# Can we use ML to do anything else other than predicting (in the case of mathematical problems)?

(The math problem here just serves as an example, my question is on this type of problems in general).

Given two Schur polynomials, $$s_\mu$$, $$s_\nu$$, we know that we can decompose their product into a linear combination of other Schur polynomials.

$$s_\mu s_\nu = \sum_\lambda c_{\mu,\nu}^\lambda s_\lambda$$

and we call $$c_{\mu,\nu}^\lambda$$ the LR coefficient (always an non-negative integer).

Hence, a natural supervised learning problem is to predict whether the LR coefficient is of a certain value or not given the tuple $$<\mu, \nu, \lambda>$$. This is not difficult.

My question is: can we either use ML/RL to do anything else other than predicting (in this situation) or extract anything from the prediction result? In other words, a statement like "oh, I am 98% confident that this LR coefficient is 0" does not imply anything mathematically interesting?

• I've edited this post in order to try to clarify what you're asking. I'm still not sure what you were asking and the given answer below just confirms that your question was a bit open to interpretation, which is bad. Please, now that you probably have a clearer idea of what you had in mind, review this post (including the title that I've added) and try to clarify what you were really asking. What does it mean "do anything else other than predicting"? Are you asking whether an ML model can do something else other than what it was trained to do?
– nbro
Jan 17, 2021 at 16:55