Questions: Are we really taking students into account FULLY when writing textbooks for various areas? Also, are we being unintentionally elitist or dismissive when neglecting to take a more humble approach in writing explanations/proofs and making decisions about providing solutions to exercises?
Let me explain: (using geometry as an example I'm familiar with)
Many textbooks (for (a well known) example, the Topological, Smooth and Riemannian Manifolds texts by Jack Lee) are written with exercises and no solutions to better encourage learning and reduce the undesired yielding to temptation by even more conscientious students etc etc.
My issue with this approach in Math education is that it really stands in the way of self-learners. There is also a tendency to write some books with super concise notation (a common one being little more than a passing mention of 'oh these are Christoffel symbols') in the name of brevity and with the far too common reference to 'mathematical maturity'. My personal feeling about this last bit is that it often gives an escape for simply bad pedagogy. But putting aside personal feelings, I would again say this is a great hindrance to self learners!
Consider how students often progress to become knowledgeable and move on to serious graduate work for instance. A lot of it depends on the school itself. Take a large school like Waterloo or UChicago that offers every course under the sun and the programs are geared towards a more thorough treatment of prerequisites leading to tougher courses (like Symplectic geometry, say). A student in these elite places has access to Profs and fellow students and even seminars that are instrumental to their progress but are not available at smaller schools or certain entire countries. As a result, they have two choices if they hope to try for certain more demanding areas of Math: Move or Chalk it up to impossible.
Isn't it a duty to write in ways that don't (even unintentionally) assume you're talking to either an extraordinary student or one that is smart and has access to the right instructors?
Now I know we can't write amazing textbooks that are self-contained to cater to every student in every circumstance but I believe some obvious steps like opting for full solutions and fleshing out more details even in some 'higher level' texts will have somewhat of a democratizing effect on math education.