> Why do people keep using LLMs as algorithms?

I think they keep coming back to this because a good command of math underlies a vast domain of applications and without a way to do this as part of the reasoning process the reasoning process itself becomes susceptible to corruption.

> LLMs are not calculators. If you want a calculator use a calculator. Hell, have your LLM use a calculator.

If only it were that simple.

> I mean, no not really, digital computers are far easier to build and far more multi-purpose (and technically the underlying signals are analog).

Try building a practical analog computer for a non-trivial problem.

> Again, if you have a deterministic solution that is 100% correct all the time, use it, it will be cheaper than an LLM. People use LLMs because there are problems that are either not deterministic or the deterministic solution uses more energy than will ever be available in the local part of our universe. Furthermore a lot of AI (not even LLMs) use random noise at particular steps as a means to escape local maxima.

No, people use LLMs for anything and one of the weak points in there is that as soon as it requires slightly more complex computation there is a fair chance that the output is nonsense. I've seen this myself in a bunch of non-trivial trials regarding aerodynamic calculations, specifically rotation of airfoils relative to the direction of travel. It tends to go completely off the rails if the problem is non-trivial and the user does not break it down into roughly the same steps as you would if you were to work out the problem by hand (and even then it may subtly mess up).