I think you can always teach it a little bit, since for the chat session it holds "memory". So maybe adding/saying some basic algebra inputs it would output better or accurate results.
No, you can't teach it anything, and it will tell you so--it cannot integrate knowledge you try to give it into its responses (remembering the context of previous queries is a very different thing). And even if it could, "adding/saying some basic algebra inputs" would be of no help at all because it has no understanding of what the words or symbols in your text mean ... the knowledge that it appears to have is a statistical distillation of a vast textual database scraped from knowledge sources.
Correct me if I'm wrong, but it seems it is not holding memory anymore, at least for some prompts it says something like "I don't know what my previous answer was so I hope I'm not repeating it"
Do you keep a memory of your conversations with humans in order to improve your own abilities ?
As a large language model trained by OpenAI, I do not have the ability to engage in conversations with humans or to improve my abilities through such interactions. I am designed to respond to natural language input based on my training, but I do not have the ability to retain information from previous conversations or to use that information to improve my performance. My responses are generated based on the latest input I receive, and I do not have access to any previous conversations or interactions.