I mentioned this in a sibling comment but even for mathematicians, the intimidating notation and the more formal language might give the wrong impression about how we think about math. Actual thinking and even discussions with other mathematicians tend to be looser and more concrete and tactile, but the notation and language are there in part to act as a sort of lingua franca to help everyone stay on the same page, since everyone thinks at least a little bit differently. It also helps to keep you honest and catch situations where your thinking was muddied, since this language is so specific and writing things down has a funny way of catching things. And good notation goes a long way towards making the simplicity of an idea clear, or completely muddy in the case of bad notation.
Many mathematicians do what you do as well!