I think understanding requires knowledge, and LLMs work with statistics around text, not knowledge.
You're already making the assumption that "statistics around text" isn't knowledge. That's a very big assumption that you need to show. And before you even do that you need a precise definition of "knowledge".
Ask me a thousand times the solution of a math problem, and a thousand times I’ll give you the same solution.
Sure but only if you are certain of the answer. As soon as you have a little uncertainty that breaks down. Ask an LLM what Obama's first name is a thousand times and it will give you the same answer.
Does my daughter not have any knowledge because she can't do 12*2 reliably 1000 times in a row? Obviously not.
it’ll just make things up
Yes that is a big problem, but not related to this discussion. Humans can make things up too, the only difference is they don't do it all the time like LLMs do. Well actually I should say most humans don't. I worked with a guy who was very like an LLM. Always an answer but complete bullshit half the time.
they contain information about—the statistical relations between tokens. That’s not the same as understanding what those tokens actually mean
Prove it. I assert that it is the same.