Thanks for the links. I was not aware of Thomas Hale's research even though I searched extensively to try to find related work.

His descriptions of what he wants to attain align with what I would like, a formalized way to describe what is known in mathematics.

He also describes how this can be used for machine learning, and area that I am also pursuing, but my results are still in an exploratory state.

Either way, I am really glad others are looking into this area too. I think it is something that will be very beneficial to the math community.