> Edit: to clarify further as to what I want to know: people have been telling me that LLMs cannot solve problems that is not in their training data already. Is this really true or not?

That is not true and those people are dumb. You may be on Bluesky too much.

If your training data is a bunch of integer additions and you lossily compress this into a model which rediscovers integer addition, it can now add other numbers. Was that in the training data?

It was in the training data. There is implicit information in the way you present each addition. The context provided in the training data is what allows relationships to be perceived and modelled.

If you don't have that in your data you don't have the results.

I am not on Bluesky AT ALL. I have seen this argument here on HN, which is the only "social media" website I use.

I mean, you just said it was.