> Meanwhile, to arrive at the right answers, an understanding of the math must exist somewhere... but where?
In the grammar, you can have grammar rules like "1 + 1 = " must be followed by 2 etc. Then add a lot of dependency rules like "He did X" the He depends on some previous sentence to stuff like that, in same way "1 plus 1" translates to "1 + 1" or "add 1 to 1" is also "1 + 1", and now you have a machine that can do very complex things.
Then you take such a grammar machine and train it on all text human has ever written, and it learns a lot of such grammar structures, and can thus parse and solve some basic math problems since the solution to them is a part of the grammar it learned.
Such a machine is still unable to solve anything outside of the grammar it has learned. But it is still very useful, pose a question in a way that makes it easy to parse, and that has a lot of such grammar dependencies you know it can handle, and it will almost always output the right response.
In the grammar, you can have grammar rules like "1 + 1 = " must be followed by 2 etc. Then add a lot of dependency rules like "He did X" the He depends on some previous sentence to stuff like that, in same way "1 plus 1" translates to "1 + 1" or "add 1 to 1" is also "1 + 1", and now you have a machine that can do very complex things.
Then you take such a grammar machine and train it on all text human has ever written, and it learns a lot of such grammar structures, and can thus parse and solve some basic math problems since the solution to them is a part of the grammar it learned.
Such a machine is still unable to solve anything outside of the grammar it has learned. But it is still very useful, pose a question in a way that makes it easy to parse, and that has a lot of such grammar dependencies you know it can handle, and it will almost always output the right response.