the first time. I attacked this problem a few times, when I had several hours of free time. The last time was during my vacation in Montenegro. To be honest, I felt extremely stupid, when I gave this problem to Claude. It produced a solution that looked viable, but I couldn't understand it. So, let's review the state of SOTA neural networks. Claude: solved the problem and could discuss the solution. ChatGPT: knows the answer, heavily hallucinates. Me: almost totally understand Claude's approach. As a small bonus: when m >> M, the wheel jumps when the point accelerates upward. This happens when the dot is in the rightmost position (assuming that the wheel moves to the right and rotates clockwise). The post is already extremely long. Interesting links, the history of this problem, and recent articles - next time.