This is an excerpt from an email reply to a student, who was asking about the form of answers to assigned questions. Great questions,
keep 'em coming!
In keeping with mathematical culture, (for good or
bad) assignment solutions are generally presented in a style
that values economy of expression, elegance, and clarity over
narrative, history, storytelling, individual experience, etc.
People sometimes make an analogy for this by talking about things like the huge
stained glass windows in old cathedrals like
Notre Dame in Paris. When you look at these, they
are beautiful, airy, light, dazzling, glorious; you can see
the beauty and grace and form that the designer intended
us to see.
What you can't see is how on earth such a thing
could have been built. If you are a builder of
cathedrals, or have studied them, then you will
know what went into it and be able to steal ideas,
and admire the engineering genius, but as an outsider,
you can only guess at the scaffolds, braces, ramps,
pulleys, cranes etc. that must have been part of the process
of transforming tonnes of rock, glass, and lead into
a work of art.
It's the same with proofs, solutions, and lots of
other kinds of communication - the author presents
the only the final result, and leaves us to wonder and be inspired.