It is getting very hard to popularize modern research, especially when it is of the more abstract type (as in mathematics). The author does his best but I am no

It is getting very hard to popularize modern research, especially when it is of the more abstract type (as in mathematics). The author does his best but I am not sure it is even a solvable problem. The challenge is what level of familiarity with mathematics to assume of the reader. To transmit a sense of the actual accomplishment of the work, the actual concepts need to link to internalized concepts available to the readers (a sort of mathematical mapping that follows the pattern: A is to B what x is to y). So its important to have a coherent set of x,y to work with (the assumed level of audience knowledge) and that set has to be expressive enough to convey the essence of the new development and its importance / limitations. It feels still possible to achieve this using book-level amount of effort from author and audience (where entire early chapters lay the groundwork for the main course), but an article length might be prohibitevely short. Something that could help, given the online format, is hyperlinks to further explanations (but they must be short and at a consistent level).