Consider constructs such as "Surprisingly this is an hypothesis...", "If you are doing a history subject, or tackling a question in any subject that has an historical dimension...". It should be clear that the use of an to precede words beginning with "h" is rather clumsy. Surely, if the "h" is not silent then one should use "a" instead of "an"?
Consider the following (taken from The Decline of Grammar by Geoffrey Nunberg):
It should be a source of satisfaction that the grammar books of a hundred years hence will be decrying to good effect the tendency to misuse literally, or to confuse imply and infer.
I do not think that "...an hundred..." would read better. See also the Elegant Variation and All That by Jesse Sheidlower.
I quote Neville March Hunnings from the (UK) Times of September 17, 1998:
A common-gender singular pronoun now needs an elegant solution. "Him/her" and "s/he" are ugly; "him" or "her" is cumbersome. On the other hand, "they" has a respectable grammatical precedent. We no longer object to an individual being addressed as "you" rather than "thou". Why not "they" instead of "s/he"?
Many academics and researchers get annoyed when students use computer algebra programs such as Mathematica to evaluate simple integrals that they maintain should be done by hand. The question I ask is "At what point do you expect your students to switch over to using a computer?". Most mathematical examples are artificial in that closed form expressions exist. However, in nearly any real problem, this is not the case.
I learnt mathematics using slide rules and tables, then calculators, then computers, then symbolic algebra. To me, this is a valid progression -- but not one that everyone should have to go through. I feel that the only way true progress can be made is if we don't have to learn a whole set of rules. If we had to do calculus using Newton's geometrical constructs then progress would be very slow. The real question is what are the essential tools and lessons. To me, knowing what a derivative and integral mean "physically" is far more important than knowing how to compute a specific integral.
Many people feel that reliance on computer algebra means that students can't do calculus by hand and hence the really don't understand what's going on, just how to get the answer by computer. Calculus concepts are subtle. However, just knowing the mechanics of computing an integral or derivative does not imply understanding. I believe that it is possible to have true understanding without computation.