[zengid]

Usually mathematics is taught in a progression, and layers are built upon more basic layers. A 'non-mathematician' is someone who does not consider it their life's goal to solidify their expertise in mathematics, so they may choose other disciplines to obsess over, or no disciplines at all. Either way, a teacher of a class for 'non-mathematicians' who wants to explore depth in a certain area of mathematics cannot assume that this population of 'non-maths' will understand jargon or any concepts that aren't specifically explained within the scope of the class. Thus they must proceed axiomatically, being sure to avoid using concepts that haven't previously been defined.

Conversely, a class for "mathematicians" would be one with some background that can be used to begin from, depending on the average grade-level or prior education of the students.

So in a nutshell to teach deep math concepts to 'non-maths', one has to start from the beginning and define each concept in order, ignoring wider scope for the sake of reaching the goal. 'Math' students can start at a middle-depth, depending on their background.