Are there any general purpose models that are good at learning math? I mainly know basic feed-forward neural nets, but I don't think they do well outside their training region. Math, of course, has an infinite training region.
I would assume that state-of-the-art ML models could "convert a word problem into an equation", then feed that equation into a 30 year-old graphing calculator to "do the math"
The fact that no one has done this is an indicator that "there are more important things to work on", and it is just a matter of time that someone connects the two together
If the teachers don't love math, how can we expect students to?
I'm not at all surprised they don't do well at maths, because while there are maths texts online, I doubt there is enough material to give these models the same experience of repetition and reinforcement to help sufficiently generalise an understanding of the underlying rules.
Isn't this a huge step? It's not a minor detail remaining to be solved, but possibly the largest step!
The enumeration inherently includes functions of several variables, so I wasn't restricted to examples such as 1->1, 2->4, 3->9, 4->16 etc.
I could try it out on examples such as (1,2)->3 (2,1)->3 (0,2)->2, etc. Perhaps with enough it would "learn to add" = find a primitive recursive function that did addition.
I got as far as finding the first problem. The enumeration technique that I used was effectively doing a tree recursion, like that function for computing Fibonacci numbers that bogs down because Fib(10) is computing Fib(5) lots of times. I had a lot of numbers that coded for the identity function, lots of numbers that coded for the first few functions, making the whole thing bog down, trying the same few functions over and over under different numerical disguises.
I thought that I could see my way to fixing this first problem. Have some way of recognizing numbers that give forms that give the same function. I guessed that I could approximate this by saying that if two functions give the same value on a variety of arguments they are probably the same. Then I parameterise this criterion and tune. That opens the way to creating a consolidated enumeration, analogous to fixing the tree recursive fibonacci function by memoization, except trickier.
But my health is poor and I ran out of energy.
Also, I have a guess for the second problem. What happens if I fix the first problem and my enumeration reaches decently complicated primitive recursive functions. While they will all terminate, some might run for far too long, causing the process to bog down. Rejecting them on the basis of limiting the run time might work well. We are happy to only learn reasonably effect functions for doing maths.
It is a fun idea and I encourage others to have a go.
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