[Axiom-developer] Literate programming

[daly]

This quote by Bill Thurston[1] makes it clear why we need to document
the algorithms in Axiom (emphasis mine):

  Mathematical understanding does not expand in a monotone direction.
  Our understanding frequently deteriorates as well. There are several
  obvious mechanisms of decay. THE EXPERTS IN A SUBJECT RETIRE AND DIE,
  OR SIMPLY MOVE ON TO OTHER SUBJECTS AND FORGET. Mathematics is
  commonly explained and recorded in symbolic and concrete forms that
  are easy to communicate, rather than in conceptual forms that are easy
  to understand once communicated. Translation in the direction
  conceptual -> concrete and symbolic is much easier than translation in
  the reverse direction, and symbolic forms often replaces the
  conceptual forms of understanding. And mathematical conventions and
  taken-for-granted knowledge change, so older texts may become hard to
  understand. In short, mathematics only exists in a living community of
  mathematicians that spreads understanding and breaths life into ideas
  both old and new.

The people who wrote the vast bulk of Axiom's algorithms have either
retired or died. They no longer maintain the code. We really must
collect the papers and document the algorithms. This is especially
critical going forward as open source projects tend to fall out of
interest when real life makes it inconvenient to maintain code.

Tim

[1] 
http://blog.computationalcomplexity.org/2015/07/will-our-understanding-of-math.html