Current LLMs can absolutely multiply floats without a tool call. In fact, that's a much more rote symbol-manipulation task than doing original math research.

With what accuracy? And with how many intermediate tokens?

We can replace multiplication with any class of problems which should go from 0->100% solution almost immediately if there was actually a concept learned.

There is not. Because they are plain ol' fits. And there are no "emergent" features that pop out without having a sufficient set, where "sufficient" is absolutely gigantic and equivalent to memorizing enough of the space to compress the problem. LLMs are Rain Man.

They interpolate within a known distribution. Search allows places outside of distribution to be explored.

This paper should be required reading [1]. You can explore the curves yourself. You can see exactly what it's doing. And you also have this nagging thing—which you know and I know—that all these models converge and do not diverge upwards. An "emergent" "hyperintelligence"—a characteristic that could be found if something was actually learned and combined with a new concept—would not have this problem.

Exponentials on exponentials added to compute and data and the problem classes still sit at not great places, and require agents, feedback loops, and trial and error to solve. The models are the problem, but more importantly, the people selling things these models could never do are the problem.

[1] https://hai.stanford.edu/news/ais-ostensible-emergent-abilit...

Edit: It should be mentioned, if there's some scary neural architecture that's super-de-duper and doing something beyond the very obvious next string prediction that LLMs clearly do, it can't do what absolutely ancient ML models could do; a network to multiply two floating point numbers should pop out somewhere without symbolic computation, no?

It does not. There's no magic other than the run-of-the-mill SV fake it til you make it magic. And that magic has failed.