I doubt words are involved when we e.g. solve a mathematical problem.

To me, solving problems happens in a logico/aesthetical space which may be the same as when you are intellectually affected by a work of art. I don't remember myself being able to translate directly into words what I feel for a great movie or piece of music, even if in the late I can translate this "complex mental entity" into words, exactly like I can tell to someone how we need to change the architecture of a program in order to solve something after having looked up and right for a few seconds.

It seems to me that we have an inner system that is much faster than language, that creates entities that can then beslowly and sometimes painfully translated to language.

I do note that I'm not sure about any of the previous statements though'