This project-based course explores the mathematical reasonings of AI systems like GPT and DeepSeek. Students will work on exercises drawn from topics in Math 8, linear algebra, and calculus. For each project, the student will obtain an AI-generated solution, carefully examine it for errors, and then analyze and correct the AI's mistakes. Students will submit all project materials. Most projects will be provided by the instructor, but students will also be encouraged to find some on their own, with all projects receiving necessary instruction.