Some Machine Learning methods thanks to math are able to produce predictable results, enabling us to understand exactly what these AIs can do.
However, most practical system models due to their high non linearity are unpredictable by the ordinary math, because they are so complex and they may use randomness within their algorithms. An example is to forecast the industrial pollution from historical data.
So from one side we do not have mathematics to predict the capabilities of a new AI, but from another side we do have mathematics that tells us about the limits of computation.
Thanks to Alan Turing. who invented theoretical computer science, we know that there is a limit where we can never predict if any arbitrary algorithm (including an AI) will ever halt in its calculations or not (Turing, 1937).
We also can consider “No Free Lunch Theorem” which tells us there is no algorithm that will outperform all others for all problems – in other words this means that we need a new AI algorithm tailored for each new problem if we want the most effective intelligence (Wolpert, 1996; Wolpert and Macready, 1997).
We even have Rice’s Theorem which tells us that it is impossible for one algorithm to debug another algorithm perfectly – which means that, even if an AI can modify itself, it will never be able to tell if the modification works for all cases without empirical testing (Rice, 1953).
https://www.randieri.com/en/english-why-cant-we-use-maths-to-make-ais/
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