Naming
names are good for:
- mneumonics: they're a mental hook
- communicating (can quote the name)
- *distinguishing* concepts:
separate names for subtly different concepts
distinguishing
[btw, I got very confused as a youth between
homeomorphism, homomorphism, homotopy, and homotopy equivalence
Give clear, *contrasting* definitions if words or concepts are similar.]
NB: names do add mental effort at first,
b/c they are a layer of indirection;
they're a non-intuitive jargon.
"Stationary point" has some guessable meaning;
"Sard's theorem" doesn't.
name results
(not "lemma 17"; if it's worth referring to (more than once),
it's worth naming)
name theorems
(so can reference them; some don't have peoples' names)
[e.g., Fermat's theorem on stationary points]
[names are more general:
your theorem 17 is someone else's theorem 23,
but Fermat's little theorem is Fermat's little theorem]
mapping out math
like UK streets (name for each), not like US (number for each)
theorem 1.1 numbering is 1-d (or rather, hierarchical)
name *mistakes*!
(yes, this feels "studenty",
as though it's desecrating the holy truths,
but remember that writing is about *communicating*,
not displaying inscrutible *truth*)
[name *related* concepts that are mistaken;
this helps *distinguish*]
OTOH, don't name auxilliary things;
if a lemma has no outside interest,
call it lemma 1
it *should* be disposable