Re: [Maxima-discuss] ML for symbolic math

[Gunter K. <gu...@pe...>]

In my experience Blockchain, xxxML and AI are buzzwords that stand for
claims that are often hard to believe: You could say Mathematics itself
is a try to find a language that contains only a few handfuls of words,
not a lot of grammatical rules and in which you can solve many a problem
just by reformulating it. If you find a less ambiguous way to express
the things you can epress as an equation you can claim this to be a ML.
But you didn't gain anything magic mathematics didn't originally contain.

If you use a lot of raw computing power and beat a human being in doing
anything that can be solved using raw computing power you have won a
chess game. But if the program just looks forward many steps and looks
if what you do looks like winning (like big blue did) or if you train an
AI that does the same except you don't know which criterion it chose as
"looks like winning" that looks like magic. But it doesn't tell the
computer is intelligent. And when you then find out that your artificial
"intelligence" when trained to look for street signs just looks for the
lower edge, ignores the number and thinks this must be a Stop sign. Or
if it is completely confused by noise you see what AI is: A mechanism
that mimics the magic our brain uses for getting a first impression of
whatever you look at or hear in the first moment.

Showing a trained mathematician an expression and asking this persion
"Does this look familiar? What do you think the integral looks like"
definitively is a valid method that might be faster or more exact than
using a list of integral tables and trying things out. But it isn't a
silver bullet. Asking an AI will have similar, but not exactly the same
result as you try to imitate a brain but don't actually use it.

Giving an AI a list of valid operations that cannot go wrong, a bunch of
equations and telling it to find an algorithm that solves most of these
problems using educated guesses woud be another approach. This approach
might actually result in creative algorithms as you can tell the AI to
use 1000 years of CPU time and an AI is fast. It can result in
algorithms that only work for this set of data or it can result in
algorithms that are hideously complex and maybe if anyone finds out what
they actually do something quite simple and obvious. If such an
algorithm actually works perhaps it will be documented good enough that
we can translate it into lisp code.

That is at least my opinion.