How AI knows things no one told it
A missing part that AI needs is a experimental way to verify its results. In some contexts, like math, this is entirely possible because it does not involve manipulation of real world objects. For example, i asked GTP-4, In the context of optimization, does the generalized assignment problem satisfy total unimodularity. Then experimental way would be to look up the formulas of the integer program on the internet or in its training data, write down the constraint matrix of the given problem, fill it with values, and check if the matrix is unimodular. Instead, the way gpt-4 answered this question, correctly, albeit with a weak reasoning, is by saying that researchers worked on heuristics to solve the problem, thus it is probably not unimodular as that would allow a quick solution without resorting to heuristics.