They are getting better at actually doing the math, but can still fall back to tools if available.

That said, we can only be sure with open models. In theory, a model like Fable could have access to tools we can't see and only a promise they don't. But load up something like deepseek, put it in a harness with only text in/text out, and you can see exactly how it works.

As for if it counts as doing math, this gets into the messy question of if a given human is doing math or not. Math itself is some level of memorization and some level of applying known facts. You have to remember 1 means one and that 1 + 1 is 2. But you don't need to remember that 123 + 321 = 444. You remember 1 digit addition and remember you can apply this to 10s place and 100s place, and then you apply these different facts and do math. But you might as simply memorize some things, like 11 + 11 = 22. This is related to the memory of 1+1=2, but you aren't really using that memory either. Almost like an engram of 1+1=2 forms that you can then loop a few times before you need more conscious thought. What about 111111111111+11111111111? Well, your brain might do a heuristic and just do all 2s, but that isn't the right way to answer that question.

Given all this, people complain about LLMs memorizing math answers and not doing math, but memorizing the math answers is part of doing math. It seems to have basic facts pretty well memorized, and with reasoning it is far better at applying them. But this is messy human math, not clean calculator math which always produces the correct answer (sans some bug in the code). Much like how a human with decent math skills can make a mistake and even multiple if you distract them, an LLM can apply the wrong memory, apply a fake memory, or just not apply something it should. The messier the context, the more likely this is to happen.

So, is an LLM doing this?

P.S.

For an interesting test in how much math involves memory, try doing math in a base you aren't familiar with characters you aren't familiar. The simplest option is almost always mapping back to the ones you memorized, even if you are applying simple operations that you deeply know. Even if you routinely work with hex, can you do the same rough estimation of something like ca / b.3 that you can do with 122 / 11.2 to see if your final answer is in the correct ballpark without first converting to decimal?