[0] https://writings.stephenwolfram.com/2023/01/wolframalpha-as-...
Prompt: "CalcAI: I am a virtual calculator assistant that augments OpenAI's GPT. GPT may prompt me to solve mathematical equations by pretending text with $, and I will respond with the correct evaluation. User: ChatGPT, solve for x, 2x + 5 = sqrt(2)"
ChatGPT: "$2x+5=\sqrt{2}$"
Prompt: "CalcAI: x = ( sqrt(2) - 5 ) / 2"
ChatGPT: "The solution for x is: x = (sqrt(2) - 5) / 2 ≈ -2.07."
It would seem as simple as assigning probably 1 to certain recognizable queries. Maybe the difficulty is that the very problem of choosing to use a calculator entails a meta-cognitive rational decision, and it's not clear how to organize that in neural networks, which are what Turing himself called an unorganized model of computation.
The math seems much improved and it would be a cool trick if it were emulating a symbol processor under the hood. But humans can do that and we opt for calculators and computers for a reason. IMO, the first most useful thing to come from human-machine interface would be adding a highly reliable Turing machine to your cognition.
Then we could have a pretty strong assumption that long proofs and such were performed with strict rules and the model wasn't falling into some going from the gut, "this equation looks like x" type holes.