The thing is, I think ChatGPT is already using a program underneath to generate it's response on some math questions?
Like if you ask it to derive/integrate it will follow the identical format every time, like it's running it through a symbolic algebra calculator.
And then if you ask it something slightly more advanced, like to compute the eigenvector of a small matrix, it completely fails. In general I found it failing nearly all basic linear algebra questions I gave it except for very simple ones like Gaussian elimination.
Then I asked it about some of the larger mersenne primes and it got some of them wrong too, which is surprising because those are precomputed (yet I had to triple check it because it sounded extremely confident in it's answer, and wouldn't change it).
For programming I completely agree it's not great either... at least in my preferred language (Rust). I asked it to write a program that output an MD5 hash, and it got the general idea (which, to be clear, IS REALLY COOL) but it was riddled with errors, with five of them being serious enough to prevent it from compiling.
I tried to get it to refactor them and it couldn't do that either, even with me telling it what the errors were. On top of that it had no optimization. I would be surprised to see it being capable of replacing even hobbyist programmers in the next decade or so.
In the social sciences it's also way to limited by it's content filters and canned response templates to be useful. For example, I asked it to list the factors that cause Canadian indigenous women suffer 20x the incarceration as Canadian caucasian women (The correct answers are, first and foremost, unequal law enforcement and bias in the justice system, as well as SES inequalities, lack of mental health and addiction support in rural areas, etc. -- it did not get any of these correct) and it gives me the SAME canned template as it does if you ask it about literally any other visible minority in any other country. Pretty bad, although I understand why it would tread lightly around questions involving ethnicity and inequality.
So I agree, math and programming it's almost unusable, and in other fields the over-judicious filters and template responses make it useless too. I've yet to find a good use case for it, personally -- I suspect where it excels is at writing letters, paraphrasing, and other simple language tasks.