Can we Trust Chatbots for now? Accuracy, reproducibility, traceability; a Case Study on Leonardo da Vinci's Contribution to Astronomy

Large Language Models (LLM) are studied. Applications to chatbots and education are considered. A case study on Leonardo's contribution to astronomy is presented. Major problems with accuracy, reproducibility and traceability of answers are reported for ChatGPT, GPT-4, BLOOM and Google Bard. Possible reasons for problems are discussed and some solutions are proposed.