In this study, "Can Machines Think?" Based on the question, the aim is to examine the non-routine problem-solving skills of the artificial intelligence (chatgpt4o) algorithm, which is the GPT-4o (Omni) update of ChatGPT developed by OpenAI. Studying is important in determining and evaluating artificial intelligence’s role in mathematics education. The study is qualitative research with a case study pattern. Data was collected from 7 non-routine problems asked to ChatGPT. Data analysis was carried out according to Polya’s problem-solving steps. According to the findings of the research, it was seen that ChatGPT encountered some limitations in the field of mathematics, that it solved fundamental mathematical problems very quickly and was quite capable in this respect, but when the problems became complex, its mistakes emerged. It has been determined that ChatGPT has difficulty solving problems significantly when solving multi-step or multi-parameter problems. It has been determined that ChatGPT needs help understanding the problem, planning and implementing the plan, and ignoring the solution evaluation phase in the non-routine problem-solving process. In this context, further development of such algorithms is emphasized in mathematics education so that students can use artificial intelligence tools effectively and correctly without needing an instructor.